Physics Book - User contributions [en]

Newton's Laws and Linear Momentum

2017-04-09T02:50:42Z

Lkrishnan7: /* Elastic Collision: */

Edited by Lakshmi Krishnan, 4/8/17
== Linear Momentum ==

Linear momentum, denoted by the letter '''p''', is a vector quantity which represents the product of an object's velocity, '''v''', and mass, '''m''', as it moves along a straight line. As a vector quantity, an object's linear momentum possesses momentum and direction and is therefore always in the same direction as its velocity vector. Linear momentum can be expressed by the equation: '''p = mv'''

[[File:Momentum_pic.jpg]]

When an object is moving, it has a non-zero momentum. If an object is standing still, then its momentum is zero.

By Newton's Second Law, '''F=ma''', the conservation of linear momentum is supported. Since acceleration can be expressed as ∆v/∆t, Newton's Second Law could therefore be expressed as '''F = m∆v/∆t'''. Since '''m∆v''' is equal to momentum, '''p''', an expression of Newton's Second Law can be expressed in terms of momentum as '''F=∆p/∆t'''. In many ways, this expression of Newton's Second Law is more versatile than the equation F=ma, because it can be used to analyze systems where the velocity changes and the mass of a body changes. For instance, it can be applied to a motorcycle burning fuel by taking in to account not only the velocity change, but also the change in the mass of the body, which in this case would be the fuel burning and thus lowering the total body mass of the motorcycle.

Newton's laws of motion also play a role in supporting the [[law of conservation of linear momentum]]. Linear momentum is a conserved quantity, and therefore in a closed system (a system that does not allow transfers of mass or energy into or out of the system), the total momentum of the system will not change. This allows one to calculate and predict the outcomes when objects bounce into one another. Or, by knowing the outcome of a collision, one can reason what was the initial state of the system.

== Real World Examples ==

===Newton’s 3rd Law:===

'''Scenario''': There is a car that is stuck, nestled in the trees. Woman appears healthy and stable.

'''Witness Statement:''' Witness says that as a car was making a turn, the car “somehow lost its balance and skid”, deviating off its regular path, and ended up sliding towards the trees, around 30 metres from where she was. The witness claims the car was travelling at 25 miles per hour.

'''Report''': This is a classic combination case of NEWTON’S 1st and 3rd LAW. The first law says that objects at a fixed velocity will stay at that velocity unless acted upon by an unbalanced, external force. It is worth pointing out that when the car was skidding, it was displaying inertia, or the tendency to resist a change in motion. In the car, as the wheels go around, it’s static friction. The force that is pushing the car along the road is a friction force... we need to the road to move the car, cause the road provides the friction. This is Newton’s 3rd Law. The tires are pushing backwards on the road, and the road is pushing forward on the tires. This “push force” is what we’re relying on keep the car on the road, so essentially, we’re relying on this static friction force. When the car starts to skid, it changes to force of kinetic friction, because the wheels are now slipping and having some motion. It slides and is moving, so it becomes kinetic friction.

The witness claimed that the car was going at 25 miles per hour. With this being said, an official wanted check and make sure this really was the speed. Since the car is now 30 metres from the place it lost its balance, we can use this information to calculate the speed.
Assuming the brakes work properly, the stopping distance would’ve been determined by the coefficient of friction between the tires and the road. This is because the force of friction must do enough work on the car to reduce the kinetic energy of the car, as outlined in the work-energy principle.
Net Work = change in kinetic energy of an object
Net Work = (1/2)mv(final)^2 - (1/2)mv(initial)^2
When we look at the equation for static friction:
Ms = Ff / Fn
Fn x Ms = Ff
Ms x mg = Fr
Mu static x mg = Force of friction
Since the road was a bit slippery, and the road a little wet, the coefficient of static friction was 0.4. The normal coefficient is around 0.7 for dry roads and becomes smaller for wet or oily roads. Gravity was 10, so the equation would’ve been:
Work Friction = -μmgd = - (1/2) mv^2
If we cancel out the m’s, we can get
D = (v^2) / (2)(μ)(g)
Plugging in what we have and what we know:
30 = (V^2) / 2 x .4 x 10
30 = (V^2) / 8
V = 15 metre / second, so around 35 miles per hour. The witness’ account of the speed was a little off!

'''Conclusion''': Like most skids, as soon as this car started to skid, it was at the mercy of inertia. It would keep going at the same speed unless some other force stopped it, and in this case, that “other force” was the tress.

=== Newton’s 2nd Law: ===

'''Scenario''': A lady has hit a lamppost. She appears fine, but the car has been totalled.

'''Witness Statement:''' As a lady cruised by in her Honda Civic, she momentarily took her eyes off the road, and found her car in front of a lamppost and crashed into it.

'''Report''': This case is a Newton’s 2nd law case, and impluse. According to the law, F = MA, which means that F = M x (ΔV / ΔT), or F = M((Vf -Vi) / T)
F ΔT = M(Vf - Vi)
The extent of her injury is determined by the force that hit her. So, the size of the force she’s subjected to is determined by the interaction time. If the T becomes smaller, the force is bigger; if T is bigger, the force gets smaller. The sudden change of velocity also played a part in her injury. The car should’ve had safety features that made the interaction time as long as possible, because if you can spread the reaction time, you can do the deceleration with a smaller force - We can reduce the size of the force if we reduce the time.

One must also look at the impact force this car has faced. A crash like this one, that stops the car completely, must take away all the kinetic energy of the car, and as highlighted by the work-energy principle, it would take a longer stopping distance to decrease the impact force.

Net Work = (1/2)mv(final)^2 - (1/2)mv(initial)^2
The change in the kinetic energy of an object is equal to the net work done on the object.

The car is noted to be 1600 kgs, or 16,000 N, and travelling at a speed of 10 m/s. The work required by the lamppost to stop the car would be F(avg)D = -(1/2)mv^2
What would be the force on the car?

Mass = Weight/ Acceleration of Gravity
Mass = 16,000 N / 10 (M/S^2)
Mass = 1600 kgs

KE = (1/2)mv^2
KE = (1/2)x1600x(10m/s)^2
= 80000 Joules = kg x m^2 / s^2

d=1 metre, or 3 feet after impact

F(avg) = KE / d

80000 / 1 = 80,000 newtons, or 8.96 tons!

'''Conclusion''': Thus, the “crumple zones” in the front of the car, and the airbags came in handy, because rather than allowing sudden stop, the car was allowed to halt over a larger period of time, making the force less than it would’ve been without them. Thanks, impulse!

===Inertia / Newton’s 1st Law: ===

'''Scenario''': At a stop light, a car halts and waits for a green. However, the car behind it doesn’t stop in time, and bumps the in front of it, from the behind. A lady in the car, who has just been in a car accident, is complaining of severe neck pain

'''Report''': This has almost everything to do with law of inertia, or Newton’s 1st Law. In Newton’s first law, he states that an object at rest stays at rest, or an object in motion will stay in motion, unless acted upon by an unbalanced force. That is, if an object (be it a head, moving at a certain velocity because of the car) will tend to stay at the same speed and in the same direction, unless something stops it. Back to the scenario: In a way, it’s a good things this lady was wearing a seatbelt... it slows down the inertia. For example, if a kid was in the car, and was NOT wearing a seatbelt, people would think that the kid launched forward. Really, it’s just that the car is brought to a halt, but the kid just continues at their original velocity. This is inertia in action -- that is, the tendency to resist change in the state of motion they are already in. However, in this case, the seatbelt was (kind of!) bad, as it caused the overextension of head. The head weighs around 4-5 kilos, and we know that when car comes to a sudden halt, body is stopped, skull continues on, it’s called whiplash. In this case, when the person bumped into the other car from behind... your car is stunned forward, body with it... head is stationary, is remaining in the same, position, the lady’s car’s inertia wants to stay where it was originally. The body was moved, but the head wanted to stay in its original velocity, but followed the body in the seconds after.

'''Conclusion''': If the lady complains of any neck pain, it’s probably because of inertia, and the possibility that the lady has overextended her neck beyond elastic limits. She will be wearing a neck brace if this is the case!

===Elastic Collision:===

'''Scenario''': A woman is lying on the side of the road, appears to have been hit by a car.

'''Witness Statement''': Witness says that there was a lady walking across the road and at the middle of the road, she paused for a second because she saw a car coming at her. The car was unable to stop in time, and hit the lady at a speed of 25 miles per hour, or around 10 metres per second. The witness also notes the layer of ice on the road.

'''Report''': This is an example of the Law of Conservation of Momentum, which states that in the absence of an external force, there is conserved quantity of momentum, or
P initial = P final (where P = momentum)
MOMENTUM = M X V
M1V1 + M2V2= M1U1 + M2U2 (M = mass , V1 and V2 = initial velocity of object 1 and 2, U1 and U2 = velocities after collision
Essentially, the momentum that was lost by the car, is equal to the momentum gained by the lady.
The lady would’ve had no velocity when the car hit her, and according to the law of conservation of momentum - whatever momentum you have at the start, you have at the end. This means that there would’ve been a redistribution of momentum between car and lady. The car will give some momentum to the lady... however, the car can’t give mass, so the only thing it can her give is velocity.

If we investigate further, we can see that this system was an isolated system. Normally, in collisions like these, we are not dealing with isolated systems... because that would mean that force is free from the influence of a net external force, or a force that can alter the momentum. Most of the time, friction between the car and the road, being an external force, would contribute to a change in total momentum. However, after observing the road, we can say that conditions were such that any external force (ie. friction and air resistance) was negligible, and thus, the total momentum of the two particles are conserved.

What we see here is a case of elastic collision - which means that there was no loss of kinetic energy. In an elastic collision, the objects “bounce” off each other, and don’t stick together to become one body - because this would be an inelastic collision, where part of the kinetic energy is changed to some other form of energy in the collision. But, as said before, this was an elastic collision, it would’ve looked something like this:

[[File:Elastic.jpg]]

It was noted that the car weighed 1600 kgs, while the woman weighs 50 kgs.
The speed of the car was 10 metres/second, while the women's speed was 0 m/s (she stood still)
We can figure out the velocities of both the woman and and the cars after the collision by deriving the formula

[[File:derivation2.png]]

Velocities after the collision

V1 =[ M1 - M2 / (M1+ M2) ] V
V2 = [ 2M1/ M1 + M2 ] V

*Conclusion: If we make a table, we can see the distribution of momentum.
Because of the fact that the mass of the second object (Lady) is much smaller compared to the mass of the first object (car), the person is thrown back at a relatively high velocity.

[[File:wikitable.png]]

Some of the velocity of the bus was given to the lady, which caused her to go flying and land on the other side of the road. This is common of road traffic accident and this redistribution of momentum, in the form of velocity, is where part of her injury comes from.

==Resources==

https://www.youtube.com/watch?v=gVTOf33UlDA

http://www.physicsclassroom.com/class/momentum/u4l2b.cfm

http://www.physicsclassroom.com/class/newtlaws/Lesson-1/Newton-s-First-Law

http://teachertech.rice.edu/Participants/louviere/Newton/law2.html

http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law

http://www.physicsclassroom.com/class/newtlaws/Lesson-1/Inertia-and-Mass

http://www.physicsclassroom.com/mmedia/energy/cs.cfm

http://hyperphysics.phy-astr.gsu.edu/hbase/elacol2.html#c1

http://www.physicsclassroom.com/class/momentum/u4l2b.cfm

http://www.laserpablo.com/teacherresources/files/APLabs_CCPhysics/10-Billiard_Ball_Physics.pdf

http://hyperphysics.phy-astr.gsu.edu/hbase/inecol.html#c1

http://hyperphysics.phy-astr.gsu.edu/hbase/impulse.html#c1

http://hyperphysics.phy-astr.gsu.edu/hbase/seatb.html#cc1

http://hyperphysics.phy-astr.gsu.edu/hbase/work.html#wepr

http://hyperphysics.phy-astr.gsu.edu/hbase/elacol2.html#c1

https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/v/introduction-to-work-and-energy

Inertia

2017-04-09T02:47:02Z

Lkrishnan7: /* Relationship to Modern Day Life */

Newton's Laws and Linear Momentum

2017-04-09T02:45:59Z

Lkrishnan7: /* Newton’s 2nd Law: */

Newton's Third Law of Motion

2017-04-09T02:44:44Z

Lkrishnan7: /* Real World Application */

Elastic Collisions

2017-04-09T02:43:57Z

Lkrishnan7: /* Real World Example */

'''CLAIMED BY SEAN FISCHER'''
==The Main Idea==

So what exactly is an elastic collision? I know you’re thinking, “Oh I know all about elasticity,” but LOL this is not bubble gum or rubber bands guys!

An elastic collision is a collision between two or more objects in which there is no loss in kinetic energy before and after the collision. If we assume that the colliding objects are part of the system and that there is no force from the surroundings, the final kinetic energy is still in the same form as it was initially. To keep it simple, this means that kinetic energy in= kinetic energy out. Remember how your parents always told you what goes in must come out? They were talking about elastic collisions... probably.

Additionally, elastic collisions are a wonderful representation of the conservation of momentum which states that the momentum of an isolated system is constant. For an isolated system undergoing an elastic collision momentum in = momentum out.

And I love playing pool because every time a ball hits another and they bounce off one another I’m witnessing an elastic collision so basically I’m a physicist in the lab. The image below demonstrates the main idea of an elastic collision. Boing!!

It's important to note that with macroscopic systems there are no perfectly elastic collisions because there's always at least a dab of dissipation (like some thermal energy given off), but most are nearly elastic. The only time there are perfect collisions is on a microscopic level when atomic systems with quantized energy collide, but that's only if there is enough energy available to raise the systems to an excited quantum state-- but quantum energy is really a whole other topic. Let's focus on elastic collisions!

[[File: boing.gif]]

[[File:Elastischer_stoß2.gif]]

Check out this funny video on elastic collisions also! https://www.youtube.com/watch?v=W9EqU1_DXUw

Now check out this more informative video on elastic collisions: https://www.youtube.com/watch?v=V4vzNk4qppw

===A Mathematical Model===

Now lets take what we know about elastic collisions and talk about it in mathematical terms. There are three main mathematical concepts surrounding elastic collisions:
[[File: CodeCogsEqn.gif]]
----

[[File: CodeCogsEqn copy.gif]]
----

[[File: CodeCogsEqn_copy_2.gif]]

Example Problem

Cart 1, moving in the positive x direction, collides with cart 2 moving in the negative x direction. Both carts have identical masses and the collisions is (nearly) elastic, as it would be if the carts interacted magnetically or repelled each other through soft springs. What are the final momenta of the two carts?

[[File:Example1good.jpg|350px|thumb|right]]

1. After choosing a correct system, surroundings, and initial and final states, we can apply the momentum principle mentioned above to get a relationship
between the initial and final momentums of the two carts.

2. Next, by applying the energy principle we can gain knowledge about the final and initial kinetic energies. By acknowledging the fact that the change in internal energy is 0 and the fact the reaction happens so quickly that not work or heat transfer is done by the surroundings, the equation can be simplified to include just initial and final kinetic energies.

3. Once we have simplified the momentum and energy principles, one can use the relationship between kinetic energy and momentum mentioned above to get a relationship involving both energy and momentum. Once this is obtained, the equation can be shifted around to get both the final momentums.

===A Computational Model===

The link below demonstrates a basic car crash elastic collision using MATLAB. Take note of the changes in displacement and the time.

[https://www.youtube.com/watch?v=AfCfCS6O2VM Elastic Collision MATLAB model]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible. For a lot of the complicated problems, starting with a diagram and writing down the given information and plugging that into either the momentum or energy principle can help you move forward in the problem. If you still get stuck, try finding similar examples to that problem and look at the solutions to get on the right track.

===Simple===

Okay let’s start with a simple example like the ones you don't see on the test.

Jay and Sarah are best friends. Since they’re best friends they both weigh 55 kg. Jay hadn’t seen Sarah in a long time so when she saw her she ran to her with a velocity of <4,0,0> m/s. Instead of a hug, they were both too excited and collided and bounced back off of each other, and Sarah flew back with a velocity of <7,0,0> m/s. What was Jay’s final velocity?

[[File:Problem1.0.png|300px|Problem 1]]

In a lot of simple elastic collision problems, the momentum principle is all you need to solve them. Most problems will the initial velocities, masses, and one final velocity and you will be asked to solve for a either a final velocity or final momentum. By setting up an equation like the one in this problem, one can easily handle this type of problem.

===Middling===

When far apart, the momentum of a proton is <5.2 ✕ 10−21, 0, 0> kg · m/s as it approaches another proton that is initially at rest. The two protons repel each other electrically, but they are not close enough to touch. When they are far apart again later, one of the protons now has a velocity of <1.75, .82, 0> m/s. At that instant, what is the momentum of the other proton? HINT: Mass of proton is 1.7 *10^-21 kg.

[[File:Problem2.0.png|300px]]

A lot of people freak out when they see problems involving atomic particles and electrical forces, but the concept is the same no matter the scale. For this problem we are given masses, velocities, and momentum, but the equation p = mv allows us to easily handle these different values. Once again drawing a diagram helps to understand what is actually happening in the problem, making it easier to put the values in the correct places and solve.

===Difficult===

Okay, let's get a little bit trickier here...

There is a 400 kg train traveling at 55 m/s that collides, elastically of course, with a random 2 kg trashcan that's stationary on the tracks. So afterwards, what are the speeds of both the train and the trashcan after the collision?

[[File:Problem3.0.png|400px]]

This was a difficult problem because of the assumptions we had to make in order to solve it. Because the collision was elastic we were able to disregard the change in internal energy in the energy principle, and since it happened so quickly the work done by the track and heat transfer between the surroundings was negligible. It is tough to tell what assumptions you can make and which ones you can't in problems like these, which is what can make them difficult. On most exams or quizzes the collision problems will be inelastic simply because they are harder, but it is important to understand the fundementals of elastic collisions and how to solve problems involving them.

==Connectedness==

So how are collisions connected to the real world? Collisions are all around us!

One main example is cars! Lots of car companies will purposely test and wreck cars to test collisions! Data is then sent to places like the Insurance Institute for Highway Safety where we can learn about car agility and more.

[[File:crash-test.jpg]]

Another example of collisions in real life is billiards. This is one of the most accurate real life examples of elastic collisions. One ball hits another ball at rest, and if done right the first ball stops and transfers nearly all its kinetic energy into kinetic energy in the second ball.

[[File:Pool1.0.jpg]]

Another example is hitting a baseball. Hitting a ball off the end or to close the hands of a bat will cause some vibrational energy from the collision, but if the ball catches the sweet spot the collision is very elastic, and you don't feel any vibration when you strike the ball.

[[File:Hittingabaseball.jpg|500px]]

==History==

Collisions are certainly not a knew concept in the world. Ever since the beginning or time things have been colliding and reacting in different ways. It was experiments done by scientists like Newton or Rutherford that started to characterize collisions into categories and apply fundamental principles of physics to the reactions.

