Physics Book - User contributions [en]

Air Resistance

2016-04-22T19:33:49Z

Lbond9: I took out where it still said "Put this idea in historical context. Give the reader the Who, What, When, Where, and Why." in the History section.

This page was completed by Jayanth Chintham (jchintham3). 11/29/15

==The Main Idea==

The forces acting opposite to the direction of motion are called air resistance. Another term for this restraining effect is called "drag." Air resistance is an example of energy dissipation.

[[File:Air resistance.jpg]]

You may have noticed that moving objects quickly through any substance is harder than moving objects slowly through a substance. This is due to the air resistance. The magnitude of air resistance directly correlates to the speed of the object. Another aspect that impacts air resistance is the cross sectional area of a system. An example is a skydiver with an open parachute has more air resistance than a closed parachute. Air resistance force has an effect on the shape of an object as well. An example of this is a coffee filter, which is blunt object. A ball with the same cross sectional area as a coffee filter has less air resistance. The last effect that impacts air resistance is air density. An example is at higher altitudes (less air density) where there is less air resistance.
===A Mathematical Model===
The four factors that impact air resistance are cross sectional area, shape, air density, and speed. As you can see in the formula below, these four factors are included in the formula for the air resistance.

[[File:Formula.png]]

===A Computational Model===

[Air Resistance Using Glowscript][http://www.glowscript.org/#/user/jayanthchintham/folder/Public/program/AirResistance]

===Rotational Motion on Air Resistance===

[[File:Pressure.png]]

If a ball has spin, there is an effect of fluid flow around the ball that raises the air pressure on the side where the rotational motion is in the same direction as the ball's velocity, and lowers the air pressure on the other side, where the rotational motion is in the opposite direction to the velocity. In the figure above, the force points upward due to "backspin" and lifts the ball extending the range. In the case where there is topspin on the ball, the force is downward decreasing the range. This topic is related to fluid dynamics.

==Examples==

===Problem 1===

You are standing at the top of a 20 building. You throw a ball in the horizontal direction with speed of 10 m/s. If you neglect air resistance, where would you expect the ball to hit on the plain surface below? Do you think your prediction without air resistance is too large or too small?

Solution:

height = (initial velocity in y direction)(time) + .5(acceleration from gravity)(time)^2

Since there is no initial velocity in the y direction, the equation is just:

height = .5(acceleration from gravity)(time)^2

20 = .5(9.8)(t)^2

Solve for t.

t = 2.02 seconds

range = (initial velocity in x direction)(time) + .5(acceleration in x direction)(time)^2

Since there is no acceleration in the x direction, the equation is just:

range = (initial velocity in x direction)(time)

range = (10)(2.02)

range = 20.2 meters

Our prediction without air resistance is too large, because air resistance has a force opposite to motion. This in turn would make the landing distance shorter.

===Problem 2===

John is going sky diving for the first time. His mass is 70 kg and his terminal speed is 38 m/s. What is the magnitude of the force of the air on John?

Solution:

At the terminal speed, the force of air (air resistance) is equal to the force of gravity.

Force air = Force gravity

Force air = (mass) (acceleration from gravity)

Force air = (70)(9.8)

Force air = 686 Newtons

===Problem 3===

Sarah is doing an air resistance experiment in class. The experiment requires Sarah to drop a coffee filter from a height of 2 meters. Let's say that the mass of the coffee filter was 2.0 grams, and it reached the ground with a speed of 1.0 m/s. How much kinetic energy did the air gain when Sarah dropped the coffee filter?

Solution:

[[File:coffee filter.png]]

Potential energy = (mass)(acceleration from gravity)(height)

Potential energy = (.002)(9.8)(2)

Potential energy = .0392 Joules

Kinetic Energy = .5(mass)(velocity)^2

Kinetic Energy = .5(.002)(1.0)^2

Kinetic Energy = .001 Joules

Total Energy = Potential Energy + Kinetic Energy

Total Energy = 0.0392 + 0.001 = 0.0402 Joules

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

As an adventurous person, I have always been interested in skydiving. Air resistance is a huge factor in skydiving, as it allows you to reach the ground safely just with a parachute. There are many factors in releasing a parachute to have the safest possible landing. When you release your parachute and how to control your parachute are very important in having a safe landing. Also, there is obviously a lot of air resistance in a parachute because of the large cross sectional area.