The history of collisions originates from the Rutherford Scattering experiment. As Rutherford studied the scattering of alpha particles through metal foils, he first noticed a collision with a single massive positive particle. This lead to the conclusion that the positive charge of the mass was concentrated in the center, the atomic nucleus!

[[File:gold-foil-experiment.jpg]]

== See also ==

http://physicsbook.gatech.edu/Collisions for a general understanding of all collisions.

http://physicsbook.gatech.edu/inelastic_collisions to contrast them from elastic collisions.

===Further reading===

http://www.britannica.com/science/elastic-collision

===External links===

[http://www.physicsclassroom.com/mmedia/momentum/trece.cfm]

[http://hyperphysics.phy-astr.gsu.edu/hbase/elacol2.html]

[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/linear-momentum-and-collisions-7/collisions-70/elastic-collisions-in-one-dimension-298-6220/]

==References==

Main Idea:

''Matter and Interactions, 4th Edition''

http://www.sparknotes.com/testprep/books/sat2/physics/chapter9section4.rhtml

http://blogs.bu.edu/ggarber/archive/bua-physics/collisions-and-conservation-of-momentum/

History:

https://en.wikipedia.org/wiki/Elastic_collision

Connectedness:

http://www.iihs.org/

Additionally used references from ''see also''.

Newton's Laws and Linear Momentum

2017-04-09T02:43:44Z

Lkrishnan7: /* Linear Momentum */

Edited by Lakshmi Krishnan, 4/8/17
== Linear Momentum ==

Linear momentum, denoted by the letter '''p''', is a vector quantity which represents the product of an object's velocity, '''v''', and mass, '''m''', as it moves along a straight line. As a vector quantity, an object's linear momentum possesses momentum and direction and is therefore always in the same direction as its velocity vector. Linear momentum can be expressed by the equation: '''p = mv'''

[[File:Momentum_pic.jpg]]

When an object is moving, it has a non-zero momentum. If an object is standing still, then its momentum is zero.

By Newton's Second Law, '''F=ma''', the conservation of linear momentum is supported. Since acceleration can be expressed as ∆v/∆t, Newton's Second Law could therefore be expressed as '''F = m∆v/∆t'''. Since '''m∆v''' is equal to momentum, '''p''', an expression of Newton's Second Law can be expressed in terms of momentum as '''F=∆p/∆t'''. In many ways, this expression of Newton's Second Law is more versatile than the equation F=ma, because it can be used to analyze systems where the velocity changes and the mass of a body changes. For instance, it can be applied to a motorcycle burning fuel by taking in to account not only the velocity change, but also the change in the mass of the body, which in this case would be the fuel burning and thus lowering the total body mass of the motorcycle.

Newton's laws of motion also play a role in supporting the [[law of conservation of linear momentum]]. Linear momentum is a conserved quantity, and therefore in a closed system (a system that does not allow transfers of mass or energy into or out of the system), the total momentum of the system will not change. This allows one to calculate and predict the outcomes when objects bounce into one another. Or, by knowing the outcome of a collision, one can reason what was the initial state of the system.

== Real World Examples ==

===Newton’s 3rd Law:===

'''Scenario''': There is a car that is stuck, nestled in the trees. Woman appears healthy and stable.

'''Witness Statement:''' Witness says that as a car was making a turn, the car “somehow lost its balance and skid”, deviating off its regular path, and ended up sliding towards the trees, around 30 metres from where she was. The witness claims the car was travelling at 25 miles per hour.

'''Report''': This is a classic combination case of NEWTON’S 1st and 3rd LAW. The first law says that objects at a fixed velocity will stay at that velocity unless acted upon by an unbalanced, external force. It is worth pointing out that when the car was skidding, it was displaying inertia, or the tendency to resist a change in motion. In the car, as the wheels go around, it’s static friction. The force that is pushing the car along the road is a friction force... we need to the road to move the car, cause the road provides the friction. This is Newton’s 3rd Law. The tires are pushing backwards on the road, and the road is pushing forward on the tires. This “push force” is what we’re relying on keep the car on the road, so essentially, we’re relying on this static friction force. When the car starts to skid, it changes to force of kinetic friction, because the wheels are now slipping and having some motion. It slides and is moving, so it becomes kinetic friction.

The witness claimed that the car was going at 25 miles per hour. With this being said, an official wanted check and make sure this really was the speed. Since the car is now 30 metres from the place it lost its balance, we can use this information to calculate the speed.
Assuming the brakes work properly, the stopping distance would’ve been determined by the coefficient of friction between the tires and the road. This is because the force of friction must do enough work on the car to reduce the kinetic energy of the car, as outlined in the work-energy principle.
Net Work = change in kinetic energy of an object
Net Work = (1/2)mv(final)^2 - (1/2)mv(initial)^2
When we look at the equation for static friction:
Ms = Ff / Fn
Fn x Ms = Ff
Ms x mg = Fr
Mu static x mg = Force of friction
Since the road was a bit slippery, and the road a little wet, the coefficient of static friction was 0.4. The normal coefficient is around 0.7 for dry roads and becomes smaller for wet or oily roads. Gravity was 10, so the equation would’ve been:
Work Friction = -μmgd = - (1/2) mv^2
If we cancel out the m’s, we can get
D = (v^2) / (2)(μ)(g)
Plugging in what we have and what we know:
30 = (V^2) / 2 x .4 x 10
30 = (V^2) / 8
V = 15 metre / second, so around 35 miles per hour. The witness’ account of the speed was a little off!

'''Conclusion''': Like most skids, as soon as this car started to skid, it was at the mercy of inertia. It would keep going at the same speed unless some other force stopped it, and in this case, that “other force” was the tress.

=== Newton’s 2nd Law: ===

'''Scenario''': A lady has hit a lamppost. She appears fine, but the car has been totalled.

'''Witness Statement:''' As a lady cruised by in her Honda Civic, she momentarily took her eyes off the road, and found her car in front of a lamppost and crashed into it.

'''Report''': This case is a Newton’s 2nd law case. According to the law, F = MA, which means that F = M x (ΔV / ΔT), or F = M((Vf -Vi) / T)
F ΔT = M(Vf - Vi)
The extent of her injury is determined by the force that hit her. So, the size of the force she’s subjected to is determined by the interaction time. If the T becomes smaller, the force is bigger; if T is bigger, the force gets smaller. The sudden change of velocity also played a part in her injury. The car should’ve had safety features that made the interaction time as long as possible, because if you can spread the reaction time, you can do the deceleration with a smaller force - We can reduce the size of the force if we reduce the time.

One must also look at the impact force this car has faced. A crash like this one, that stops the car completely, must take away all the kinetic energy of the car, and as highlighted by the work-energy principle, it would take a longer stopping distance to decrease the impact force.

Net Work = (1/2)mv(final)^2 - (1/2)mv(initial)^2
The change in the kinetic energy of an object is equal to the net work done on the object.

The car is noted to be 1600 kgs, or 16,000 N, and travelling at a speed of 10 m/s. The work required by the lamppost to stop the car would be F(avg)D = -(1/2)mv^2
What would be the force on the car?

Mass = Weight/ Acceleration of Gravity
Mass = 16,000 N / 10 (M/S^2)
Mass = 1600 kgs

KE = (1/2)mv^2
KE = (1/2)x1600x(10m/s)^2
= 80000 Joules = kg x m^2 / s^2

d=1 metre, or 3 feet after impact

F(avg) = KE / d

80000 / 1 = 80,000 newtons, or 8.96 tons!

'''Conclusion''': Thus, the “crumple zones” in the front of the car, and the airbags came in handy, because rather than allowing sudden stop, the car was allowed to halt over a larger period of time, making the force less than it would’ve been without them.

===Inertia / Newton’s 1st Law: ===

'''Scenario''': At a stop light, a car halts and waits for a green. However, the car behind it doesn’t stop in time, and bumps the in front of it, from the behind. A lady in the car, who has just been in a car accident, is complaining of severe neck pain

'''Report''': This has almost everything to do with law of inertia, or Newton’s 1st Law. In Newton’s first law, he states that an object at rest stays at rest, or an object in motion will stay in motion, unless acted upon by an unbalanced force. That is, if an object (be it a head, moving at a certain velocity because of the car) will tend to stay at the same speed and in the same direction, unless something stops it. Back to the scenario: In a way, it’s a good things this lady was wearing a seatbelt... it slows down the inertia. For example, if a kid was in the car, and was NOT wearing a seatbelt, people would think that the kid launched forward. Really, it’s just that the car is brought to a halt, but the kid just continues at their original velocity. This is inertia in action -- that is, the tendency to resist change in the state of motion they are already in. However, in this case, the seatbelt was (kind of!) bad, as it caused the overextension of head. The head weighs around 4-5 kilos, and we know that when car comes to a sudden halt, body is stopped, skull continues on, it’s called whiplash. In this case, when the person bumped into the other car from behind... your car is stunned forward, body with it... head is stationary, is remaining in the same, position, the lady’s car’s inertia wants to stay where it was originally. The body was moved, but the head wanted to stay in its original velocity, but followed the body in the seconds after.

'''Conclusion''': If the lady complains of any neck pain, it’s probably because of inertia, and the possibility that the lady has overextended her neck beyond elastic limits. She will be wearing a neck brace if this is the case!

===Elastic Collision:===

'''Scenario''': A woman is lying on the side of the road, appears to have been hit by a car.

'''Witness Statement''': Witness says that there was a lady walking across the road and at the middle of the road, she paused for a second because she saw a car coming at her. The car was unable to stop in time, and hit the lady at a speed of 25 miles per hour, or around 10 metres per second. The witness also notes the layer of ice on the road.

'''Report''': This is an example of the Law of Conservation of Momentum, which states that in the absence of an external force, there is conserved quantity of momentum, or
P initial = P final (where P = momentum)
MOMENTUM = M X V
M1V1 + M2V2= M1U1 + M2U2 (M = mass , V1 and V2 = initial velocity of object 1 and 2, U1 and U2 = velocities after collision
Essentially, the momentum that was lost by the car, is equal to the momentum gained by the lady.
The lady would’ve had no velocity when the car hit her, and according to the law of conservation of momentum - whatever momentum you have at the start, you have at the end. This means that there would’ve been a redistribution of momentum between car and lady. The car will give some momentum to the lady... however, the car can’t give mass, so the only thing it can her give is velocity.

If we investigate further, we can see that this system was an isolated system. Normally, in collisions like these, we are not dealing with isolated systems... because that would mean that force is free from the influence of a net external force, or a force that can alter the momentum. Most of the time, friction between the car and the road, being an external force, would contribute to a change in total momentum. However, after observing the road, we can say that conditions were such that any external force (ie. friction and air resistance) was negligible, and thus, the total momentum of the two particles are conserved.

What we see here is a case of elastic collision - which means that there was no loss of kinetic energy. In an elastic collision, the objects “bounce” off each other, and don’t stick together to become one body - because this would be an inelastic collision, where part of the kinetic energy is changed to some other form of energy in the collision. But, as said before, this was an elastic collision, it would’ve looked something like this:

[[File:Elastic.jpg]]

It was noted that the car weighed 1600 kgs, while the woman weighs 50 kgs.
The speed of the car was 10 metres/second, while the women's speed was 0 m/s (she stood still)
We can figure out the velocities of both the woman and and the cars after the collision by deriving the formula

[[File:derivation2.png]]

Velocities after the collision

V1 =[ M1 - M2 / (M1+ M2) ] V
V2 = [ 2M1/ M1 + M2 ] V

*Conclusion: If we make a table, we can see the distribution of momentum.
Because of the fact that the mass of the second object (Lady) is much smaller compared to the mass of the first object (car), the person is thrown back at a relatively high velocity.

[[File:wikitable.png]]

Some of the velocity of the bus was given to the lady, which caused her to go flying and land on the other side of the road. This is common of road traffic accident and this redistribution of momentum, in the form of velocity, is where part of her injury comes from.

File:Derivation2.png

2017-04-08T21:18:20Z

Lkrishnan7:

Elastic Collisions

2017-04-08T21:17:47Z

Lkrishnan7: /* Real World Example */

'''CLAIMED BY SEAN FISCHER'''
==The Main Idea==

So what exactly is an elastic collision? I know you’re thinking, “Oh I know all about elasticity,” but LOL this is not bubble gum or rubber bands guys!

An elastic collision is a collision between two or more objects in which there is no loss in kinetic energy before and after the collision. If we assume that the colliding objects are part of the system and that there is no force from the surroundings, the final kinetic energy is still in the same form as it was initially. To keep it simple, this means that kinetic energy in= kinetic energy out. Remember how your parents always told you what goes in must come out? They were talking about elastic collisions... probably.

Additionally, elastic collisions are a wonderful representation of the conservation of momentum which states that the momentum of an isolated system is constant. For an isolated system undergoing an elastic collision momentum in = momentum out.

And I love playing pool because every time a ball hits another and they bounce off one another I’m witnessing an elastic collision so basically I’m a physicist in the lab. The image below demonstrates the main idea of an elastic collision. Boing!!

It's important to note that with macroscopic systems there are no perfectly elastic collisions because there's always at least a dab of dissipation (like some thermal energy given off), but most are nearly elastic. The only time there are perfect collisions is on a microscopic level when atomic systems with quantized energy collide, but that's only if there is enough energy available to raise the systems to an excited quantum state-- but quantum energy is really a whole other topic. Let's focus on elastic collisions!

[[File: boing.gif]]

[[File:Elastischer_stoß2.gif]]

Check out this funny video on elastic collisions also! https://www.youtube.com/watch?v=W9EqU1_DXUw

Now check out this more informative video on elastic collisions: https://www.youtube.com/watch?v=V4vzNk4qppw

===A Mathematical Model===

Now lets take what we know about elastic collisions and talk about it in mathematical terms. There are three main mathematical concepts surrounding elastic collisions:
[[File: CodeCogsEqn.gif]]
----

[[File: CodeCogsEqn copy.gif]]
----

[[File: CodeCogsEqn_copy_2.gif]]

Example Problem

Cart 1, moving in the positive x direction, collides with cart 2 moving in the negative x direction. Both carts have identical masses and the collisions is (nearly) elastic, as it would be if the carts interacted magnetically or repelled each other through soft springs. What are the final momenta of the two carts?

[[File:Example1good.jpg|350px|thumb|right]]

1. After choosing a correct system, surroundings, and initial and final states, we can apply the momentum principle mentioned above to get a relationship
between the initial and final momentums of the two carts.

2. Next, by applying the energy principle we can gain knowledge about the final and initial kinetic energies. By acknowledging the fact that the change in internal energy is 0 and the fact the reaction happens so quickly that not work or heat transfer is done by the surroundings, the equation can be simplified to include just initial and final kinetic energies.

3. Once we have simplified the momentum and energy principles, one can use the relationship between kinetic energy and momentum mentioned above to get a relationship involving both energy and momentum. Once this is obtained, the equation can be shifted around to get both the final momentums.

===A Computational Model===

The link below demonstrates a basic car crash elastic collision using MATLAB. Take note of the changes in displacement and the time.

[https://www.youtube.com/watch?v=AfCfCS6O2VM Elastic Collision MATLAB model]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible. For a lot of the complicated problems, starting with a diagram and writing down the given information and plugging that into either the momentum or energy principle can help you move forward in the problem. If you still get stuck, try finding similar examples to that problem and look at the solutions to get on the right track.

===Simple===

Okay let’s start with a simple example like the ones you don't see on the test.

Jay and Sarah are best friends. Since they’re best friends they both weigh 55 kg. Jay hadn’t seen Sarah in a long time so when she saw her she ran to her with a velocity of <4,0,0> m/s. Instead of a hug, they were both too excited and collided and bounced back off of each other, and Sarah flew back with a velocity of <7,0,0> m/s. What was Jay’s final velocity?

[[File:Problem1.0.png|300px|Problem 1]]

In a lot of simple elastic collision problems, the momentum principle is all you need to solve them. Most problems will the initial velocities, masses, and one final velocity and you will be asked to solve for a either a final velocity or final momentum. By setting up an equation like the one in this problem, one can easily handle this type of problem.

===Middling===

When far apart, the momentum of a proton is <5.2 ✕ 10−21, 0, 0> kg · m/s as it approaches another proton that is initially at rest. The two protons repel each other electrically, but they are not close enough to touch. When they are far apart again later, one of the protons now has a velocity of <1.75, .82, 0> m/s. At that instant, what is the momentum of the other proton? HINT: Mass of proton is 1.7 *10^-21 kg.

[[File:Problem2.0.png|300px]]

A lot of people freak out when they see problems involving atomic particles and electrical forces, but the concept is the same no matter the scale. For this problem we are given masses, velocities, and momentum, but the equation p = mv allows us to easily handle these different values. Once again drawing a diagram helps to understand what is actually happening in the problem, making it easier to put the values in the correct places and solve.

===Difficult===

Okay, let's get a little bit trickier here...

There is a 400 kg train traveling at 55 m/s that collides, elastically of course, with a random 2 kg trashcan that's stationary on the tracks. So afterwards, what are the speeds of both the train and the trashcan after the collision?

[[File:Problem3.0.png|400px]]

This was a difficult problem because of the assumptions we had to make in order to solve it. Because the collision was elastic we were able to disregard the change in internal energy in the energy principle, and since it happened so quickly the work done by the track and heat transfer between the surroundings was negligible. It is tough to tell what assumptions you can make and which ones you can't in problems like these, which is what can make them difficult. On most exams or quizzes the collision problems will be inelastic simply because they are harder, but it is important to understand the fundementals of elastic collisions and how to solve problems involving them.

===Real World Example===

(Edit by Lakshmi Krishnan (lkrishnan7))

Now, let's look at a real world example of elastic collisions: car crashes.

'''Scenario''': A woman is lying on the side of the road, appears to have been hit by a car.

'''Witness Statement''': Witness says that there was a lady walking across the road and at the middle of the road, she paused for a second because she saw a car coming at her. The car was unable to stop in time, and hit the lady at a speed of 25 miles per hour, or around 10 metres per second. The witness also notes the layer of ice on the road.

'''Report''': This is an example of the Law of Conservation of Momentum, which states that in the absence of an external force, there is conserved quantity of momentum, or
P initial = P final (where P = momentum)
MOMENTUM = M X V
M1V1 + M2V2= M1U1 + M2U2 (M = mass , V1 and V2 = initial velocity of object 1 and 2, U1 and U2 = velocities after collision
Essentially, the momentum that was lost by the car, is equal to the momentum gained by the lady.
The lady would’ve had no velocity when the car hit her, and according to the law of conservation of momentum - whatever momentum you have at the start, you have at the end. This means that there would’ve been a redistribution of momentum between car and lady. The car will give some momentum to the lady... however, the car can’t give mass, so the only thing it can her give is velocity.

If we investigate further, we can see that this system was an isolated system. Normally, in collisions like these, we are not dealing with isolated systems... because that would mean that force is free from the influence of a net external force, or a force that can alter the momentum. Most of the time, friction between the car and the road, being an external force, would contribute to a change in total momentum. However, after observing the road, we can say that conditions were such that any external force (ie. friction and air resistance) was negligible, and thus, the total momentum of the two particles are conserved.

What we see here is a case of elastic collision - which means that there was no loss of kinetic energy. In an elastic collision, the objects “bounce” off each other, and don’t stick together to become one body - because this would be an inelastic collision, where part of the kinetic energy is changed to some other form of energy in the collision. But, as said before, this was an elastic collision, it would’ve looked something like this:

[[File:Elastic.jpg]]

It was noted that the car weighed 1600 kgs, while the woman weighs 50 kgs.
The speed of the car was 10 metres/second, while the women's speed was 0 m/s (she stood still)
We can figure out the velocities of both the woman and and the cars after the collision by deriving the formula

[[File:derivation2.png]]

Velocities after the collision

V1 =[ M1 - M2 / (M1+ M2) ] V
V2 = [ 2M1/ M1 + M2 ] V

*Conclusion: If we make a table, we can see the distribution of momentum.
Because of the fact that the mass of the second object (Lady) is much smaller compared to the mass of the first object (car), the person is thrown back at a relatively high velocity.

[[File:wikitable.png]]

Some of the velocity of the bus was given to the lady, which caused her to go flying and land on the other side of the road. This is common of road traffic accident and this redistribution of momentum, in the form of velocity, is where part of her injury comes from.

==Connectedness==

So how are collisions connected to the real world? Collisions are all around us!

One main example is cars! Lots of car companies will purposely test and wreck cars to test collisions! Data is then sent to places like the Insurance Institute for Highway Safety where we can learn about car agility and more.

[[File:crash-test.jpg]]

Another example of collisions in real life is billiards. This is one of the most accurate real life examples of elastic collisions. One ball hits another ball at rest, and if done right the first ball stops and transfers nearly all its kinetic energy into kinetic energy in the second ball.

[[File:Pool1.0.jpg]]

Another example is hitting a baseball. Hitting a ball off the end or to close the hands of a bat will cause some vibrational energy from the collision, but if the ball catches the sweet spot the collision is very elastic, and you don't feel any vibration when you strike the ball.

[[File:Hittingabaseball.jpg|500px]]

==History==

Collisions are certainly not a knew concept in the world. Ever since the beginning or time things have been colliding and reacting in different ways. It was experiments done by scientists like Newton or Rutherford that started to characterize collisions into categories and apply fundamental principles of physics to the reactions.

The history of collisions originates from the Rutherford Scattering experiment. As Rutherford studied the scattering of alpha particles through metal foils, he first noticed a collision with a single massive positive particle. This lead to the conclusion that the positive charge of the mass was concentrated in the center, the atomic nucleus!

[[File:gold-foil-experiment.jpg]]

== See also ==

http://physicsbook.gatech.edu/Collisions for a general understanding of all collisions.

http://physicsbook.gatech.edu/inelastic_collisions to contrast them from elastic collisions.

===Further reading===

http://www.britannica.com/science/elastic-collision

===External links===

[http://www.physicsclassroom.com/mmedia/momentum/trece.cfm]

[http://hyperphysics.phy-astr.gsu.edu/hbase/elacol2.html]

[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/linear-momentum-and-collisions-7/collisions-70/elastic-collisions-in-one-dimension-298-6220/]

==References==

Main Idea:

''Matter and Interactions, 4th Edition''

http://www.sparknotes.com/testprep/books/sat2/physics/chapter9section4.rhtml

http://blogs.bu.edu/ggarber/archive/bua-physics/collisions-and-conservation-of-momentum/

History:

https://en.wikipedia.org/wiki/Elastic_collision

Connectedness:

http://www.iihs.org/

Additionally used references from ''see also''.

Elastic Collisions

2017-04-08T21:06:54Z

Lkrishnan7: /* Real World Example */

'''CLAIMED BY SEAN FISCHER'''
==The Main Idea==

So what exactly is an elastic collision? I know you’re thinking, “Oh I know all about elasticity,” but LOL this is not bubble gum or rubber bands guys!

An elastic collision is a collision between two or more objects in which there is no loss in kinetic energy before and after the collision. If we assume that the colliding objects are part of the system and that there is no force from the surroundings, the final kinetic energy is still in the same form as it was initially. To keep it simple, this means that kinetic energy in= kinetic energy out. Remember how your parents always told you what goes in must come out? They were talking about elastic collisions... probably.

Additionally, elastic collisions are a wonderful representation of the conservation of momentum which states that the momentum of an isolated system is constant. For an isolated system undergoing an elastic collision momentum in = momentum out.

And I love playing pool because every time a ball hits another and they bounce off one another I’m witnessing an elastic collision so basically I’m a physicist in the lab. The image below demonstrates the main idea of an elastic collision. Boing!!

It's important to note that with macroscopic systems there are no perfectly elastic collisions because there's always at least a dab of dissipation (like some thermal energy given off), but most are nearly elastic. The only time there are perfect collisions is on a microscopic level when atomic systems with quantized energy collide, but that's only if there is enough energy available to raise the systems to an excited quantum state-- but quantum energy is really a whole other topic. Let's focus on elastic collisions!

[[File: boing.gif]]

[[File:Elastischer_stoß2.gif]]

Check out this funny video on elastic collisions also! https://www.youtube.com/watch?v=W9EqU1_DXUw

Now check out this more informative video on elastic collisions: https://www.youtube.com/watch?v=V4vzNk4qppw

===A Mathematical Model===

Now lets take what we know about elastic collisions and talk about it in mathematical terms. There are three main mathematical concepts surrounding elastic collisions:
[[File: CodeCogsEqn.gif]]
----

[[File: CodeCogsEqn copy.gif]]
----

[[File: CodeCogsEqn_copy_2.gif]]

Example Problem

Cart 1, moving in the positive x direction, collides with cart 2 moving in the negative x direction. Both carts have identical masses and the collisions is (nearly) elastic, as it would be if the carts interacted magnetically or repelled each other through soft springs. What are the final momenta of the two carts?

[[File:Example1good.jpg|350px|thumb|right]]

1. After choosing a correct system, surroundings, and initial and final states, we can apply the momentum principle mentioned above to get a relationship
between the initial and final momentums of the two carts.

2. Next, by applying the energy principle we can gain knowledge about the final and initial kinetic energies. By acknowledging the fact that the change in internal energy is 0 and the fact the reaction happens so quickly that not work or heat transfer is done by the surroundings, the equation can be simplified to include just initial and final kinetic energies.

3. Once we have simplified the momentum and energy principles, one can use the relationship between kinetic energy and momentum mentioned above to get a relationship involving both energy and momentum. Once this is obtained, the equation can be shifted around to get both the final momentums.

===A Computational Model===

The link below demonstrates a basic car crash elastic collision using MATLAB. Take note of the changes in displacement and the time.

[https://www.youtube.com/watch?v=AfCfCS6O2VM Elastic Collision MATLAB model]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible. For a lot of the complicated problems, starting with a diagram and writing down the given information and plugging that into either the momentum or energy principle can help you move forward in the problem. If you still get stuck, try finding similar examples to that problem and look at the solutions to get on the right track.

===Simple===

Okay let’s start with a simple example like the ones you don't see on the test.

Jay and Sarah are best friends. Since they’re best friends they both weigh 55 kg. Jay hadn’t seen Sarah in a long time so when she saw her she ran to her with a velocity of <4,0,0> m/s. Instead of a hug, they were both too excited and collided and bounced back off of each other, and Sarah flew back with a velocity of <7,0,0> m/s. What was Jay’s final velocity?

[[File:Problem1.0.png|300px|Problem 1]]

In a lot of simple elastic collision problems, the momentum principle is all you need to solve them. Most problems will the initial velocities, masses, and one final velocity and you will be asked to solve for a either a final velocity or final momentum. By setting up an equation like the one in this problem, one can easily handle this type of problem.

===Middling===

When far apart, the momentum of a proton is <5.2 ✕ 10−21, 0, 0> kg · m/s as it approaches another proton that is initially at rest. The two protons repel each other electrically, but they are not close enough to touch. When they are far apart again later, one of the protons now has a velocity of <1.75, .82, 0> m/s. At that instant, what is the momentum of the other proton? HINT: Mass of proton is 1.7 *10^-21 kg.

[[File:Problem2.0.png|300px]]

A lot of people freak out when they see problems involving atomic particles and electrical forces, but the concept is the same no matter the scale. For this problem we are given masses, velocities, and momentum, but the equation p = mv allows us to easily handle these different values. Once again drawing a diagram helps to understand what is actually happening in the problem, making it easier to put the values in the correct places and solve.

===Difficult===

Okay, let's get a little bit trickier here...

There is a 400 kg train traveling at 55 m/s that collides, elastically of course, with a random 2 kg trashcan that's stationary on the tracks. So afterwards, what are the speeds of both the train and the trashcan after the collision?

[[File:Problem3.0.png|400px]]

This was a difficult problem because of the assumptions we had to make in order to solve it. Because the collision was elastic we were able to disregard the change in internal energy in the energy principle, and since it happened so quickly the work done by the track and heat transfer between the surroundings was negligible. It is tough to tell what assumptions you can make and which ones you can't in problems like these, which is what can make them difficult. On most exams or quizzes the collision problems will be inelastic simply because they are harder, but it is important to understand the fundementals of elastic collisions and how to solve problems involving them.

===Real World Example===

(Edit by Lakshmi Krishnan (lkrishnan7))

Now, let's look at a real world example of elastic collisions: car crashes.

'''Scenario''': A woman is lying on the side of the road, appears to have been hit by a car.

'''Witness Statement''': Witness says that there was a lady walking across the road and at the middle of the road, she paused for a second because she saw a car coming at her. The car was unable to stop in time, and hit the lady at a speed of 25 miles per hour, or around 10 metres per second. The witness also notes the layer of ice on the road.

'''Report''': This is an example of the Law of Conservation of Momentum, which states that in the absence of an external force, there is conserved quantity of momentum, or
P initial = P final (where P = momentum)
MOMENTUM = M X V
M1V1 + M2V2= M1U1 + M2U2 (M = mass , V1 and V2 = initial velocity of object 1 and 2, U1 and U2 = velocities after collision
Essentially, the momentum that was lost by the car, is equal to the momentum gained by the lady.
The lady would’ve had no velocity when the car hit her, and according to the law of conservation of momentum - whatever momentum you have at the start, you have at the end. This means that there would’ve been a redistribution of momentum between car and lady. The car will give some momentum to the lady... however, the car can’t give mass, so the only thing it can her give is velocity.

If we investigate further, we can see that this system was an isolated system. Normally, in collisions like these, we are not dealing with isolated systems... because that would mean that force is free from the influence of a net external force, or a force that can alter the momentum. Most of the time, friction between the car and the road, being an external force, would contribute to a change in total momentum. However, after observing the road, we can say that conditions were such that any external force (ie. friction and air resistance) was negligible, and thus, the total momentum of the two particles are conserved.

What we see here is a case of elastic collision - which means that there was no loss of kinetic energy. In an elastic collision, the objects “bounce” off each other, and don’t stick together to become one body - because this would be an inelastic collision, where part of the kinetic energy is changed to some other form of energy in the collision. But, as said before, this was an elastic collision, it would’ve looked something like this:

[[File:Elastic.jpg]]

It was noted that the car weighed 1600 kgs, while the woman weighs 50 kgs.
The speed of the car was 10 metres/second, while the women's speed was 0 m/s (she stood still)
We can figure out the velocities of both the woman and and the cars after the collision by deriving the formula

[[File:derivation.jpg]]

Velocities after the collision

V1 =[ M1 - M2 / (M1+ M2) ] V
V2 = [ 2M1/ M1 + M2 ] V

*Conclusion: If we make a table, we can see the distribution of momentum.
Because of the fact that the mass of the second object (Lady) is much smaller compared to the mass of the first object (car), the person is thrown back at a relatively high velocity.

[[File:wikitable.png]]

Some of the velocity of the bus was given to the lady, which caused her to go flying and land on the other side of the road. This is common of road traffic accident and this redistribution of momentum, in the form of velocity, is where part of her injury comes from.

==Connectedness==

So how are collisions connected to the real world? Collisions are all around us!

One main example is cars! Lots of car companies will purposely test and wreck cars to test collisions! Data is then sent to places like the Insurance Institute for Highway Safety where we can learn about car agility and more.

[[File:crash-test.jpg]]

Another example of collisions in real life is billiards. This is one of the most accurate real life examples of elastic collisions. One ball hits another ball at rest, and if done right the first ball stops and transfers nearly all its kinetic energy into kinetic energy in the second ball.

[[File:Pool1.0.jpg]]

Another example is hitting a baseball. Hitting a ball off the end or to close the hands of a bat will cause some vibrational energy from the collision, but if the ball catches the sweet spot the collision is very elastic, and you don't feel any vibration when you strike the ball.

[[File:Hittingabaseball.jpg|500px]]

==History==

Collisions are certainly not a knew concept in the world. Ever since the beginning or time things have been colliding and reacting in different ways. It was experiments done by scientists like Newton or Rutherford that started to characterize collisions into categories and apply fundamental principles of physics to the reactions.

The history of collisions originates from the Rutherford Scattering experiment. As Rutherford studied the scattering of alpha particles through metal foils, he first noticed a collision with a single massive positive particle. This lead to the conclusion that the positive charge of the mass was concentrated in the center, the atomic nucleus!

[[File:gold-foil-experiment.jpg]]

== See also ==

http://physicsbook.gatech.edu/Collisions for a general understanding of all collisions.

http://physicsbook.gatech.edu/inelastic_collisions to contrast them from elastic collisions.

===Further reading===

http://www.britannica.com/science/elastic-collision

===External links===

[http://www.physicsclassroom.com/mmedia/momentum/trece.cfm]

[http://hyperphysics.phy-astr.gsu.edu/hbase/elacol2.html]

[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/linear-momentum-and-collisions-7/collisions-70/elastic-collisions-in-one-dimension-298-6220/]

==References==

Main Idea:

''Matter and Interactions, 4th Edition''

http://www.sparknotes.com/testprep/books/sat2/physics/chapter9section4.rhtml

http://blogs.bu.edu/ggarber/archive/bua-physics/collisions-and-conservation-of-momentum/

History:

https://en.wikipedia.org/wiki/Elastic_collision

Connectedness:

http://www.iihs.org/

Additionally used references from ''see also''.

File:Elastic.jpg

2017-04-08T21:06:19Z

Lkrishnan7:

Elastic Collisions

2017-04-08T20:58:10Z

Lkrishnan7: /* Real World Example */

'''CLAIMED BY SEAN FISCHER'''
==The Main Idea==

So what exactly is an elastic collision? I know you’re thinking, “Oh I know all about elasticity,” but LOL this is not bubble gum or rubber bands guys!

An elastic collision is a collision between two or more objects in which there is no loss in kinetic energy before and after the collision. If we assume that the colliding objects are part of the system and that there is no force from the surroundings, the final kinetic energy is still in the same form as it was initially. To keep it simple, this means that kinetic energy in= kinetic energy out. Remember how your parents always told you what goes in must come out? They were talking about elastic collisions... probably.

Additionally, elastic collisions are a wonderful representation of the conservation of momentum which states that the momentum of an isolated system is constant. For an isolated system undergoing an elastic collision momentum in = momentum out.

And I love playing pool because every time a ball hits another and they bounce off one another I’m witnessing an elastic collision so basically I’m a physicist in the lab. The image below demonstrates the main idea of an elastic collision. Boing!!

It's important to note that with macroscopic systems there are no perfectly elastic collisions because there's always at least a dab of dissipation (like some thermal energy given off), but most are nearly elastic. The only time there are perfect collisions is on a microscopic level when atomic systems with quantized energy collide, but that's only if there is enough energy available to raise the systems to an excited quantum state-- but quantum energy is really a whole other topic. Let's focus on elastic collisions!

[[File: boing.gif]]

[[File:Elastischer_stoß2.gif]]

Check out this funny video on elastic collisions also! https://www.youtube.com/watch?v=W9EqU1_DXUw

Now check out this more informative video on elastic collisions: https://www.youtube.com/watch?v=V4vzNk4qppw

===A Mathematical Model===

Now lets take what we know about elastic collisions and talk about it in mathematical terms. There are three main mathematical concepts surrounding elastic collisions:
[[File: CodeCogsEqn.gif]]
----

[[File: CodeCogsEqn copy.gif]]
----

[[File: CodeCogsEqn_copy_2.gif]]

Example Problem

Cart 1, moving in the positive x direction, collides with cart 2 moving in the negative x direction. Both carts have identical masses and the collisions is (nearly) elastic, as it would be if the carts interacted magnetically or repelled each other through soft springs. What are the final momenta of the two carts?

[[File:Example1good.jpg|350px|thumb|right]]

1. After choosing a correct system, surroundings, and initial and final states, we can apply the momentum principle mentioned above to get a relationship
between the initial and final momentums of the two carts.

2. Next, by applying the energy principle we can gain knowledge about the final and initial kinetic energies. By acknowledging the fact that the change in internal energy is 0 and the fact the reaction happens so quickly that not work or heat transfer is done by the surroundings, the equation can be simplified to include just initial and final kinetic energies.

3. Once we have simplified the momentum and energy principles, one can use the relationship between kinetic energy and momentum mentioned above to get a relationship involving both energy and momentum. Once this is obtained, the equation can be shifted around to get both the final momentums.

===A Computational Model===

The link below demonstrates a basic car crash elastic collision using MATLAB. Take note of the changes in displacement and the time.

[https://www.youtube.com/watch?v=AfCfCS6O2VM Elastic Collision MATLAB model]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible. For a lot of the complicated problems, starting with a diagram and writing down the given information and plugging that into either the momentum or energy principle can help you move forward in the problem. If you still get stuck, try finding similar examples to that problem and look at the solutions to get on the right track.

===Simple===

Okay let’s start with a simple example like the ones you don't see on the test.

Jay and Sarah are best friends. Since they’re best friends they both weigh 55 kg. Jay hadn’t seen Sarah in a long time so when she saw her she ran to her with a velocity of <4,0,0> m/s. Instead of a hug, they were both too excited and collided and bounced back off of each other, and Sarah flew back with a velocity of <7,0,0> m/s. What was Jay’s final velocity?

[[File:Problem1.0.png|300px|Problem 1]]

In a lot of simple elastic collision problems, the momentum principle is all you need to solve them. Most problems will the initial velocities, masses, and one final velocity and you will be asked to solve for a either a final velocity or final momentum. By setting up an equation like the one in this problem, one can easily handle this type of problem.