Another topic that air resistance plays a factor in is sports. A specific sport that air resistance impacts is tennis. Spin is very important in tennis, because it allows you to control where the ball lands. If there is topspin on a ball, the air resistance is less allowing the ball to come down faster. If there is backspin, the ball stays in the air longer being controlled by the air.

How is it connected to your major?

I am an aerospace engineer, so air resistance has a lot of application in my field. Especially in aircraft design and manufacturing, aerospace engineers must design a aircraft that allows for the least air resistance. This allows for more control over the plane.

Is there an interesting industrial application?

Air resistance has a lot of application in speed sports. Also, air resistance plays a big factor in skydiving and anything with a parachute. Lastly, the aircraft industry factors in air resistance into all of their products, as this force is very important in certain situations.

==History==

Aristotle was the first to write about air resistance in the 4th century BC. In the 15th century, Leonardo da Vinci published the Codex Leicester, in which he rejected Aristotle's theory and attempted to prove that the only effect of air on a thrown object was to resist its motion. The first equation for air resistance was:

[[File:drag.png]]

This equation overestimates drag in most cases, and was often used in the 19th century to argue the impossibility of human flight.

Louis Charles Breguet's paper of 1922 began efforts to reduce drag by streamlining. A further major call for streamlining was made by Sir Melvill Jones who provided the theoretical concepts to demonstrate emphatically the importance of streamlining in aircraft design. The aspect of Jones’s paper that most shocked the designers of the time was his plot of the horse power required versus velocity, for an actual and an ideal plane.

==Further reading==

http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Free-Fall-and-Air-Resistance

http://www.forbes.com/sites/chadorzel/2015/09/29/the-annoying-physics-of-air-resistance/[http://www.forbes.com/sites/chadorzel/2015/09/29/the-annoying-physics-of-air-resistance/]

==References==

Chabay, Ruth, and Bruce Sherwood. "Internal Energy." Matters and Interactions. 4th ed. Vol. 1. Wiley, 2015. Print.

More information can be found on drag[https://en.wikipedia.org/wiki/Drag_(physics)] and aerodynamics[https://en.wikipedia.org/wiki/History_of_aerodynamics]

Net Force

2016-04-14T02:55:12Z

Lbond9: I'm just making small improvements throughout the whole page

by Julia Logan

editing claimed by Leila Bond

==Definition==

===A Mathematical Model===
In order to calculate net force, all EXTERNAL forces acting on a system are added together. The mathematical definition is <center><math> Fnet = F1 + F2 + F3... </math></center>
Additionally,
<center><math> Fnet = m*a </math> 
where m=mass of the object, and a = acceleration of the object.</center>
If there is a nonzero net force acting on an object, that object is accelerating (not traveling at a constant velocity). A net force of zero can mean that the object is at rest, but it can also mean that the object is moving with constant velocity. Both cases have acceleration = 0, so they both satisfy <math>Fnet = m*a</math> because <math>Fnet = 0</math> and <math>a = 0</math>. It may seem strange that an object can be moving and still have net force = zero, but remember Newton's first law, which states that objects at rest tend to remain at rest and objects in motion tend to continue going the same way at the same speed unless acted on by an outside force. Imagine an astronaut has a rock that he or she throws out of the space ship while in space: the rock would float away at a constant speed and unless a meteor hit it or something, it would keep moving forever in the same direction at the same speed.

===A Computational Model===

Net force is an essential component of the Momentum Principle! We can use the Momentum Principle in vpython to update the position of a moving object. But first, we have to find net force.
[[File:netforce.png|200px|thumb|left|Tracing the path of a ball/spring model in vpython using net force and the momentum principle.]]