===Middling===

When far apart, the momentum of a proton is <5.2 ✕ 10−21, 0, 0> kg · m/s as it approaches another proton that is initially at rest. The two protons repel each other electrically, but they are not close enough to touch. When they are far apart again later, one of the protons now has a velocity of <1.75, .82, 0> m/s. At that instant, what is the momentum of the other proton? HINT: Mass of proton is 1.7 *10^-21 kg.

[[File:Problem2.0.png|300px]]

A lot of people freak out when they see problems involving atomic particles and electrical forces, but the concept is the same no matter the scale. For this problem we are given masses, velocities, and momentum, but the equation p = mv allows us to easily handle these different values. Once again drawing a diagram helps to understand what is actually happening in the problem, making it easier to put the values in the correct places and solve.

===Difficult===

Okay, let's get a little bit trickier here...

There is a 400 kg train traveling at 55 m/s that collides, elastically of course, with a random 2 kg trashcan that's stationary on the tracks. So afterwards, what are the speeds of both the train and the trashcan after the collision?

[[File:Problem3.0.png|400px]]

This was a difficult problem because of the assumptions we had to make in order to solve it. Because the collision was elastic we were able to disregard the change in internal energy in the energy principle, and since it happened so quickly the work done by the track and heat transfer between the surroundings was negligible. It is tough to tell what assumptions you can make and which ones you can't in problems like these, which is what can make them difficult. On most exams or quizzes the collision problems will be inelastic simply because they are harder, but it is important to understand the fundementals of elastic collisions and how to solve problems involving them.

===Real World Example===

(Edit by Lakshmi Krishnan (lkrishnan7))

Now, let's look at a real world example of elastic collisions: car crashes.

'''Scenario''': A woman is lying on the side of the road, appears to have been hit by a car.

'''Witness Statement''': Witness says that there was a lady walking across the road and at the middle of the road, she paused for a second because she saw a car coming at her. The car was unable to stop in time, and hit the lady at a speed of 25 miles per hour, or around 10 metres per second. The witness also notes the layer of ice on the road.

'''Report''': This is an example of the Law of Conservation of Momentum, which states that in the absence of an external force, there is conserved quantity of momentum, or
P initial = P final (where P = momentum)
MOMENTUM = M X V
M1V1 + M2V2= M1U1 + M2U2 (M = mass , V1 and V2 = initial velocity of object 1 and 2, U1 and U2 = velocities after collision
Essentially, the momentum that was lost by the car, is equal to the momentum gained by the lady.
The lady would’ve had no velocity when the car hit her, and according to the law of conservation of momentum - whatever momentum you have at the start, you have at the end. This means that there would’ve been a redistribution of momentum between car and lady. The car will give some momentum to the lady... however, the car can’t give mass, so the only thing it can her give is velocity.

If we investigate further, we can see that this system was an isolated system. Normally, in collisions like these, we are not dealing with isolated systems... because that would mean that force is free from the influence of a net external force, or a force that can alter the momentum. Most of the time, friction between the car and the road, being an external force, would contribute to a change in total momentum. However, after observing the road, we can say that conditions were such that any external force (ie. friction and air resistance) was negligible, and thus, the total momentum of the two particles are conserved.

What we see here is a case of elastic collision - which means that there was no loss of kinetic energy. In an elastic collision, the objects “bounce” off each other, and don’t stick together to become one body - because this would be an inelastic collision, where part of the kinetic energy is changed to some other form of energy in the collision. But, as said before, this was an elastic collision, it would’ve looked something like this:

[[File:elastic.jpg]]

It was noted that the car weighed 1600 kgs, while the woman weighs 50 kgs.
The speed of the car was 10 metres/second, while the women's speed was 0 m/s (she stood still)
We can figure out the velocities of both the woman and and the cars after the collision by deriving the formula

[[File:derivation.jpg]]

Velocities after the collision

V1 =[ M1 - M2 / (M1+ M2) ] V
V2 = [ 2M1/ M1 + M2 ] V

*Conclusion: If we make a table, we can see the distribution of momentum.
Because of the fact that the mass of the second object (Lady) is much smaller compared to the mass of the first object (car), the person is thrown back at a relatively high velocity.

[[File:wikitable.png]]

Some of the velocity of the bus was given to the lady, which caused her to go flying and land on the other side of the road. This is common of road traffic accident and this redistribution of momentum, in the form of velocity, is where part of her injury comes from.

==Connectedness==

So how are collisions connected to the real world? Collisions are all around us!

One main example is cars! Lots of car companies will purposely test and wreck cars to test collisions! Data is then sent to places like the Insurance Institute for Highway Safety where we can learn about car agility and more.

[[File:crash-test.jpg]]

Another example of collisions in real life is billiards. This is one of the most accurate real life examples of elastic collisions. One ball hits another ball at rest, and if done right the first ball stops and transfers nearly all its kinetic energy into kinetic energy in the second ball.

[[File:Pool1.0.jpg]]

Another example is hitting a baseball. Hitting a ball off the end or to close the hands of a bat will cause some vibrational energy from the collision, but if the ball catches the sweet spot the collision is very elastic, and you don't feel any vibration when you strike the ball.

[[File:Hittingabaseball.jpg|500px]]

==History==

Collisions are certainly not a knew concept in the world. Ever since the beginning or time things have been colliding and reacting in different ways. It was experiments done by scientists like Newton or Rutherford that started to characterize collisions into categories and apply fundamental principles of physics to the reactions.

The history of collisions originates from the Rutherford Scattering experiment. As Rutherford studied the scattering of alpha particles through metal foils, he first noticed a collision with a single massive positive particle. This lead to the conclusion that the positive charge of the mass was concentrated in the center, the atomic nucleus!

[[File:gold-foil-experiment.jpg]]

== See also ==

http://physicsbook.gatech.edu/Collisions for a general understanding of all collisions.

http://physicsbook.gatech.edu/inelastic_collisions to contrast them from elastic collisions.

===Further reading===

http://www.britannica.com/science/elastic-collision

===External links===

[http://www.physicsclassroom.com/mmedia/momentum/trece.cfm]

[http://hyperphysics.phy-astr.gsu.edu/hbase/elacol2.html]

[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/linear-momentum-and-collisions-7/collisions-70/elastic-collisions-in-one-dimension-298-6220/]

==References==

Main Idea:

''Matter and Interactions, 4th Edition''

http://www.sparknotes.com/testprep/books/sat2/physics/chapter9section4.rhtml

http://blogs.bu.edu/ggarber/archive/bua-physics/collisions-and-conservation-of-momentum/

History:

https://en.wikipedia.org/wiki/Elastic_collision

Connectedness:

http://www.iihs.org/

Additionally used references from ''see also''.

File:Derivation.jpg

2017-04-08T20:55:04Z

Lkrishnan7:

Elastic Collisions

2017-04-08T20:54:29Z

Lkrishnan7: /* Real World Example */

'''CLAIMED BY SEAN FISCHER'''
==The Main Idea==

So what exactly is an elastic collision? I know you’re thinking, “Oh I know all about elasticity,” but LOL this is not bubble gum or rubber bands guys!

An elastic collision is a collision between two or more objects in which there is no loss in kinetic energy before and after the collision. If we assume that the colliding objects are part of the system and that there is no force from the surroundings, the final kinetic energy is still in the same form as it was initially. To keep it simple, this means that kinetic energy in= kinetic energy out. Remember how your parents always told you what goes in must come out? They were talking about elastic collisions... probably.

Additionally, elastic collisions are a wonderful representation of the conservation of momentum which states that the momentum of an isolated system is constant. For an isolated system undergoing an elastic collision momentum in = momentum out.

And I love playing pool because every time a ball hits another and they bounce off one another I’m witnessing an elastic collision so basically I’m a physicist in the lab. The image below demonstrates the main idea of an elastic collision. Boing!!

It's important to note that with macroscopic systems there are no perfectly elastic collisions because there's always at least a dab of dissipation (like some thermal energy given off), but most are nearly elastic. The only time there are perfect collisions is on a microscopic level when atomic systems with quantized energy collide, but that's only if there is enough energy available to raise the systems to an excited quantum state-- but quantum energy is really a whole other topic. Let's focus on elastic collisions!

[[File: boing.gif]]

[[File:Elastischer_stoß2.gif]]

Check out this funny video on elastic collisions also! https://www.youtube.com/watch?v=W9EqU1_DXUw

Now check out this more informative video on elastic collisions: https://www.youtube.com/watch?v=V4vzNk4qppw

===A Mathematical Model===

Now lets take what we know about elastic collisions and talk about it in mathematical terms. There are three main mathematical concepts surrounding elastic collisions:
[[File: CodeCogsEqn.gif]]
----

[[File: CodeCogsEqn copy.gif]]
----

[[File: CodeCogsEqn_copy_2.gif]]

Example Problem

Cart 1, moving in the positive x direction, collides with cart 2 moving in the negative x direction. Both carts have identical masses and the collisions is (nearly) elastic, as it would be if the carts interacted magnetically or repelled each other through soft springs. What are the final momenta of the two carts?

[[File:Example1good.jpg|350px|thumb|right]]

1. After choosing a correct system, surroundings, and initial and final states, we can apply the momentum principle mentioned above to get a relationship
between the initial and final momentums of the two carts.

2. Next, by applying the energy principle we can gain knowledge about the final and initial kinetic energies. By acknowledging the fact that the change in internal energy is 0 and the fact the reaction happens so quickly that not work or heat transfer is done by the surroundings, the equation can be simplified to include just initial and final kinetic energies.

3. Once we have simplified the momentum and energy principles, one can use the relationship between kinetic energy and momentum mentioned above to get a relationship involving both energy and momentum. Once this is obtained, the equation can be shifted around to get both the final momentums.

===A Computational Model===

The link below demonstrates a basic car crash elastic collision using MATLAB. Take note of the changes in displacement and the time.

[https://www.youtube.com/watch?v=AfCfCS6O2VM Elastic Collision MATLAB model]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible. For a lot of the complicated problems, starting with a diagram and writing down the given information and plugging that into either the momentum or energy principle can help you move forward in the problem. If you still get stuck, try finding similar examples to that problem and look at the solutions to get on the right track.

===Simple===

Okay let’s start with a simple example like the ones you don't see on the test.

Jay and Sarah are best friends. Since they’re best friends they both weigh 55 kg. Jay hadn’t seen Sarah in a long time so when she saw her she ran to her with a velocity of <4,0,0> m/s. Instead of a hug, they were both too excited and collided and bounced back off of each other, and Sarah flew back with a velocity of <7,0,0> m/s. What was Jay’s final velocity?

[[File:Problem1.0.png|300px|Problem 1]]

In a lot of simple elastic collision problems, the momentum principle is all you need to solve them. Most problems will the initial velocities, masses, and one final velocity and you will be asked to solve for a either a final velocity or final momentum. By setting up an equation like the one in this problem, one can easily handle this type of problem.

===Middling===

When far apart, the momentum of a proton is <5.2 ✕ 10−21, 0, 0> kg · m/s as it approaches another proton that is initially at rest. The two protons repel each other electrically, but they are not close enough to touch. When they are far apart again later, one of the protons now has a velocity of <1.75, .82, 0> m/s. At that instant, what is the momentum of the other proton? HINT: Mass of proton is 1.7 *10^-21 kg.

[[File:Problem2.0.png|300px]]

A lot of people freak out when they see problems involving atomic particles and electrical forces, but the concept is the same no matter the scale. For this problem we are given masses, velocities, and momentum, but the equation p = mv allows us to easily handle these different values. Once again drawing a diagram helps to understand what is actually happening in the problem, making it easier to put the values in the correct places and solve.

===Difficult===

Okay, let's get a little bit trickier here...

There is a 400 kg train traveling at 55 m/s that collides, elastically of course, with a random 2 kg trashcan that's stationary on the tracks. So afterwards, what are the speeds of both the train and the trashcan after the collision?

[[File:Problem3.0.png|400px]]

This was a difficult problem because of the assumptions we had to make in order to solve it. Because the collision was elastic we were able to disregard the change in internal energy in the energy principle, and since it happened so quickly the work done by the track and heat transfer between the surroundings was negligible. It is tough to tell what assumptions you can make and which ones you can't in problems like these, which is what can make them difficult. On most exams or quizzes the collision problems will be inelastic simply because they are harder, but it is important to understand the fundementals of elastic collisions and how to solve problems involving them.

===Real World Example===

(Edit by Lakshmi Krishnan (lkrishnan7))

Now, let's look at a real world example of elastic collisions: car crashes.

'''Scenario''': A woman is lying on the side of the road, appears to have been hit by a car.

'''Witness Statement''': Witness says that there was a lady walking across the road and at the middle of the road, she paused for a second because she saw a car coming at her. The car was unable to stop in time, and hit the lady at a speed of 25 miles per hour, or around 10 metres per second. The witness also notes the layer of ice on the road.

'''Report''': This is an example of the Law of Conservation of Momentum, which states that in the absence of an external force, there is conserved quantity of momentum, or
P initial = P final (where P = momentum)
MOMENTUM = M X V
M1V1 + M2V2= M1U1 + M2U2 (M = mass , V1 and V2 = initial velocity of object 1 and 2, U1 and U2 = velocities after collision
Essentially, the momentum that was lost by the car, is equal to the momentum gained by the lady.
The lady would’ve had no velocity when the car hit her, and according to the law of conservation of momentum - whatever momentum you have at the start, you have at the end. This means that there would’ve been a redistribution of momentum between car and lady. The car will give some momentum to the lady... however, the car can’t give mass, so the only thing it can her give is velocity.

If we investigate further, we can see that this system was an isolated system. Normally, in collisions like these, we are not dealing with isolated systems... because that would mean that force is free from the influence of a net external force, or a force that can alter the momentum. Most of the time, friction between the car and the road, being an external force, would contribute to a change in total momentum. However, after observing the road, we can say that conditions were such that any external force (ie. friction and air resistance) was negligible, and thus, the total momentum of the two particles are conserved.

What we see here is a case of elastic collision - which means that there was no loss of kinetic energy. In an elastic collision, the objects “bounce” off each other, and don’t stick together to become one body - because this would be an inelastic collision, where part of the kinetic energy is changed to some other form of energy in the collision. But, as said before, this was an elastic collision, it would’ve looked something like this:

[[File:elastic.jpg]]

It was noted that the car weighed 1600 kgs, while the woman weighs 50 kgs.
The speed of the car was 10 metres/second, while the women's speed was 0 m/s (she stood still)
We can figure out the velocities of both the woman and and the cars after the collision by deriving the formula

[[File:IMG_5564.jpg]]

Velocities after the collision

V1 =[ M1 - M2 / (M1+ M2) ] V
V2 = [ 2M1/ M1 + M2 ] V

*Conclusion: If we make a table, we can see the distribution of momentum.
Because of the fact that the mass of the second object (Lady) is much smaller compared to the mass of the first object (car), the person is thrown back at a relatively high velocity.

[[File:wikitable.png]]

Some of the velocity of the bus was given to the lady, which caused her to go flying and land on the other side of the road. This is common of road traffic accident and this redistribution of momentum, in the form of velocity, is where part of her injury comes from.

==Connectedness==

So how are collisions connected to the real world? Collisions are all around us!

One main example is cars! Lots of car companies will purposely test and wreck cars to test collisions! Data is then sent to places like the Insurance Institute for Highway Safety where we can learn about car agility and more.

[[File:crash-test.jpg]]

Another example of collisions in real life is billiards. This is one of the most accurate real life examples of elastic collisions. One ball hits another ball at rest, and if done right the first ball stops and transfers nearly all its kinetic energy into kinetic energy in the second ball.

[[File:Pool1.0.jpg]]

Another example is hitting a baseball. Hitting a ball off the end or to close the hands of a bat will cause some vibrational energy from the collision, but if the ball catches the sweet spot the collision is very elastic, and you don't feel any vibration when you strike the ball.

[[File:Hittingabaseball.jpg|500px]]

==History==

Collisions are certainly not a knew concept in the world. Ever since the beginning or time things have been colliding and reacting in different ways. It was experiments done by scientists like Newton or Rutherford that started to characterize collisions into categories and apply fundamental principles of physics to the reactions.

The history of collisions originates from the Rutherford Scattering experiment. As Rutherford studied the scattering of alpha particles through metal foils, he first noticed a collision with a single massive positive particle. This lead to the conclusion that the positive charge of the mass was concentrated in the center, the atomic nucleus!

[[File:gold-foil-experiment.jpg]]

== See also ==

http://physicsbook.gatech.edu/Collisions for a general understanding of all collisions.

http://physicsbook.gatech.edu/inelastic_collisions to contrast them from elastic collisions.

===Further reading===

http://www.britannica.com/science/elastic-collision

===External links===

[http://www.physicsclassroom.com/mmedia/momentum/trece.cfm]

[http://hyperphysics.phy-astr.gsu.edu/hbase/elacol2.html]

[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/linear-momentum-and-collisions-7/collisions-70/elastic-collisions-in-one-dimension-298-6220/]

==References==

Main Idea:

''Matter and Interactions, 4th Edition''

http://www.sparknotes.com/testprep/books/sat2/physics/chapter9section4.rhtml

http://blogs.bu.edu/ggarber/archive/bua-physics/collisions-and-conservation-of-momentum/

History:

https://en.wikipedia.org/wiki/Elastic_collision

Connectedness:

http://www.iihs.org/

Additionally used references from ''see also''.

File:Wikitable.png

2017-04-08T20:53:56Z

Lkrishnan7:

Elastic Collisions

2017-04-08T20:50:31Z

Lkrishnan7: /* Real World Example */

'''CLAIMED BY SEAN FISCHER'''
==The Main Idea==

So what exactly is an elastic collision? I know you’re thinking, “Oh I know all about elasticity,” but LOL this is not bubble gum or rubber bands guys!

An elastic collision is a collision between two or more objects in which there is no loss in kinetic energy before and after the collision. If we assume that the colliding objects are part of the system and that there is no force from the surroundings, the final kinetic energy is still in the same form as it was initially. To keep it simple, this means that kinetic energy in= kinetic energy out. Remember how your parents always told you what goes in must come out? They were talking about elastic collisions... probably.

Additionally, elastic collisions are a wonderful representation of the conservation of momentum which states that the momentum of an isolated system is constant. For an isolated system undergoing an elastic collision momentum in = momentum out.

And I love playing pool because every time a ball hits another and they bounce off one another I’m witnessing an elastic collision so basically I’m a physicist in the lab. The image below demonstrates the main idea of an elastic collision. Boing!!

It's important to note that with macroscopic systems there are no perfectly elastic collisions because there's always at least a dab of dissipation (like some thermal energy given off), but most are nearly elastic. The only time there are perfect collisions is on a microscopic level when atomic systems with quantized energy collide, but that's only if there is enough energy available to raise the systems to an excited quantum state-- but quantum energy is really a whole other topic. Let's focus on elastic collisions!

[[File: boing.gif]]

[[File:Elastischer_stoß2.gif]]

Check out this funny video on elastic collisions also! https://www.youtube.com/watch?v=W9EqU1_DXUw

Now check out this more informative video on elastic collisions: https://www.youtube.com/watch?v=V4vzNk4qppw

===A Mathematical Model===

Now lets take what we know about elastic collisions and talk about it in mathematical terms. There are three main mathematical concepts surrounding elastic collisions:
[[File: CodeCogsEqn.gif]]
----

[[File: CodeCogsEqn copy.gif]]
----

[[File: CodeCogsEqn_copy_2.gif]]

Example Problem

Cart 1, moving in the positive x direction, collides with cart 2 moving in the negative x direction. Both carts have identical masses and the collisions is (nearly) elastic, as it would be if the carts interacted magnetically or repelled each other through soft springs. What are the final momenta of the two carts?

[[File:Example1good.jpg|350px|thumb|right]]

1. After choosing a correct system, surroundings, and initial and final states, we can apply the momentum principle mentioned above to get a relationship
between the initial and final momentums of the two carts.

2. Next, by applying the energy principle we can gain knowledge about the final and initial kinetic energies. By acknowledging the fact that the change in internal energy is 0 and the fact the reaction happens so quickly that not work or heat transfer is done by the surroundings, the equation can be simplified to include just initial and final kinetic energies.

3. Once we have simplified the momentum and energy principles, one can use the relationship between kinetic energy and momentum mentioned above to get a relationship involving both energy and momentum. Once this is obtained, the equation can be shifted around to get both the final momentums.

===A Computational Model===

The link below demonstrates a basic car crash elastic collision using MATLAB. Take note of the changes in displacement and the time.

[https://www.youtube.com/watch?v=AfCfCS6O2VM Elastic Collision MATLAB model]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible. For a lot of the complicated problems, starting with a diagram and writing down the given information and plugging that into either the momentum or energy principle can help you move forward in the problem. If you still get stuck, try finding similar examples to that problem and look at the solutions to get on the right track.

===Simple===

Okay let’s start with a simple example like the ones you don't see on the test.

Jay and Sarah are best friends. Since they’re best friends they both weigh 55 kg. Jay hadn’t seen Sarah in a long time so when she saw her she ran to her with a velocity of <4,0,0> m/s. Instead of a hug, they were both too excited and collided and bounced back off of each other, and Sarah flew back with a velocity of <7,0,0> m/s. What was Jay’s final velocity?

[[File:Problem1.0.png|300px|Problem 1]]

In a lot of simple elastic collision problems, the momentum principle is all you need to solve them. Most problems will the initial velocities, masses, and one final velocity and you will be asked to solve for a either a final velocity or final momentum. By setting up an equation like the one in this problem, one can easily handle this type of problem.

===Middling===

When far apart, the momentum of a proton is <5.2 ✕ 10−21, 0, 0> kg · m/s as it approaches another proton that is initially at rest. The two protons repel each other electrically, but they are not close enough to touch. When they are far apart again later, one of the protons now has a velocity of <1.75, .82, 0> m/s. At that instant, what is the momentum of the other proton? HINT: Mass of proton is 1.7 *10^-21 kg.

[[File:Problem2.0.png|300px]]

A lot of people freak out when they see problems involving atomic particles and electrical forces, but the concept is the same no matter the scale. For this problem we are given masses, velocities, and momentum, but the equation p = mv allows us to easily handle these different values. Once again drawing a diagram helps to understand what is actually happening in the problem, making it easier to put the values in the correct places and solve.

===Difficult===

Okay, let's get a little bit trickier here...

There is a 400 kg train traveling at 55 m/s that collides, elastically of course, with a random 2 kg trashcan that's stationary on the tracks. So afterwards, what are the speeds of both the train and the trashcan after the collision?

[[File:Problem3.0.png|400px]]

This was a difficult problem because of the assumptions we had to make in order to solve it. Because the collision was elastic we were able to disregard the change in internal energy in the energy principle, and since it happened so quickly the work done by the track and heat transfer between the surroundings was negligible. It is tough to tell what assumptions you can make and which ones you can't in problems like these, which is what can make them difficult. On most exams or quizzes the collision problems will be inelastic simply because they are harder, but it is important to understand the fundementals of elastic collisions and how to solve problems involving them.

===Real World Example===

(Edit by Lakshmi Krishnan (lkrishnan7))

Now, let's look at a real world example of elastic collisions: car crashes.

'''Scenario''': A woman is lying on the side of the road, appears to have been hit by a car.

'''Witness Statement''': Witness says that there was a lady walking across the road and at the middle of the road, she paused for a second because she saw a car coming at her. The car was unable to stop in time, and hit the lady at a speed of 25 miles per hour, or around 10 metres per second. The witness also notes the layer of ice on the road.

'''Report''': This is an example of the Law of Conservation of Momentum, which states that in the absence of an external force, there is conserved quantity of momentum, or
P initial = P final (where P = momentum)
MOMENTUM = M X V
M1V1 + M2V2= M1U1 + M2U2 (M = mass , V1 and V2 = initial velocity of object 1 and 2, U1 and U2 = velocities after collision
Essentially, the momentum that was lost by the car, is equal to the momentum gained by the lady.
The lady would’ve had no velocity when the car hit her, and according to the law of conservation of momentum - whatever momentum you have at the start, you have at the end. This means that there would’ve been a redistribution of momentum between car and lady. The car will give some momentum to the lady... however, the car can’t give mass, so the only thing it can her give is velocity.

If we investigate further, we can see that this system was an isolated system. Normally, in collisions like these, we are not dealing with isolated systems... because that would mean that force is free from the influence of a net external force, or a force that can alter the momentum. Most of the time, friction between the car and the road, being an external force, would contribute to a change in total momentum. However, after observing the road, we can say that conditions were such that any external force (ie. friction and air resistance) was negligible, and thus, the total momentum of the two particles are conserved.

What we see here is a case of elastic collision - which means that there was no loss of kinetic energy. In an elastic collision, the objects “bounce” off each other, and don’t stick together to become one body - because this would be an inelastic collision, where part of the kinetic energy is changed to some other form of energy in the collision. But, as said before, this was an elastic collision, it would’ve looked something like this:

[[File:elastic.jpg]]

It was noted that the car weighed 1600 kgs, while the woman weighs 50 kgs.
The speed of the car was 10 metres/second, while the women's speed was 0 m/s (she stood still)
We can figure out the velocities of both the woman and and the cars after the collision by deriving the formula

[[File:IMG_5564.jpg]]

Velocities after the collision

V1 =[ M1 - M2 / (M1+ M2) ] V
V2 = [ 2M1/ M1 + M2 ] V

*Conclusion: If we make a table, we can see the distribution of momentum.
Because of the fact that the mass of the second object (Lady) is much smaller compared to the mass of the first object (car), the person is thrown back at a relatively high velocity.

[[File:wikitable.jpg]]

Some of the velocity of the bus was given to the lady, which caused her to go flying and land on the other side of the road. This is common of road traffic accident and this redistribution of momentum, in the form of velocity, is where part of her injury comes from.

==Connectedness==

So how are collisions connected to the real world? Collisions are all around us!

One main example is cars! Lots of car companies will purposely test and wreck cars to test collisions! Data is then sent to places like the Insurance Institute for Highway Safety where we can learn about car agility and more.

[[File:crash-test.jpg]]

Another example of collisions in real life is billiards. This is one of the most accurate real life examples of elastic collisions. One ball hits another ball at rest, and if done right the first ball stops and transfers nearly all its kinetic energy into kinetic energy in the second ball.

[[File:Pool1.0.jpg]]

Another example is hitting a baseball. Hitting a ball off the end or to close the hands of a bat will cause some vibrational energy from the collision, but if the ball catches the sweet spot the collision is very elastic, and you don't feel any vibration when you strike the ball.

[[File:Hittingabaseball.jpg|500px]]

==History==

Collisions are certainly not a knew concept in the world. Ever since the beginning or time things have been colliding and reacting in different ways. It was experiments done by scientists like Newton or Rutherford that started to characterize collisions into categories and apply fundamental principles of physics to the reactions.

The history of collisions originates from the Rutherford Scattering experiment. As Rutherford studied the scattering of alpha particles through metal foils, he first noticed a collision with a single massive positive particle. This lead to the conclusion that the positive charge of the mass was concentrated in the center, the atomic nucleus!

[[File:gold-foil-experiment.jpg]]

== See also ==

http://physicsbook.gatech.edu/Collisions for a general understanding of all collisions.

http://physicsbook.gatech.edu/inelastic_collisions to contrast them from elastic collisions.

===Further reading===

http://www.britannica.com/science/elastic-collision

===External links===

[http://www.physicsclassroom.com/mmedia/momentum/trece.cfm]

[http://hyperphysics.phy-astr.gsu.edu/hbase/elacol2.html]

[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/linear-momentum-and-collisions-7/collisions-70/elastic-collisions-in-one-dimension-298-6220/]

==References==

Main Idea:

''Matter and Interactions, 4th Edition''

http://www.sparknotes.com/testprep/books/sat2/physics/chapter9section4.rhtml

http://blogs.bu.edu/ggarber/archive/bua-physics/collisions-and-conservation-of-momentum/

History:

https://en.wikipedia.org/wiki/Elastic_collision

Connectedness:

http://www.iihs.org/

Additionally used references from ''see also''.

Elastic Collisions

2017-04-08T20:49:43Z

Lkrishnan7: /* Real World Example */

'''CLAIMED BY SEAN FISCHER'''
==The Main Idea==

So what exactly is an elastic collision? I know you’re thinking, “Oh I know all about elasticity,” but LOL this is not bubble gum or rubber bands guys!

An elastic collision is a collision between two or more objects in which there is no loss in kinetic energy before and after the collision. If we assume that the colliding objects are part of the system and that there is no force from the surroundings, the final kinetic energy is still in the same form as it was initially. To keep it simple, this means that kinetic energy in= kinetic energy out. Remember how your parents always told you what goes in must come out? They were talking about elastic collisions... probably.

Additionally, elastic collisions are a wonderful representation of the conservation of momentum which states that the momentum of an isolated system is constant. For an isolated system undergoing an elastic collision momentum in = momentum out.

And I love playing pool because every time a ball hits another and they bounce off one another I’m witnessing an elastic collision so basically I’m a physicist in the lab. The image below demonstrates the main idea of an elastic collision. Boing!!

It's important to note that with macroscopic systems there are no perfectly elastic collisions because there's always at least a dab of dissipation (like some thermal energy given off), but most are nearly elastic. The only time there are perfect collisions is on a microscopic level when atomic systems with quantized energy collide, but that's only if there is enough energy available to raise the systems to an excited quantum state-- but quantum energy is really a whole other topic. Let's focus on elastic collisions!

[[File: boing.gif]]

[[File:Elastischer_stoß2.gif]]

Check out this funny video on elastic collisions also! https://www.youtube.com/watch?v=W9EqU1_DXUw

Now check out this more informative video on elastic collisions: https://www.youtube.com/watch?v=V4vzNk4qppw

===A Mathematical Model===

Now lets take what we know about elastic collisions and talk about it in mathematical terms. There are three main mathematical concepts surrounding elastic collisions:
[[File: CodeCogsEqn.gif]]
----

[[File: CodeCogsEqn copy.gif]]
----

[[File: CodeCogsEqn_copy_2.gif]]

Example Problem

Cart 1, moving in the positive x direction, collides with cart 2 moving in the negative x direction. Both carts have identical masses and the collisions is (nearly) elastic, as it would be if the carts interacted magnetically or repelled each other through soft springs. What are the final momenta of the two carts?

[[File:Example1good.jpg|350px|thumb|right]]

1. After choosing a correct system, surroundings, and initial and final states, we can apply the momentum principle mentioned above to get a relationship
between the initial and final momentums of the two carts.

2. Next, by applying the energy principle we can gain knowledge about the final and initial kinetic energies. By acknowledging the fact that the change in internal energy is 0 and the fact the reaction happens so quickly that not work or heat transfer is done by the surroundings, the equation can be simplified to include just initial and final kinetic energies.

3. Once we have simplified the momentum and energy principles, one can use the relationship between kinetic energy and momentum mentioned above to get a relationship involving both energy and momentum. Once this is obtained, the equation can be shifted around to get both the final momentums.

===A Computational Model===

The link below demonstrates a basic car crash elastic collision using MATLAB. Take note of the changes in displacement and the time.

[https://www.youtube.com/watch?v=AfCfCS6O2VM Elastic Collision MATLAB model]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible. For a lot of the complicated problems, starting with a diagram and writing down the given information and plugging that into either the momentum or energy principle can help you move forward in the problem. If you still get stuck, try finding similar examples to that problem and look at the solutions to get on the right track.

===Simple===

Okay let’s start with a simple example like the ones you don't see on the test.

Jay and Sarah are best friends. Since they’re best friends they both weigh 55 kg. Jay hadn’t seen Sarah in a long time so when she saw her she ran to her with a velocity of <4,0,0> m/s. Instead of a hug, they were both too excited and collided and bounced back off of each other, and Sarah flew back with a velocity of <7,0,0> m/s. What was Jay’s final velocity?

[[File:Problem1.0.png|300px|Problem 1]]

In a lot of simple elastic collision problems, the momentum principle is all you need to solve them. Most problems will the initial velocities, masses, and one final velocity and you will be asked to solve for a either a final velocity or final momentum. By setting up an equation like the one in this problem, one can easily handle this type of problem.

===Middling===

When far apart, the momentum of a proton is <5.2 ✕ 10−21, 0, 0> kg · m/s as it approaches another proton that is initially at rest. The two protons repel each other electrically, but they are not close enough to touch. When they are far apart again later, one of the protons now has a velocity of <1.75, .82, 0> m/s. At that instant, what is the momentum of the other proton? HINT: Mass of proton is 1.7 *10^-21 kg.

[[File:Problem2.0.png|300px]]

A lot of people freak out when they see problems involving atomic particles and electrical forces, but the concept is the same no matter the scale. For this problem we are given masses, velocities, and momentum, but the equation p = mv allows us to easily handle these different values. Once again drawing a diagram helps to understand what is actually happening in the problem, making it easier to put the values in the correct places and solve.

===Difficult===

Okay, let's get a little bit trickier here...

There is a 400 kg train traveling at 55 m/s that collides, elastically of course, with a random 2 kg trashcan that's stationary on the tracks. So afterwards, what are the speeds of both the train and the trashcan after the collision?

[[File:Problem3.0.png|400px]]

This was a difficult problem because of the assumptions we had to make in order to solve it. Because the collision was elastic we were able to disregard the change in internal energy in the energy principle, and since it happened so quickly the work done by the track and heat transfer between the surroundings was negligible. It is tough to tell what assumptions you can make and which ones you can't in problems like these, which is what can make them difficult. On most exams or quizzes the collision problems will be inelastic simply because they are harder, but it is important to understand the fundementals of elastic collisions and how to solve problems involving them.

===Real World Example===

(Edit by Lakshmi Krishnan (lkrishnan7))

Now, let's look at a real world example of elastic collisions: car crashes.

'''Scenario''': A woman is lying on the side of the road, appears to have been hit by a car.

'''Witness Statement''': Witness says that there was a lady walking across the road and at the middle of the road, she paused for a second because she saw a car coming at her. The car was unable to stop in time, and hit the lady at a speed of 25 miles per hour, or around 10 metres per second. The witness also notes the layer of ice on the road.

'''Report''': This is an example of the Law of Conservation of Momentum, which states that in the absence of an external force, there is conserved quantity of momentum, or
P initial = P final (where P = momentum)
MOMENTUM = M X V
M1V1 + M2V2= M1U1 + M2U2 (M = mass , V1 and V2 = initial velocity of object 1 and 2, U1 and U2 = velocities after collision
Essentially, the momentum that was lost by the car, is equal to the momentum gained by the lady.
The lady would’ve had no velocity when the car hit her, and according to the law of conservation of momentum - whatever momentum you have at the start, you have at the end. This means that there would’ve been a redistribution of momentum between car and lady. The car will give some momentum to the lady... however, the car can’t give mass, so the only thing it can her give is velocity.

If we investigate further, we can see that this system was an isolated system. Normally, in collisions like these, we are not dealing with isolated systems... because that would mean that force is free from the influence of a net external force, or a force that can alter the momentum. Most of the time, friction between the car and the road, being an external force, would contribute to a change in total momentum. However, after observing the road, we can say that conditions were such that any external force (ie. friction and air resistance) was negligible, and thus, the total momentum of the two particles are conserved.

What we see here is a case of elastic collision - which means that there was no loss of kinetic energy. In an elastic collision, the objects “bounce” off each other, and don’t stick together to become one body - because this would be an inelastic collision, where part of the kinetic energy is changed to some other form of energy in the collision. But, as said before, this was an elastic collision, it would’ve looked something like this:

[[File:collision1.jpg]]

It was noted that the car weighed 1600 kgs, while the woman weighs 50 kgs.
The speed of the car was 10 metres/second, while the women's speed was 0 m/s (she stood still)
We can figure out the velocities of both the woman and and the cars after the collision by deriving the formula

[[File:IMG_5564.jpg]]

Velocities after the collision

V1 =[ M1 - M2 / (M1+ M2) ] V
V2 = [ 2M1/ M1 + M2 ] V

*Conclusion: If we make a table, we can see the distribution of momentum.
Because of the fact that the mass of the second object (Lady) is much smaller compared to the mass of the first object (car), the person is thrown back at a relatively high velocity.

[[File:wikitable.jpg]]

Some of the velocity of the bus was given to the lady, which caused her to go flying and land on the other side of the road. This is common of road traffic accident and this redistribution of momentum, in the form of velocity, is where part of her injury comes from.

==Connectedness==

So how are collisions connected to the real world? Collisions are all around us!

One main example is cars! Lots of car companies will purposely test and wreck cars to test collisions! Data is then sent to places like the Insurance Institute for Highway Safety where we can learn about car agility and more.

[[File:crash-test.jpg]]

Another example of collisions in real life is billiards. This is one of the most accurate real life examples of elastic collisions. One ball hits another ball at rest, and if done right the first ball stops and transfers nearly all its kinetic energy into kinetic energy in the second ball.

[[File:Pool1.0.jpg]]

Another example is hitting a baseball. Hitting a ball off the end or to close the hands of a bat will cause some vibrational energy from the collision, but if the ball catches the sweet spot the collision is very elastic, and you don't feel any vibration when you strike the ball.

[[File:Hittingabaseball.jpg|500px]]

==History==

Collisions are certainly not a knew concept in the world. Ever since the beginning or time things have been colliding and reacting in different ways. It was experiments done by scientists like Newton or Rutherford that started to characterize collisions into categories and apply fundamental principles of physics to the reactions.