#1 Fspring = -k*s
#2 Fgravmag = mball * g
#3 Fgrav = Fgravmag * vector(0,-1,0)
#4 Fnet = Fspring+Fgrav
#5 pball = pball + Fnet * deltat
#6 vball = pball / mball
#7 ball.pos=ball.pos+vball*deltat

Here, the spring force and the gravitational force are found using formulas (lines 1-3). Then, they are added together to get the net force on the object (in this case a ball, line 4). The net force is then used in the update form of the momentum principle (line 5). In line 6 the velocity is updated, and line 7 the position is updated. Without net force calculations, tracing an object's path would be impossible.
 
 
 
 
 

=Simple Example=
When calculating net force, it is most useful to construct a free body diagram. A free body diagram is a physical representation of the external forces applied to a system. Often, arrows are used to represent forces. In this example, forces are displayed acting on a box.

The first box is being suspended by a rope, so its free body diagram looks like this:

[[File:Net_force_wiki_4.PNG]]

Assume that down is the negative y direction, and you can easily write vector representations of the forces and add them up to find the sum, which is the net force:

<math> Fnet = (0, 1200, 0) </math>N<math> + (0, -800, 0) </math>N 
<math> Fnet = (0, 400, 0) </math>N

The second box is falling, but it has significant air resistance:

[[File:Net_force_wiki_5.PNG]]

<math> Fnet = (0, 600, 0) </math>N<math> + (0, -800, 0) </math>N 
<math> Fnet = (0, -200, 0) </math>N

The third box is on the ground and is sliding to the right, but slowing down because of friction. It has both x-component forces and y-component forces. It is important to put these in the right place in the vector coordinates.

[[File:Net_force_wiki_6.PNG]]

<math> Fnet = (0, 50, 0) </math>N<math> + (0, -50, 0) </math>N<math> + (-20, 0, 0)</math>N 
<math> Fnet = (-20, 0, 0) </math>N

=More Complicated Example=
There is a box, small enough to represented as a point, sitting on a slope inclined twenty degrees with respect to the horizontal. If its mass is 10 kg, what does the magnitude of the force of static friction (pointing up the hill) have to be for net force to be zero? In that case, what is the magnitude of the normal force? (All forces are measured in newtons, and the acceleration due to gravity <math> = g = 9.8</math> <math>m/(s^2) </math>).

Let <math> f </math> = force of friction, <math> W </math> = weight of the object, and <math> N = </math> normal force. (The pictures are not to scale.)

[[File:Net_force_wiki_1.PNG]]

First, we have to identify our coordinate axes. We could have the typical horizontal x-axis and vertical y-axis (and we know where to put <math>θ</math> using similar triangles):

[[File:Net_force_wiki_2.png]]

But, that leaves us with two forces that have to be decomposed into x- and y- components. It makes more sense to draw the axes rotated twenty degrees counterclockwise, like this:

[[File:Net_force_wiki_3.png]]

<math> W </math> is easy to find, since it's just mass times acceleration due to gravity, both of which are known quantities.

<math> W = mg = (10</math> <math>kg)*(9.8</math> <math>m/(s^2)) = 98</math> <math>newtons </math>

Now we are ready to solve for the frictional force. It acts in the positive x direction, and we know that the net force in the x direction has to be zero, so we have to identify the other forces that act in the positive or negative x direction. In this case, it's only a component of the weight, which points in the negative x direction. Using simple trigonometry, we find that that is

<math> -W*sin(θ) </math>

So we can write our equilibrium equation like this:

<math> Fnetx = f - W*sin(θ) = 0 </math>

Then, all we have to do is solve for <math> f </math>, since <math> W </math> and <math> θ </math> are known quantities.

<math> f = W*sin(θ) = (98</math> N<math>)*sin(20°) = 33.51797405</math> N, which is about equal to <math>33.5</math> N.

Now we have to solve for the normal force. It acts in the positive y direction, and we know that the net force in the y direction has to be zero, so we have to identify the other forces that act in the positive or negative y direction. In this case, the only one is the other component of the weight, which points in the negative y direction. Using simple trigonometry, we find that that is

<math> -W*cos(θ) </math>

So we can write our equilibrium equation like this:

<math> Fnety = N - W*cos(θ) = 0 </math>

Then, all we have to do is solve for <math> N </math>, since <math> W </math> and <math> θ </math> are known quantities.