The history of collisions originates from the Rutherford Scattering experiment. As Rutherford studied the scattering of alpha particles through metal foils, he first noticed a collision with a single massive positive particle. This lead to the conclusion that the positive charge of the mass was concentrated in the center, the atomic nucleus!

[[File:gold-foil-experiment.jpg]]

== See also ==

http://physicsbook.gatech.edu/Collisions for a general understanding of all collisions.

http://physicsbook.gatech.edu/inelastic_collisions to contrast them from elastic collisions.

===Further reading===

http://www.britannica.com/science/elastic-collision

===External links===

[http://www.physicsclassroom.com/mmedia/momentum/trece.cfm]

[http://hyperphysics.phy-astr.gsu.edu/hbase/elacol2.html]

[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/linear-momentum-and-collisions-7/collisions-70/elastic-collisions-in-one-dimension-298-6220/]

==References==

Main Idea:

''Matter and Interactions, 4th Edition''

http://www.sparknotes.com/testprep/books/sat2/physics/chapter9section4.rhtml

http://blogs.bu.edu/ggarber/archive/bua-physics/collisions-and-conservation-of-momentum/

History:

https://en.wikipedia.org/wiki/Elastic_collision

Connectedness:

http://www.iihs.org/

Additionally used references from ''see also''.

File:Collision1.JPG

2017-04-08T20:49:29Z

Lkrishnan7:

Elastic Collisions

2017-04-08T20:44:55Z

Lkrishnan7: /* Real World Example */

'''CLAIMED BY SEAN FISCHER'''
==The Main Idea==

So what exactly is an elastic collision? I know you’re thinking, “Oh I know all about elasticity,” but LOL this is not bubble gum or rubber bands guys!

An elastic collision is a collision between two or more objects in which there is no loss in kinetic energy before and after the collision. If we assume that the colliding objects are part of the system and that there is no force from the surroundings, the final kinetic energy is still in the same form as it was initially. To keep it simple, this means that kinetic energy in= kinetic energy out. Remember how your parents always told you what goes in must come out? They were talking about elastic collisions... probably.

Additionally, elastic collisions are a wonderful representation of the conservation of momentum which states that the momentum of an isolated system is constant. For an isolated system undergoing an elastic collision momentum in = momentum out.

And I love playing pool because every time a ball hits another and they bounce off one another I’m witnessing an elastic collision so basically I’m a physicist in the lab. The image below demonstrates the main idea of an elastic collision. Boing!!

It's important to note that with macroscopic systems there are no perfectly elastic collisions because there's always at least a dab of dissipation (like some thermal energy given off), but most are nearly elastic. The only time there are perfect collisions is on a microscopic level when atomic systems with quantized energy collide, but that's only if there is enough energy available to raise the systems to an excited quantum state-- but quantum energy is really a whole other topic. Let's focus on elastic collisions!

[[File: boing.gif]]

[[File:Elastischer_stoß2.gif]]

Check out this funny video on elastic collisions also! https://www.youtube.com/watch?v=W9EqU1_DXUw

Now check out this more informative video on elastic collisions: https://www.youtube.com/watch?v=V4vzNk4qppw

===A Mathematical Model===

Now lets take what we know about elastic collisions and talk about it in mathematical terms. There are three main mathematical concepts surrounding elastic collisions:
[[File: CodeCogsEqn.gif]]
----

[[File: CodeCogsEqn copy.gif]]
----

[[File: CodeCogsEqn_copy_2.gif]]

Example Problem

Cart 1, moving in the positive x direction, collides with cart 2 moving in the negative x direction. Both carts have identical masses and the collisions is (nearly) elastic, as it would be if the carts interacted magnetically or repelled each other through soft springs. What are the final momenta of the two carts?

[[File:Example1good.jpg|350px|thumb|right]]

1. After choosing a correct system, surroundings, and initial and final states, we can apply the momentum principle mentioned above to get a relationship
between the initial and final momentums of the two carts.

2. Next, by applying the energy principle we can gain knowledge about the final and initial kinetic energies. By acknowledging the fact that the change in internal energy is 0 and the fact the reaction happens so quickly that not work or heat transfer is done by the surroundings, the equation can be simplified to include just initial and final kinetic energies.

3. Once we have simplified the momentum and energy principles, one can use the relationship between kinetic energy and momentum mentioned above to get a relationship involving both energy and momentum. Once this is obtained, the equation can be shifted around to get both the final momentums.

===A Computational Model===

The link below demonstrates a basic car crash elastic collision using MATLAB. Take note of the changes in displacement and the time.

[https://www.youtube.com/watch?v=AfCfCS6O2VM Elastic Collision MATLAB model]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible. For a lot of the complicated problems, starting with a diagram and writing down the given information and plugging that into either the momentum or energy principle can help you move forward in the problem. If you still get stuck, try finding similar examples to that problem and look at the solutions to get on the right track.

===Simple===

Okay let’s start with a simple example like the ones you don't see on the test.

Jay and Sarah are best friends. Since they’re best friends they both weigh 55 kg. Jay hadn’t seen Sarah in a long time so when she saw her she ran to her with a velocity of <4,0,0> m/s. Instead of a hug, they were both too excited and collided and bounced back off of each other, and Sarah flew back with a velocity of <7,0,0> m/s. What was Jay’s final velocity?

[[File:Problem1.0.png|300px|Problem 1]]

In a lot of simple elastic collision problems, the momentum principle is all you need to solve them. Most problems will the initial velocities, masses, and one final velocity and you will be asked to solve for a either a final velocity or final momentum. By setting up an equation like the one in this problem, one can easily handle this type of problem.

===Middling===

When far apart, the momentum of a proton is <5.2 ✕ 10−21, 0, 0> kg · m/s as it approaches another proton that is initially at rest. The two protons repel each other electrically, but they are not close enough to touch. When they are far apart again later, one of the protons now has a velocity of <1.75, .82, 0> m/s. At that instant, what is the momentum of the other proton? HINT: Mass of proton is 1.7 *10^-21 kg.

[[File:Problem2.0.png|300px]]

A lot of people freak out when they see problems involving atomic particles and electrical forces, but the concept is the same no matter the scale. For this problem we are given masses, velocities, and momentum, but the equation p = mv allows us to easily handle these different values. Once again drawing a diagram helps to understand what is actually happening in the problem, making it easier to put the values in the correct places and solve.

===Difficult===

Okay, let's get a little bit trickier here...

There is a 400 kg train traveling at 55 m/s that collides, elastically of course, with a random 2 kg trashcan that's stationary on the tracks. So afterwards, what are the speeds of both the train and the trashcan after the collision?

[[File:Problem3.0.png|400px]]

This was a difficult problem because of the assumptions we had to make in order to solve it. Because the collision was elastic we were able to disregard the change in internal energy in the energy principle, and since it happened so quickly the work done by the track and heat transfer between the surroundings was negligible. It is tough to tell what assumptions you can make and which ones you can't in problems like these, which is what can make them difficult. On most exams or quizzes the collision problems will be inelastic simply because they are harder, but it is important to understand the fundementals of elastic collisions and how to solve problems involving them.

===Real World Example===

(Edit by Lakshmi Krishnan (lkrishnan7))

Now, let's look at a real world example of elastic collisions: car crashes.

'''Scenario''': A woman is lying on the side of the road, appears to have been hit by a car.

'''Witness Statement''': Witness says that there was a lady walking across the road and at the middle of the road, she paused for a second because she saw a car coming at her. The car was unable to stop in time, and hit the lady at a speed of 25 miles per hour, or around 10 metres per second. The witness also notes the layer of ice on the road.

'''Report''': This is an example of the Law of Conservation of Momentum, which states that in the absence of an external force, there is conserved quantity of momentum, or
P initial = P final (where P = momentum)
MOMENTUM = M X V
M1V1 + M2V2= M1U1 + M2U2 (M = mass , V1 and V2 = initial velocity of object 1 and 2, U1 and U2 = velocities after collision
Essentially, the momentum that was lost by the car, is equal to the momentum gained by the lady.
The lady would’ve had no velocity when the car hit her, and according to the law of conservation of momentum - whatever momentum you have at the start, you have at the end. This means that there would’ve been a redistribution of momentum between car and lady. The car will give some momentum to the lady... however, the car can’t give mass, so the only thing it can her give is velocity.

If we investigate further, we can see that this system was an isolated system. Normally, in collisions like these, we are not dealing with isolated systems... because that would mean that force is free from the influence of a net external force, or a force that can alter the momentum. Most of the time, friction between the car and the road, being an external force, would contribute to a change in total momentum. However, after observing the road, we can say that conditions were such that any external force (ie. friction and air resistance) was negligible, and thus, the total momentum of the two particles are conserved.

What we see here is a case of elastic collision - which means that there was no loss of kinetic energy. In an elastic collision, the objects “bounce” off each other, and don’t stick together to become one body - because this would be an inelastic collision, where part of the kinetic energy is changed to some other form of energy in the collision. But, as said before, this was an elastic collision, it would’ve looked something like this:

[[File:IMG_5563.jpg]]

It was noted that the car weighed 1600 kgs, while the woman weighs 50 kgs.
The speed of the car was 10 metres/second, while the women's speed was 0 m/s (she stood still)
We can figure out the velocities of both the woman and and the cars after the collision by deriving the formula

[[File:IMG_5564.jpg]]

Velocities after the collision

V1 =[ M1 - M2 / (M1+ M2) ] V
V2 = [ 2M1/ M1 + M2 ] V

*Conclusion: If we make a table, we can see the distribution of momentum.
Because of the fact that the mass of the second object (Lady) is much smaller compared to the mass of the first object (car), the person is thrown back at a relatively high velocity.

[[File:wikitable.jpg]]

Some of the velocity of the bus was given to the lady, which caused her to go flying and land on the other side of the road. This is common of road traffic accident and this redistribution of momentum, in the form of velocity, is where part of her injury comes from.

==Connectedness==

So how are collisions connected to the real world? Collisions are all around us!

One main example is cars! Lots of car companies will purposely test and wreck cars to test collisions! Data is then sent to places like the Insurance Institute for Highway Safety where we can learn about car agility and more.

[[File:crash-test.jpg]]

Another example of collisions in real life is billiards. This is one of the most accurate real life examples of elastic collisions. One ball hits another ball at rest, and if done right the first ball stops and transfers nearly all its kinetic energy into kinetic energy in the second ball.

[[File:Pool1.0.jpg]]

Another example is hitting a baseball. Hitting a ball off the end or to close the hands of a bat will cause some vibrational energy from the collision, but if the ball catches the sweet spot the collision is very elastic, and you don't feel any vibration when you strike the ball.

[[File:Hittingabaseball.jpg|500px]]

==History==

Collisions are certainly not a knew concept in the world. Ever since the beginning or time things have been colliding and reacting in different ways. It was experiments done by scientists like Newton or Rutherford that started to characterize collisions into categories and apply fundamental principles of physics to the reactions.

The history of collisions originates from the Rutherford Scattering experiment. As Rutherford studied the scattering of alpha particles through metal foils, he first noticed a collision with a single massive positive particle. This lead to the conclusion that the positive charge of the mass was concentrated in the center, the atomic nucleus!

[[File:gold-foil-experiment.jpg]]

== See also ==

http://physicsbook.gatech.edu/Collisions for a general understanding of all collisions.

http://physicsbook.gatech.edu/inelastic_collisions to contrast them from elastic collisions.

===Further reading===

http://www.britannica.com/science/elastic-collision

===External links===

[http://www.physicsclassroom.com/mmedia/momentum/trece.cfm]

[http://hyperphysics.phy-astr.gsu.edu/hbase/elacol2.html]

[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/linear-momentum-and-collisions-7/collisions-70/elastic-collisions-in-one-dimension-298-6220/]

==References==

Main Idea:

''Matter and Interactions, 4th Edition''

http://www.sparknotes.com/testprep/books/sat2/physics/chapter9section4.rhtml

http://blogs.bu.edu/ggarber/archive/bua-physics/collisions-and-conservation-of-momentum/

History:

https://en.wikipedia.org/wiki/Elastic_collision

Connectedness:

http://www.iihs.org/

Additionally used references from ''see also''.

Elastic Collisions

2017-04-08T20:44:22Z

Lkrishnan7: /* Real World Example */

'''CLAIMED BY SEAN FISCHER'''
==The Main Idea==

So what exactly is an elastic collision? I know you’re thinking, “Oh I know all about elasticity,” but LOL this is not bubble gum or rubber bands guys!

An elastic collision is a collision between two or more objects in which there is no loss in kinetic energy before and after the collision. If we assume that the colliding objects are part of the system and that there is no force from the surroundings, the final kinetic energy is still in the same form as it was initially. To keep it simple, this means that kinetic energy in= kinetic energy out. Remember how your parents always told you what goes in must come out? They were talking about elastic collisions... probably.

Additionally, elastic collisions are a wonderful representation of the conservation of momentum which states that the momentum of an isolated system is constant. For an isolated system undergoing an elastic collision momentum in = momentum out.

And I love playing pool because every time a ball hits another and they bounce off one another I’m witnessing an elastic collision so basically I’m a physicist in the lab. The image below demonstrates the main idea of an elastic collision. Boing!!

It's important to note that with macroscopic systems there are no perfectly elastic collisions because there's always at least a dab of dissipation (like some thermal energy given off), but most are nearly elastic. The only time there are perfect collisions is on a microscopic level when atomic systems with quantized energy collide, but that's only if there is enough energy available to raise the systems to an excited quantum state-- but quantum energy is really a whole other topic. Let's focus on elastic collisions!

[[File: boing.gif]]

[[File:Elastischer_stoß2.gif]]

Check out this funny video on elastic collisions also! https://www.youtube.com/watch?v=W9EqU1_DXUw

Now check out this more informative video on elastic collisions: https://www.youtube.com/watch?v=V4vzNk4qppw

===A Mathematical Model===

Now lets take what we know about elastic collisions and talk about it in mathematical terms. There are three main mathematical concepts surrounding elastic collisions:
[[File: CodeCogsEqn.gif]]
----

[[File: CodeCogsEqn copy.gif]]
----

[[File: CodeCogsEqn_copy_2.gif]]

Example Problem

Cart 1, moving in the positive x direction, collides with cart 2 moving in the negative x direction. Both carts have identical masses and the collisions is (nearly) elastic, as it would be if the carts interacted magnetically or repelled each other through soft springs. What are the final momenta of the two carts?

[[File:Example1good.jpg|350px|thumb|right]]

1. After choosing a correct system, surroundings, and initial and final states, we can apply the momentum principle mentioned above to get a relationship
between the initial and final momentums of the two carts.

2. Next, by applying the energy principle we can gain knowledge about the final and initial kinetic energies. By acknowledging the fact that the change in internal energy is 0 and the fact the reaction happens so quickly that not work or heat transfer is done by the surroundings, the equation can be simplified to include just initial and final kinetic energies.

3. Once we have simplified the momentum and energy principles, one can use the relationship between kinetic energy and momentum mentioned above to get a relationship involving both energy and momentum. Once this is obtained, the equation can be shifted around to get both the final momentums.

===A Computational Model===

The link below demonstrates a basic car crash elastic collision using MATLAB. Take note of the changes in displacement and the time.

[https://www.youtube.com/watch?v=AfCfCS6O2VM Elastic Collision MATLAB model]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible. For a lot of the complicated problems, starting with a diagram and writing down the given information and plugging that into either the momentum or energy principle can help you move forward in the problem. If you still get stuck, try finding similar examples to that problem and look at the solutions to get on the right track.

===Simple===

Okay let’s start with a simple example like the ones you don't see on the test.

Jay and Sarah are best friends. Since they’re best friends they both weigh 55 kg. Jay hadn’t seen Sarah in a long time so when she saw her she ran to her with a velocity of <4,0,0> m/s. Instead of a hug, they were both too excited and collided and bounced back off of each other, and Sarah flew back with a velocity of <7,0,0> m/s. What was Jay’s final velocity?

[[File:Problem1.0.png|300px|Problem 1]]

In a lot of simple elastic collision problems, the momentum principle is all you need to solve them. Most problems will the initial velocities, masses, and one final velocity and you will be asked to solve for a either a final velocity or final momentum. By setting up an equation like the one in this problem, one can easily handle this type of problem.

===Middling===

When far apart, the momentum of a proton is <5.2 ✕ 10−21, 0, 0> kg · m/s as it approaches another proton that is initially at rest. The two protons repel each other electrically, but they are not close enough to touch. When they are far apart again later, one of the protons now has a velocity of <1.75, .82, 0> m/s. At that instant, what is the momentum of the other proton? HINT: Mass of proton is 1.7 *10^-21 kg.

[[File:Problem2.0.png|300px]]

A lot of people freak out when they see problems involving atomic particles and electrical forces, but the concept is the same no matter the scale. For this problem we are given masses, velocities, and momentum, but the equation p = mv allows us to easily handle these different values. Once again drawing a diagram helps to understand what is actually happening in the problem, making it easier to put the values in the correct places and solve.

===Difficult===

Okay, let's get a little bit trickier here...

There is a 400 kg train traveling at 55 m/s that collides, elastically of course, with a random 2 kg trashcan that's stationary on the tracks. So afterwards, what are the speeds of both the train and the trashcan after the collision?

[[File:Problem3.0.png|400px]]

This was a difficult problem because of the assumptions we had to make in order to solve it. Because the collision was elastic we were able to disregard the change in internal energy in the energy principle, and since it happened so quickly the work done by the track and heat transfer between the surroundings was negligible. It is tough to tell what assumptions you can make and which ones you can't in problems like these, which is what can make them difficult. On most exams or quizzes the collision problems will be inelastic simply because they are harder, but it is important to understand the fundementals of elastic collisions and how to solve problems involving them.

===Real World Example===

(Edit by Lakshmi Krishnan (lkrishnan7))

Now, let's look at a real world example of elastic collisions: car crashes.

'''Scenario''': A woman is lying on the side of the road, appears to have been hit by a car.

'''Witness Statement''': Witness says that there was a lady walking across the road and at the middle of the road, she paused for a second because she saw a car coming at her. The car was unable to stop in time, and hit the lady at a speed of 25 miles per hour, or around 10 metres per second. The witness also notes the layer of ice on the road.

'''Report''': This is an example of the Law of Conservation of Momentum, which states that in the absence of an external force, there is conserved quantity of momentum, or
P initial = P final (where P = momentum)
MOMENTUM = M X V
M1V1 + M2V2= M1U1 + M2U2 (M = mass , V1 and V2 = initial velocity of object 1 and 2, U1 and U2 = velocities after collision
Essentially, the momentum that was lost by the car, is equal to the momentum gained by the lady.
The lady would’ve had no velocity when the car hit her, and according to the law of conservation of momentum - whatever momentum you have at the start, you have at the end. This means that there would’ve been a redistribution of momentum between car and lady. The car will give some momentum to the lady... however, the car can’t give mass, so the only thing it can her give is velocity.

If we investigate further, we can see that this system was an isolated system. Normally, in collisions like these, we are not dealing with isolated systems... because that would mean that force is free from the influence of a net external force, or a force that can alter the momentum. Most of the time, friction between the car and the road, being an external force, would contribute to a change in total momentum. However, after observing the road, we can say that conditions were such that any external force (ie. friction and air resistance) was negligible, and thus, the total momentum of the two particles are conserved.

What we see here is a case of elastic collision - which means that there was no loss of kinetic energy. In an elastic collision, the objects “bounce” off each other, and don’t stick together to become one body - because this would be an inelastic collision, where part of the kinetic energy is changed to some other form of energy in the collision. But, as said before, this was an elastic collision, it would’ve looked something like this:

[[File:IMG_5563.JPG]]

It was noted that the car weighed 1600 kgs, while the woman weighs 50 kgs.
The speed of the car was 10 metres/second, while the women's speed was 0 m/s (she stood still)
We can figure out the velocities of both the woman and and the cars after the collision by deriving the formula

[[File:IMG_5564.JPG]]

Velocities after the collision

V1 =[ M1 - M2 / (M1+ M2) ] V
V2 = [ 2M1/ M1 + M2 ] V

*Conclusion: If we make a table, we can see the distribution of momentum.
Because of the fact that the mass of the second object (Lady) is much smaller compared to the mass of the first object (car), the person is thrown back at a relatively high velocity.

[[File:wikitable.JPG]]

Some of the velocity of the bus was given to the lady, which caused her to go flying and land on the other side of the road. This is common of road traffic accident and this redistribution of momentum, in the form of velocity, is where part of her injury comes from.

==Connectedness==

So how are collisions connected to the real world? Collisions are all around us!

One main example is cars! Lots of car companies will purposely test and wreck cars to test collisions! Data is then sent to places like the Insurance Institute for Highway Safety where we can learn about car agility and more.

[[File:crash-test.jpg]]

Another example of collisions in real life is billiards. This is one of the most accurate real life examples of elastic collisions. One ball hits another ball at rest, and if done right the first ball stops and transfers nearly all its kinetic energy into kinetic energy in the second ball.

[[File:Pool1.0.jpg]]

Another example is hitting a baseball. Hitting a ball off the end or to close the hands of a bat will cause some vibrational energy from the collision, but if the ball catches the sweet spot the collision is very elastic, and you don't feel any vibration when you strike the ball.

[[File:Hittingabaseball.jpg|500px]]

==History==

Collisions are certainly not a knew concept in the world. Ever since the beginning or time things have been colliding and reacting in different ways. It was experiments done by scientists like Newton or Rutherford that started to characterize collisions into categories and apply fundamental principles of physics to the reactions.

The history of collisions originates from the Rutherford Scattering experiment. As Rutherford studied the scattering of alpha particles through metal foils, he first noticed a collision with a single massive positive particle. This lead to the conclusion that the positive charge of the mass was concentrated in the center, the atomic nucleus!

[[File:gold-foil-experiment.jpg]]

== See also ==

http://physicsbook.gatech.edu/Collisions for a general understanding of all collisions.

http://physicsbook.gatech.edu/inelastic_collisions to contrast them from elastic collisions.

===Further reading===

http://www.britannica.com/science/elastic-collision

===External links===

[http://www.physicsclassroom.com/mmedia/momentum/trece.cfm]

[http://hyperphysics.phy-astr.gsu.edu/hbase/elacol2.html]

[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/linear-momentum-and-collisions-7/collisions-70/elastic-collisions-in-one-dimension-298-6220/]

==References==

Main Idea:

''Matter and Interactions, 4th Edition''

http://www.sparknotes.com/testprep/books/sat2/physics/chapter9section4.rhtml

http://blogs.bu.edu/ggarber/archive/bua-physics/collisions-and-conservation-of-momentum/

History:

https://en.wikipedia.org/wiki/Elastic_collision

Connectedness:

http://www.iihs.org/

Additionally used references from ''see also''.

Elastic Collisions

2017-04-08T20:39:38Z

Lkrishnan7: /* Difficult */

'''CLAIMED BY SEAN FISCHER'''
==The Main Idea==

So what exactly is an elastic collision? I know you’re thinking, “Oh I know all about elasticity,” but LOL this is not bubble gum or rubber bands guys!

An elastic collision is a collision between two or more objects in which there is no loss in kinetic energy before and after the collision. If we assume that the colliding objects are part of the system and that there is no force from the surroundings, the final kinetic energy is still in the same form as it was initially. To keep it simple, this means that kinetic energy in= kinetic energy out. Remember how your parents always told you what goes in must come out? They were talking about elastic collisions... probably.

Additionally, elastic collisions are a wonderful representation of the conservation of momentum which states that the momentum of an isolated system is constant. For an isolated system undergoing an elastic collision momentum in = momentum out.

And I love playing pool because every time a ball hits another and they bounce off one another I’m witnessing an elastic collision so basically I’m a physicist in the lab. The image below demonstrates the main idea of an elastic collision. Boing!!

It's important to note that with macroscopic systems there are no perfectly elastic collisions because there's always at least a dab of dissipation (like some thermal energy given off), but most are nearly elastic. The only time there are perfect collisions is on a microscopic level when atomic systems with quantized energy collide, but that's only if there is enough energy available to raise the systems to an excited quantum state-- but quantum energy is really a whole other topic. Let's focus on elastic collisions!

[[File: boing.gif]]

[[File:Elastischer_stoß2.gif]]

Check out this funny video on elastic collisions also! https://www.youtube.com/watch?v=W9EqU1_DXUw

Now check out this more informative video on elastic collisions: https://www.youtube.com/watch?v=V4vzNk4qppw

===A Mathematical Model===

Now lets take what we know about elastic collisions and talk about it in mathematical terms. There are three main mathematical concepts surrounding elastic collisions:
[[File: CodeCogsEqn.gif]]
----

[[File: CodeCogsEqn copy.gif]]
----

[[File: CodeCogsEqn_copy_2.gif]]

Example Problem

Cart 1, moving in the positive x direction, collides with cart 2 moving in the negative x direction. Both carts have identical masses and the collisions is (nearly) elastic, as it would be if the carts interacted magnetically or repelled each other through soft springs. What are the final momenta of the two carts?

[[File:Example1good.jpg|350px|thumb|right]]

1. After choosing a correct system, surroundings, and initial and final states, we can apply the momentum principle mentioned above to get a relationship
between the initial and final momentums of the two carts.

2. Next, by applying the energy principle we can gain knowledge about the final and initial kinetic energies. By acknowledging the fact that the change in internal energy is 0 and the fact the reaction happens so quickly that not work or heat transfer is done by the surroundings, the equation can be simplified to include just initial and final kinetic energies.

3. Once we have simplified the momentum and energy principles, one can use the relationship between kinetic energy and momentum mentioned above to get a relationship involving both energy and momentum. Once this is obtained, the equation can be shifted around to get both the final momentums.

===A Computational Model===

The link below demonstrates a basic car crash elastic collision using MATLAB. Take note of the changes in displacement and the time.

[https://www.youtube.com/watch?v=AfCfCS6O2VM Elastic Collision MATLAB model]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible. For a lot of the complicated problems, starting with a diagram and writing down the given information and plugging that into either the momentum or energy principle can help you move forward in the problem. If you still get stuck, try finding similar examples to that problem and look at the solutions to get on the right track.

===Simple===

Okay let’s start with a simple example like the ones you don't see on the test.

Jay and Sarah are best friends. Since they’re best friends they both weigh 55 kg. Jay hadn’t seen Sarah in a long time so when she saw her she ran to her with a velocity of <4,0,0> m/s. Instead of a hug, they were both too excited and collided and bounced back off of each other, and Sarah flew back with a velocity of <7,0,0> m/s. What was Jay’s final velocity?

[[File:Problem1.0.png|300px|Problem 1]]

In a lot of simple elastic collision problems, the momentum principle is all you need to solve them. Most problems will the initial velocities, masses, and one final velocity and you will be asked to solve for a either a final velocity or final momentum. By setting up an equation like the one in this problem, one can easily handle this type of problem.

===Middling===

When far apart, the momentum of a proton is <5.2 ✕ 10−21, 0, 0> kg · m/s as it approaches another proton that is initially at rest. The two protons repel each other electrically, but they are not close enough to touch. When they are far apart again later, one of the protons now has a velocity of <1.75, .82, 0> m/s. At that instant, what is the momentum of the other proton? HINT: Mass of proton is 1.7 *10^-21 kg.

[[File:Problem2.0.png|300px]]

A lot of people freak out when they see problems involving atomic particles and electrical forces, but the concept is the same no matter the scale. For this problem we are given masses, velocities, and momentum, but the equation p = mv allows us to easily handle these different values. Once again drawing a diagram helps to understand what is actually happening in the problem, making it easier to put the values in the correct places and solve.

===Difficult===

Okay, let's get a little bit trickier here...

There is a 400 kg train traveling at 55 m/s that collides, elastically of course, with a random 2 kg trashcan that's stationary on the tracks. So afterwards, what are the speeds of both the train and the trashcan after the collision?

[[File:Problem3.0.png|400px]]

This was a difficult problem because of the assumptions we had to make in order to solve it. Because the collision was elastic we were able to disregard the change in internal energy in the energy principle, and since it happened so quickly the work done by the track and heat transfer between the surroundings was negligible. It is tough to tell what assumptions you can make and which ones you can't in problems like these, which is what can make them difficult. On most exams or quizzes the collision problems will be inelastic simply because they are harder, but it is important to understand the fundementals of elastic collisions and how to solve problems involving them.

===Real World Example===

(Edit by Lakshmi Krishnan (lkrishnan7))

Now, let's look at a real world example of elastic collisions: car crashes.

'''Scenario''': A woman is lying on the side of the road, appears to have been hit by a car.

'''Witness Statement''': Witness says that there was a lady walking across the road and at the middle of the road, she paused for a second because she saw a car coming at her. The car was unable to stop in time, and hit the lady at a speed of 25 miles per hour, or around 10 metres per second. The witness also notes the layer of ice on the road.

'''Report''': This is an example of the Law of Conservation of Momentum, which states that in the absence of an external force, there is conserved quantity of momentum, or
P initial = P final (where P = momentum)
MOMENTUM = M X V
M1V1 + M2V2= M1U1 + M2U2 (M = mass , V1 and V2 = initial velocity of object 1 and 2, U1 and U2 = velocities after collision
Essentially, the momentum that was lost by the car, is equal to the momentum gained by the lady.
The lady would’ve had no velocity when the car hit her, and according to the law of conservation of momentum - whatever momentum you have at the start, you have at the end. This means that there would’ve been a redistribution of momentum between car and lady. The car will give some momentum to the lady... however, the car can’t give mass, so the only thing it can her give is velocity.

If we investigate further, we can see that this system was an isolated system. Normally, in collisions like these, we are not dealing with isolated systems... because that would mean that force is free from the influence of a net external force, or a force that can alter the momentum. Most of the time, friction between the car and the road, being an external force, would contribute to a change in total momentum. However, after observing the road, we can say that conditions were such that any external force (ie. friction and air resistance) was negligible, and thus, the total momentum of the two particles are conserved.

What we see here is a case of elastic collision - which means that there was no loss of kinetic energy. In an elastic collision, the objects “bounce” off each other, and don’t stick together to become one body - because this would be an inelastic collision, where part of the kinetic energy is changed to some other form of energy in the collision. But, as said before, this was an elastic collision, it would’ve looked something like this:

[[File:IMG_5563.JPG]]

It was noted that the car weighed 1600 kgs, while the woman weighs 50 kgs.
The speed of the car was 10 metres/second, while the women's speed was 0 m/s (she stood still)
We can figure out the velocities of both the woman and and the cars after the collision by deriving the formula

[[File:IMG5564.JPG]]

Velocities after the collision

V1 =[ M1 - M2 / (M1+ M2) ] V
V2 = [ 2M1/ M1 + M2 ] V

*Conclusion: If we make a table, we can see the distribution of momentum.
Because of the fact that the mass of the second object (Lady) is much smaller compared to the mass of the first object (car), the person is thrown back at a relatively high velocity.

[[File:wikitable.JPG]]

Some of the velocity of the bus was given to the lady, which caused her to go flying and land on the other side of the road. This is common of road traffic accident and this redistribution of momentum, in the form of velocity, is where part of her injury comes from.

==Connectedness==

So how are collisions connected to the real world? Collisions are all around us!

One main example is cars! Lots of car companies will purposely test and wreck cars to test collisions! Data is then sent to places like the Insurance Institute for Highway Safety where we can learn about car agility and more.

[[File:crash-test.jpg]]

Another example of collisions in real life is billiards. This is one of the most accurate real life examples of elastic collisions. One ball hits another ball at rest, and if done right the first ball stops and transfers nearly all its kinetic energy into kinetic energy in the second ball.

[[File:Pool1.0.jpg]]

Another example is hitting a baseball. Hitting a ball off the end or to close the hands of a bat will cause some vibrational energy from the collision, but if the ball catches the sweet spot the collision is very elastic, and you don't feel any vibration when you strike the ball.

[[File:Hittingabaseball.jpg|500px]]

==History==

Collisions are certainly not a knew concept in the world. Ever since the beginning or time things have been colliding and reacting in different ways. It was experiments done by scientists like Newton or Rutherford that started to characterize collisions into categories and apply fundamental principles of physics to the reactions.

The history of collisions originates from the Rutherford Scattering experiment. As Rutherford studied the scattering of alpha particles through metal foils, he first noticed a collision with a single massive positive particle. This lead to the conclusion that the positive charge of the mass was concentrated in the center, the atomic nucleus!

[[File:gold-foil-experiment.jpg]]

== See also ==

http://physicsbook.gatech.edu/Collisions for a general understanding of all collisions.

http://physicsbook.gatech.edu/inelastic_collisions to contrast them from elastic collisions.

===Further reading===

http://www.britannica.com/science/elastic-collision

===External links===

[http://www.physicsclassroom.com/mmedia/momentum/trece.cfm]

[http://hyperphysics.phy-astr.gsu.edu/hbase/elacol2.html]

[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/linear-momentum-and-collisions-7/collisions-70/elastic-collisions-in-one-dimension-298-6220/]

==References==

Main Idea:

''Matter and Interactions, 4th Edition''

http://www.sparknotes.com/testprep/books/sat2/physics/chapter9section4.rhtml

http://blogs.bu.edu/ggarber/archive/bua-physics/collisions-and-conservation-of-momentum/

History:

https://en.wikipedia.org/wiki/Elastic_collision

Connectedness:

http://www.iihs.org/

Additionally used references from ''see also''.

Newton's Third Law of Motion

2017-04-08T20:10:33Z

Lkrishnan7: /* Examples */

By Karan Shah
[[File: Newton's Third Law Explained.png | thumb | right | 400px |Newton's Third Law Explained]]

==Main Idea==

Newton’s Third Law of Motion describes a push or pull that acts on an object as a result of its interaction with another object. According to this law for every action there is an equal and opposite re-action. This means that for every force there is a reaction force that is equal in size, but opposite in direction. Meaning that when an object 1 pushes another object 2 then object 1 gets pushed back with equal force but in the opposite direction. [[File: Law3 f1.gif | thumb | left | 250px |If you push an object with 100N it will push back on you with equal but opposite force.]][[File: Snip20151127_7.png| thumb | right | 200px| Mathematically Formula to describe Newton's Third Law ]]

The third law of motion is also referred to as the action-reaction law because both objects are part of a single interaction and neither force can exist without the other. An important concept to remember about Newton's Third Law of Motion is that the two forces are of the same type. For example, when you throw a ball in the sky the Earth exerts a gravitational force on the ball and the ball also exerts a [[File: 924.gif | thumb | right | 250px | The canon pushes the canon ball forward and the canon pushes the canon back with equal force.]] gravitational force that is equal in magnitude and opposite in direction on the earth. Another example, that can sum up the concept of Newton's Third Law is when you walk. When you push down upon the ground and ground pushes with the same force upward. Similarly, the tires of a car push against the road while the road pushes back on the tires.

==Examples==

Here are some problems regarding Newton's Third Law.

===Simple===

==== Question ====

[[File: Snip20151128_10.png| thumb | left | 250px |Simple Example]]Car B is stopped at a red light. The brakes in Car A have failed and Car A is coming towards Car B at 60 kmh. Car B then runs into the back of Car A, What can be said about the force on Car A on Car B and the force on Car B on Car A?

==== Answer ====

B exerts the same amount of force on A as A exerts on B.
Just the direction of both the forces will be in the opposite direction.

===Middle===

====Question====

Blocks with masses of 1 kg, 2 kg, and 3 kg are lined up in a row on a frictionless table. All three are pushed forward by a 8 N force applied to the 1 kg block. (a) How much force does the 2 kg block exert on the 3 kg block? (b) How much force does the 2 kg block exert on the 1 kg block?

====Answer====

(a)
Find the Acceleration of the Whole Object:
Total Mass: 6kg
8 = (6) a
a = 8 / 6 = 1.33 m/s^2
Total Acceleration: 1.33 m/s^2 (Acceleration will be the same for all three blocks)
F(2 on 3) = m(3) * a
3 * 1.33 = 3.999 N

(b)
Total Acceleration: 1.33 m/s^2
Mass to push: 5 kg (Because we are also pushing the 3 kg block)
F(1 on 2) = 5 * 1.33
F(1 on 2) = 5.33 N

===Difficult===

====Question====
A massive steel cable drags a 30 kg block across a horizontal, frictionless surface. A 100 N force applied to the cable causes the block to reach a speed of 5.0 m/s in a distance of 5.0 m. What is the mass of the cable?

====Answer====

a = V² / (2x) = 2.5 m/s²
F = M * a → 100 = (30+m) * 2.5
m = 10 kg

===Real World Application===
(Edit by Lakshmi Krishnan (lkrishnan7))

'''Scenario''': There is a car that is stuck, nestled in the trees. Woman appears healthy and stable.

'''Witness Statement''': Witness says that as a car was making a turn, the car “somehow lost its balance and skid”, deviating off its regular path, and ended up sliding towards the trees, around 30 metres from where she was. The witness claims the car was travelling at 25 miles per hour.

'''Report''': This is a classic combination case of NEWTON’S 1st and 3rd LAW. The first law says that objects at a fixed velocity will stay at that velocity unless acted upon by an unbalanced, external force. It is worth pointing out that when the car was skidding, it was displaying inertia, or the tendency to resist a change in motion. In the car, as the wheels go around, it’s static friction. The force that is pushing the car along the road is a friction force... we need to the road to move the car, cause the road provides the friction. This is Newton’s 3rd Law. The tires are pushing backwards on the road, and the road is pushing forward on the tires. This “push force” is what we’re relying on keep the car on the road, so essentially, we’re relying on this static friction force. When the car starts to skid, it changes to force of kinetic friction, because the wheels are now slipping and having some motion. It slides and is moving, so it becomes kinetic friction.