<math> N = W*cos(θ) = (98</math> N<math>)*cos(20°) = 92.08987684</math> N, which is about equal to <math>92.1</math> N.

=Connectedness=
Net force is one of the building blocks of Intro Physics, and I would assume all of physics. It's really important for all motion-related topics, specifically [[Curving Motion]]. A net force due to the gravitational pull of the Sun in the perpendicular direction is how the Earth revolves around the Sun -- why we have days and nights and years! We can see from the derivative form of the Momentum Principle that any change in momentum is due to a nonzero net force acting on a system. All changes in motion can be attributed to a net force acting in some direction. 
<math> dP/dt=Fnet </math> (<math>P</math> is the symbol for momentum.)

My major is biomedical engineering, and I haven't taken any BME classes yet, but physics is a requirement so it has to be relevant. Statics is also a requirement for BMEs, and that class deals with net force in every single problem because you have to be able to analyze systems and structures based on the forces they provide and support.

=History=

Some of the earliest records of humans' musings about force come from Aristotle. Aristotle observed the natural world and made assumptions and equations based on what he saw. He described all motion as being either "natural"--circular and infinite OR finite, up and down, in a straight line--or "violent." Aristotle had issues with projectile motion as he could not reconcile the continuing movement of the object with the lack of force being applied. He ended up concluding that the air provides a simultaneous resistant and accelerating force to the object. 

These ideas were challenged by Renaissance men such as John Philoponus, John Buridan, and Oresme, with a clear understanding of the conservation of linear momentum not arriving to the world until Descartes. The most famous face we associate with forces in Physics is Sir Isaac Newton, and he certainly played a huge role in the understanding of net force and momentum. However, he initially believed in the idea of impetus, that a projectile has a certain internal force that keeps it moving, and also the idea of transfer, that objects give up parts of their force during a collision. Though he was wrong, these ideas are not at all silly--in fact they seem quite logical--and he later corrected them after a series of experiments. Thus, the second law of motion was established and with it the relationship between force and motion.

== See also ==
These other wiki pages might help: 
[[Momentum Principle]] 
[[Conservation of Momentum]] 
[[Newton's Laws and Linear Momentum]]

===External links===
[http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Determining-the-Net-Force Physics Classroom: Net Force]
[http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Drawing-Free-Body-Diagrams Physics Classroom: Drawing Free Body Diagrams]

==References==

Cardenas, Richard. "What is Net Force? - Definition, Magnitude & Equations." Web. 30 Nov 2015. http://study.com/academy/lesson/what-is-net-force-definition-magnitude-equations.html 

"Net Force." Wikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc. Web. 30 Nov 2015. https://en.wikipedia.org/wiki/Net_force 

The Physics Classroom. "Determining the Net Force." Web. 30 Nov 2015. http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Determining-the-Net-Force 

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. Modern Mechanics. Hoboken, NJ: Wiley, 2011. Print. 

Stinner, Arthur. "The story of force: from Aristotle to Einstein." Physics Education. 1994. Web. 30 Nov 2015. http://www.arthurstinner.com/stinner/pdfs/1994-storyofforce.pdf 
[[Category:Which Category did you place this in?]]

Net Force

2016-04-14T00:48:48Z

Lbond9: I made the original "simple example" clearer and easier to follow, and I added to the connectedness section.

by Julia Logan

editing claimed by Leila Bond

==Definition==

===A Mathematical Model===
In order to calculate net force, all EXTERNAL forces acting on a system are added together. The mathematical definition is <center><math> Fnet = F1 + F2 + F3... </math></center>
Additionally,
<center><math> Fnet = ma </math> 
where m=mass of the object, and a = acceleration of the object.</center>
This is a result of Newton's Second Law of motion. If there is a nonzero net force acting on an object, that object is accelerating (not traveling at a constant velocity). Interestingly, there is zero net force acting on an object if its velocity is constant. This seems counter-intuitive (surely something is causing the object to move!) but makes sense in the context of Newton's Second Law. The forces are balanced (sum to zero) if there is no acceleration, despite any movement that may be happening.

===A Computational Model===

Net force is an essential component of the Momentum Principle! We can use the Momentum Principle in vpython to update the position of a moving object. But first, we have to find net force.
[[File:netforce.png|200px|thumb|left|Tracing the path of a ball/spring model in vpython using net force and the momentum principle.]]

#1 Fspring = -k*s
#2 Fgravmag = mball * g
#3 Fgrav = Fgravmag * vector(0,-1,0)
#4 Fnet = Fspring+Fgrav
#5 pball = pball + Fnet * deltat
#6 vball = pball / mball
#7 ball.pos=ball.pos+vball*deltat

Here, the spring force and the gravitational force are found using formulas (lines 1-3). Then, they are added together to get the net force on the object (in this case a ball, line 4). The net force is then used in the update form of the momentum principle (line 5). In line 6 the velocity is updated, and line 7 the position is updated. Without net force calculations, tracing an object's path would be impossible.
 
 
 
 
 

=Simple Example=
When calculating net force, it is most useful to construct a free body diagram. A free body diagram is a physical representation of the external forces applied to a system. Often, arrows are used to represent forces. In this example, forces are displayed acting on a box.

The first box is being suspended by a rope, so its free body diagram looks like this:

[[File:Net_force_wiki_4.PNG]]

Assume that down is the negative y direction, and you can easily write vector representations of the forces and add them up to find the sum, which is the net force:

<math> Fnet = (0, 1200, 0) </math>N<math> + (0, -800, 0) </math>N 
<math> Fnet = (0, 400, 0) </math>N

The second box is falling, but it has significant air resistance:

[[File:Net_force_wiki_5.PNG]]

<math> Fnet = (0, 600, 0) </math>N<math> + (0, -800, 0) </math>N 
<math> Fnet = (0, -200, 0) </math>N

The third box is on the ground and is sliding to the right, but slowing down because of friction. It has both x-component forces and y-component forces. It is important to put these in the right place in the vector coordinates.

[[File:Net_force_wiki_6.PNG]]

<math> Fnet = (0, 50, 0) </math>N<math> + (0, -50, 0) </math>N<math> + (-20, 0, 0)</math>N 
<math> Fnet = (-20, 0, 0) </math>N

=More Complicated Example=
There is a box, small enough to represented as a point, sitting on a slope inclined twenty degrees with respect to the horizontal. If its mass is 10 kg, what does the magnitude of the force of static friction (pointing up the hill) have to be for net force to be zero? In that case, what is the magnitude of the normal force? (All forces are measured in newtons, and the acceleration due to gravity <math> = g = 9.8</math> <math>m/(s^2) </math>).

Let <math> f </math> = force of friction, <math> W </math> = weight of the object, and <math> N = </math> normal force. (The pictures are not to scale.)

[[File:Net_force_wiki_1.PNG]]

First, we have to identify our coordinate axes. We could have the typical horizontal x-axis and vertical y-axis (and we know where to put <math>θ</math> using similar triangles):

[[File:Net_force_wiki_2.png]]

But, that leaves us with two forces that have to be decomposed into x- and y- components. It makes more sense to draw the axes rotated twenty degrees counterclockwise, like this:

[[File:Net_force_wiki_3.png]]

<math> W </math> is easy to find, since it's just mass times acceleration due to gravity, both of which are known quantities.

<math> W = mg = (10</math> <math>kg)*(9.8</math> <math>m/(s^2)) = 98</math> <math>newtons </math>

Now we are ready to solve for the frictional force. It acts in the positive x direction, and we know that the net force in the x direction has to be zero, so we have to identify the other forces that act in the positive or negative x direction. In this case, it's only a component of the weight, which points in the negative x direction. Using simple trigonometry, we find that that is

<math> -W*sin(θ) </math>

So we can write our equilibrium equation like this:

<math> Fnetx = f - W*sin(θ) = 0 </math>

Then, all we have to do is solve for <math> f </math>, since <math> W </math> and <math> θ </math> are known quantities.