The witness claimed that the car was going at 25 miles per hour. With this being said, an official wanted check and make sure this really was the speed. Since the car is now 30 metres from the place it lost its balance, we can use this information to calculate the speed.
Assuming the brakes work properly, the stopping distance would’ve been determined by the coefficient of friction between the tires and the road. This is because the force of friction must do enough work on the car to reduce the kinetic energy of the car, as outlined in the work-energy principle.
Net Work = change in kinetic energy of an object
Net Work = (1/2)mv(final)^2 - (1/2)mv(initial)^2
When we look at the equation for static friction:
Ms = Ff / Fn
Fn x Ms = Ff
Ms x mg = Fr
Mu static x mg = Force of friction
Since the road was a bit slippery, and the road a little wet, the coefficient of static friction was 0.4. The normal coefficient is around 0.7 for dry roads and becomes smaller for wet or oily roads. Gravity was 10, so the equation would’ve been:
Work Friction = -μmgd = - (1/2) mv^2
If we cancel out the m’s, we can get
D = (v^2) / (2)(μ)(g)
Plugging in what we have and what we know:
30 = (V^2) / 2 x .4 x 10
30 = (V^2) / 8
V = 15 metre / second, so around 35 miles per hour. The witness’ account of the speed was a little off!

Conclusion: Like most skids, as soon as this car started to skid, it was at the mercy of inertia. It would keep going at the same speed unless some other force stopped it, and in this case, that “other force” was the tress.

==Connectedness==

#How is this topic connected to something that you are interested in?

Newton's Third Law is connected to the concept of a spacecraft flying in space. When a spacecraft
fires a thruster rocket, the exhaust gas pushes against the thruster and the thruster pushes
against the exhaust gas. The gas and rocket move in opposite directions. This is an
example of Newton's Third Law because both forces are equal in magnitude and opposite
in direction. This topic is related to space travel a topic that I am interested in and
passionate about learning more.

==History==

Sir Isaac Newton was a renowned scientist and mathematician who helped create a foundation for modern studies. He was born in England in 1643 and worked his way to earn a bachelor’s and master’s degree from Trinity College Cambridge. He was highly interested in math, physics, and astronomy and wrote many of his ideas in a journal. One of those ideas was about the three laws of motion. [[File: Sir_Isaac_Newton_(1643-1727).jpg| thumb | left | 150px| Sir Isaac Newton (1643 - 1727)]] In 1687 Isaac Newton made his work on his book, Philosophiae Naturalis Principia Mathematic or Principia known to the public. He discussed the principles of time, force, and motion that helped create modern physical science and helped account for much of the phenomena viewed in the world. Some of the principles he discusses include acceleration, initial movement, fluid dynamics, and motion. Newton’s Laws first appeared in the Principia and discussed the relationship that exists between forces acting on a body and the motion of the body. For the third law, he stated that for every action/force in nature, there will be an equal and opposite reaction.

== See also ==

===Further reading===

Books, Articles or other print media on this topic

[http://www.wired.com/2013/10/a-closer-look-at-newtons-third-law/ A Closer Look at Newton’s Third Law]

[http://phys.org/news/2015-05-newton-law-broken.html What happens when Newton's third law is broken?]

[http://www.livestrong.com/article/423739-newtons-three-laws-motion-used-baseball/ How Are Newton's Three Laws of Motion Used in Baseball?]

[https://www.newscientist.com/article/dn24411-light-can-break-newtons-third-law-by-cheating/ Light can break Newton’s third law – by cheating]

[http://science360.gov/obj/video/d0e16d27-05d4-4511-9394-2758aa066981/science-nfl-football-newtons-third-law-motion Science of Football]

===External links===

Internet resources on this topic

[http://teachertech.rice.edu/Participants/louviere/Newton/law3.html The Third Law of Motion]

[http://www.physicsclassroom.com/class/newtlaws/Lesson-4/Newton-s-Third-Law Newton's Third Law of Motion]

[https://www.grc.nasa.gov/www/k-12/WindTunnel/Activities/third_law_motion.html Newton's Third Law of Motion]

==References==

This section contains the the references you used while writing this page

Knight, R., & Jones, B. (n.d.). College physics: A strategic approach (Third edition, Global ed.).

http://www.physicsclassroom.com/class/newtlaws/Lesson-4/Newton-s-Third-Law

https://www.grc.nasa.gov/www/k-12/airplane/newton3.html

http://hyperphysics.phy-astr.gsu.edu/hbase/newt.html

http://science360.gov/obj/video/d0e16d27-05d4-4511-9394-2758aa066981/science-nfl-football-newtons-third-law-motion

http://www.livescience.com/46561-newton-third-law.html

[[Category:Which Category did you place this in?]]

Newton's Third Law of Motion

2017-04-08T20:09:54Z

Lkrishnan7: /* Examples */

By Karan Shah
[[File: Newton's Third Law Explained.png | thumb | right | 400px |Newton's Third Law Explained]]

==Main Idea==

Newton’s Third Law of Motion describes a push or pull that acts on an object as a result of its interaction with another object. According to this law for every action there is an equal and opposite re-action. This means that for every force there is a reaction force that is equal in size, but opposite in direction. Meaning that when an object 1 pushes another object 2 then object 1 gets pushed back with equal force but in the opposite direction. [[File: Law3 f1.gif | thumb | left | 250px |If you push an object with 100N it will push back on you with equal but opposite force.]][[File: Snip20151127_7.png| thumb | right | 200px| Mathematically Formula to describe Newton's Third Law ]]

The third law of motion is also referred to as the action-reaction law because both objects are part of a single interaction and neither force can exist without the other. An important concept to remember about Newton's Third Law of Motion is that the two forces are of the same type. For example, when you throw a ball in the sky the Earth exerts a gravitational force on the ball and the ball also exerts a [[File: 924.gif | thumb | right | 250px | The canon pushes the canon ball forward and the canon pushes the canon back with equal force.]] gravitational force that is equal in magnitude and opposite in direction on the earth. Another example, that can sum up the concept of Newton's Third Law is when you walk. When you push down upon the ground and ground pushes with the same force upward. Similarly, the tires of a car push against the road while the road pushes back on the tires.

==Examples==

Here are some problems regarding Newton's Third Law.

===Simple===

==== Question ====

[[File: Snip20151128_10.png| thumb | left | 250px |Simple Example]]Car B is stopped at a red light. The brakes in Car A have failed and Car A is coming towards Car B at 60 kmh. Car B then runs into the back of Car A, What can be said about the force on Car A on Car B and the force on Car B on Car A?

==== Answer ====

B exerts the same amount of force on A as A exerts on B.
Just the direction of both the forces will be in the opposite direction.

===Middle===

====Question====

Blocks with masses of 1 kg, 2 kg, and 3 kg are lined up in a row on a frictionless table. All three are pushed forward by a 8 N force applied to the 1 kg block. (a) How much force does the 2 kg block exert on the 3 kg block? (b) How much force does the 2 kg block exert on the 1 kg block?

====Answer====

(a)
Find the Acceleration of the Whole Object:
Total Mass: 6kg
8 = (6) a
a = 8 / 6 = 1.33 m/s^2
Total Acceleration: 1.33 m/s^2 (Acceleration will be the same for all three blocks)
F(2 on 3) = m(3) * a
3 * 1.33 = 3.999 N

(b)
Total Acceleration: 1.33 m/s^2
Mass to push: 5 kg (Because we are also pushing the 3 kg block)
F(1 on 2) = 5 * 1.33
F(1 on 2) = 5.33 N

===Difficult===

====Question====
A massive steel cable drags a 30 kg block across a horizontal, frictionless surface. A 100 N force applied to the cable causes the block to reach a speed of 5.0 m/s in a distance of 5.0 m. What is the mass of the cable?

====Answer====

a = V² / (2x) = 2.5 m/s²
F = M * a → 100 = (30+m) * 2.5
m = 10 kg

===Real World Application===

'''Scenario''': There is a car that is stuck, nestled in the trees. Woman appears healthy and stable.

'''Witness Statement''': Witness says that as a car was making a turn, the car “somehow lost its balance and skid”, deviating off its regular path, and ended up sliding towards the trees, around 30 metres from where she was. The witness claims the car was travelling at 25 miles per hour.

'''Report''': This is a classic combination case of NEWTON’S 1st and 3rd LAW. The first law says that objects at a fixed velocity will stay at that velocity unless acted upon by an unbalanced, external force. It is worth pointing out that when the car was skidding, it was displaying inertia, or the tendency to resist a change in motion. In the car, as the wheels go around, it’s static friction. The force that is pushing the car along the road is a friction force... we need to the road to move the car, cause the road provides the friction. This is Newton’s 3rd Law. The tires are pushing backwards on the road, and the road is pushing forward on the tires. This “push force” is what we’re relying on keep the car on the road, so essentially, we’re relying on this static friction force. When the car starts to skid, it changes to force of kinetic friction, because the wheels are now slipping and having some motion. It slides and is moving, so it becomes kinetic friction.

The witness claimed that the car was going at 25 miles per hour. With this being said, an official wanted check and make sure this really was the speed. Since the car is now 30 metres from the place it lost its balance, we can use this information to calculate the speed.
Assuming the brakes work properly, the stopping distance would’ve been determined by the coefficient of friction between the tires and the road. This is because the force of friction must do enough work on the car to reduce the kinetic energy of the car, as outlined in the work-energy principle.
Net Work = change in kinetic energy of an object
Net Work = (1/2)mv(final)^2 - (1/2)mv(initial)^2
When we look at the equation for static friction:
Ms = Ff / Fn
Fn x Ms = Ff
Ms x mg = Fr
Mu static x mg = Force of friction
Since the road was a bit slippery, and the road a little wet, the coefficient of static friction was 0.4. The normal coefficient is around 0.7 for dry roads and becomes smaller for wet or oily roads. Gravity was 10, so the equation would’ve been:
Work Friction = -μmgd = - (1/2) mv^2
If we cancel out the m’s, we can get
D = (v^2) / (2)(μ)(g)
Plugging in what we have and what we know:
30 = (V^2) / 2 x .4 x 10
30 = (V^2) / 8
V = 15 metre / second, so around 35 miles per hour. The witness’ account of the speed was a little off!

Conclusion: Like most skids, as soon as this car started to skid, it was at the mercy of inertia. It would keep going at the same speed unless some other force stopped it, and in this case, that “other force” was the tress.

==Connectedness==

#How is this topic connected to something that you are interested in?

Newton's Third Law is connected to the concept of a spacecraft flying in space. When a spacecraft
fires a thruster rocket, the exhaust gas pushes against the thruster and the thruster pushes
against the exhaust gas. The gas and rocket move in opposite directions. This is an
example of Newton's Third Law because both forces are equal in magnitude and opposite
in direction. This topic is related to space travel a topic that I am interested in and
passionate about learning more.

==History==

Sir Isaac Newton was a renowned scientist and mathematician who helped create a foundation for modern studies. He was born in England in 1643 and worked his way to earn a bachelor’s and master’s degree from Trinity College Cambridge. He was highly interested in math, physics, and astronomy and wrote many of his ideas in a journal. One of those ideas was about the three laws of motion. [[File: Sir_Isaac_Newton_(1643-1727).jpg| thumb | left | 150px| Sir Isaac Newton (1643 - 1727)]] In 1687 Isaac Newton made his work on his book, Philosophiae Naturalis Principia Mathematic or Principia known to the public. He discussed the principles of time, force, and motion that helped create modern physical science and helped account for much of the phenomena viewed in the world. Some of the principles he discusses include acceleration, initial movement, fluid dynamics, and motion. Newton’s Laws first appeared in the Principia and discussed the relationship that exists between forces acting on a body and the motion of the body. For the third law, he stated that for every action/force in nature, there will be an equal and opposite reaction.

== See also ==

===Further reading===

Books, Articles or other print media on this topic

[http://www.wired.com/2013/10/a-closer-look-at-newtons-third-law/ A Closer Look at Newton’s Third Law]

[http://phys.org/news/2015-05-newton-law-broken.html What happens when Newton's third law is broken?]

[http://www.livestrong.com/article/423739-newtons-three-laws-motion-used-baseball/ How Are Newton's Three Laws of Motion Used in Baseball?]

[https://www.newscientist.com/article/dn24411-light-can-break-newtons-third-law-by-cheating/ Light can break Newton’s third law – by cheating]

[http://science360.gov/obj/video/d0e16d27-05d4-4511-9394-2758aa066981/science-nfl-football-newtons-third-law-motion Science of Football]

===External links===

Internet resources on this topic

[http://teachertech.rice.edu/Participants/louviere/Newton/law3.html The Third Law of Motion]

[http://www.physicsclassroom.com/class/newtlaws/Lesson-4/Newton-s-Third-Law Newton's Third Law of Motion]

[https://www.grc.nasa.gov/www/k-12/WindTunnel/Activities/third_law_motion.html Newton's Third Law of Motion]

==References==

This section contains the the references you used while writing this page

Knight, R., & Jones, B. (n.d.). College physics: A strategic approach (Third edition, Global ed.).

http://www.physicsclassroom.com/class/newtlaws/Lesson-4/Newton-s-Third-Law

https://www.grc.nasa.gov/www/k-12/airplane/newton3.html

http://hyperphysics.phy-astr.gsu.edu/hbase/newt.html

http://science360.gov/obj/video/d0e16d27-05d4-4511-9394-2758aa066981/science-nfl-football-newtons-third-law-motion

http://www.livescience.com/46561-newton-third-law.html

[[Category:Which Category did you place this in?]]

Inertia

2017-04-08T20:01:18Z

Lkrishnan7: /* Relationship to Modern Day Life */

'''Claimed by Dev Mandavia'''

In kinematics, momentum and inertia, while similar, are very different entities. Momentum usually refers to mass that is undergoing translational motion and is defined as the mass multiplied by the mass's corresponding velocity component. Inertia is the resistance to changes in the motion or projected motion of a specified body of mass. It can exist in terms of a standard moment of inertia or a rotational moment of inertia, which is the resistance to changes in the rotation or projected rotation of a specified body of mass.

==The Main Idea==

The motivation behind the quantifiable term known as inertia is to have the ability to study and predict the motion of systems of specified mass in terms of torsion, translation, and deformation.

==History==

Before the Renaissance period, the theory of motion that reigned was garnered by Aristotle who claimed that "in the absence of external motive power, all objects [on Earth] would come to rest and moving objects would only continue to move so long as there is power inducing them to do so."[http://etext.library.adelaide.edu.au/a/aristotle/a8ph/]

Galileo performed an experiment with two ramps and a bronze ball. To begin, the two were set up at the same angle. Galileo observed that if a ball was released at one height, it would roll to the same height at which the ball was released. He then experimented with altering the angle of the second ramp. He concluded that even though it may take longer, when the angle is smaller, the ball will still roll up to the same height. Because the height was conserved, Galileo believed that if a ball was rolled from a ramp to a flat surface, it would stay in motion unless a force stopped it.

Newton delved deeper on past assertions regarding laws of motion with his concept that objects in motion tend to stay in motion unless acted on by an external force; some examples for external forces in the real world are: gravity, friction, contact, etc. This definition remained unchanged event in Einstein's theory of special relativity as proposed during the 20th century.

[[File:newtonsexperiment.png|frameless|600px]]

==Calculating Inertia==

The formula for the standard moment of inertia, typically denoted as I, depends on what the particular statically determinate object is as well as its rotational axis.

[[File:Inertia1.png|850px]]

Calculating the polar moment of inertia, typically denoted as J, depends on what the deformable body is and also depends on the rotational axis; the cross sectional area, distance from the center of mass, and projected deformation are also key components. J comes from the relationship between the total internal torque at a cross section and the stress distribution at a cross section.

[[File:Inertia2.png|1100px]]

==Examples==

Area Moment of InertiExample.jpg:

[[File:AreaI.jpeg|1000px]]

Polar Moment of Inertia Example:

[[File:PolarJ.jpeg|1000px]]

==Relationship to Modern Day Life==

[[File:inertia_fail.png|border|500px]]

Anything in life involving motion is inertia, whether it is you walking, riding a scooter, or running. A ball's motion or lack of motion is inertia as well. An everyday example of inertia would be a car in motion. As a car accelerates and attains a higher velocity, the amount of momentum of the vehicle increases. A higher inertia makes it more difficult for a car to brake quickly and come to a halt in an emergency scenario.

(Edit by Lakshmi Krishnan (lkrishnan7))

Take the scenario of a car accident, for example.

'''Scenario''': At a stop light, a car halts and waits for a green. However, the car behind it doesn’t stop in time, and bumps the in front of it, from the behind.

'''Report''': This has almost everything to do with law of inertia, or Newton’s 1st Law. In Newton’s first law, he states that an object at rest stays at rest, or an object in motion will stay in motion, unless acted upon by an unbalanced force. That is, if an object (be it a head, moving at a certain velocity because of the car) will tend to stay at the same speed and in the same direction, unless something stops it. Back to the scenario: In a way, it’s a good things this lady was wearing a seatbelt... it slows down the inertia. For example, if a kid was in the car, and was NOT wearing a seatbelt, people would think that the kid launched forward. Really, it’s just that the car is brought to a halt, but the kid just continues at their original velocity. This is inertia in action -- that is, the tendency to resist change in the state of motion they are already in. However, in this case, the seatbelt was (kind of!) bad, as it caused the overextension of head. The head weighs around 4-5 kilos, and we know that when car comes to a sudden halt, body is stopped, skull continues on, it’s called whiplash. In this case, when the person bumped into the other car from behind... your car is stunned forward, body with it... head is stationary, is remaining in the same, position, the lady’s car’s inertia wants to stay where it was originally. The body was moved, but the head wanted to stay in its original velocity, but followed the body in the seconds after.

'''Conclusion''': If the lady complains of any neck pain, it’s probably because of inertia, and the possibility that the lady has overextended her neck beyond elastic limits. She will be wearing a neck brace if this is the case!

== See also ==
[[Galileo Galilei]]

[[Conservation of Momentum]]

[[Newton's Laws and Linear Momentum]]

[[The Moments of Inertia]]

==References==

[http://www.scienceclarified.com/everyday/Real-Life-Chemistry-Vol-3-Physics-Vol-1/Laws-of-Motion-Real-life-applications.html]
[http://education.seattlepi.com/galileos-experiments-theory-rolling-balls-down-inclined-planes-4831.html]
[http://www.physicsclassroom.com/class/newtlaws/Lesson-1/Inertia-and-Mass]
[http://etext.library.adelaide.edu.au/a/aristotle/a8ph/]