<math> f = W*sin(θ) = (98</math> N<math>)*sin(20°) = 33.51797405</math> N, which is about equal to <math>33.5</math> N.

Now we have to solve for the normal force. It acts in the positive y direction, and we know that the net force in the y direction has to be zero, so we have to identify the other forces that act in the positive or negative y direction. In this case, the only one is the other component of the weight, which points in the negative y direction. Using simple trigonometry, we find that that is

<math> -W*cos(θ) </math>

So we can write our equilibrium equation like this:

<math> Fnety = N - W*cos(θ) = 0 </math>

Then, all we have to do is solve for <math> N </math>, since <math> W </math> and <math> θ </math> are known quantities.

<math> N = W*cos(θ) = (98</math> N<math>)*cos(20°) = 92.08987684</math> N, which is about equal to <math>92.1</math> N.

=Connectedness=
Net force is one of the building blocks of Intro Physics, and I would assume all of physics. It's really important for all motion-related topics, specifically [[Curving Motion]]. A net force due to the gravitational pull of the Sun in the perpendicular direction is how the Earth revolves around the Sun -- why we have days and nights and years! We can see from the derivative form of the Momentum Principle that any change in momentum is due to a nonzero net force acting on a system. All changes in motion can be attributed to a net force acting in some direction. 
<math> dP/dt=Fnet </math> (<math>P</math> is the symbol for momentum.)

My major is biomedical engineering, and I haven't taken any BME classes yet, but physics is a requirement so it has to be relevant. Statics is also a requirement for BMEs, and that class deals with net force in every single problem because you have to be able to analyze systems and structures based on the forces they provide and support.

=History=

Some of the earliest records of humans' musings about force come from Aristotle. Aristotle observed the natural world and made assumptions and equations based on what he saw. He described all motion as being either "natural"--circular and infinite OR finite, up and down, in a straight line--or "violent." Aristotle had issues with projectile motion as he could not reconcile the continuing movement of the object with the lack of force being applied. He ended up concluding that the air provides a simultaneous resistant and accelerating force to the object. 

These ideas were challenged by Renaissance men such as John Philoponus, John Buridan, and Oresme, with a clear understanding of the conservation of linear momentum not arriving to the world until Descartes. The most famous face we associate with forces in Physics is Sir Isaac Newton, and he certainly played a huge role in the understanding of net force and momentum. However, he initially believed in the idea of impetus, that a projectile has a certain internal force that keeps it moving, and also the idea of transfer, that objects give up parts of their force during a collision. Though he was wrong, these ideas are not at all silly--in fact they seem quite logical--and he later corrected them after a series of experiments. Thus, the second law of motion was established and with it the relationship between force and motion.

== See also ==
These other wiki pages might help: 
[[Momentum Principle]] 
[[Conservation of Momentum]] 
[[Newton's Laws and Linear Momentum]]

===External links===
[http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Determining-the-Net-Force Physics Classroom: Net Force]
[http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Drawing-Free-Body-Diagrams Physics Classroom: Drawing Free Body Diagrams]

==References==

Cardenas, Richard. "What is Net Force? - Definition, Magnitude & Equations." Web. 30 Nov 2015. http://study.com/academy/lesson/what-is-net-force-definition-magnitude-equations.html 

"Net Force." Wikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc. Web. 30 Nov 2015. https://en.wikipedia.org/wiki/Net_force 

The Physics Classroom. "Determining the Net Force." Web. 30 Nov 2015. http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Determining-the-Net-Force 

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. Modern Mechanics. Hoboken, NJ: Wiley, 2011. Print. 

Stinner, Arthur. "The story of force: from Aristotle to Einstein." Physics Education. 1994. Web. 30 Nov 2015. http://www.arthurstinner.com/stinner/pdfs/1994-storyofforce.pdf 
[[Category:Which Category did you place this in?]]

File:Net force wiki 6.PNG

2016-04-14T00:36:05Z

Lbond9:

File:Net force wiki 5.PNG

2016-04-14T00:29:30Z

Lbond9:

File:Net force wiki 4.PNG

2016-04-14T00:27:38Z

Lbond9:

Net Force

2016-04-12T18:45:49Z

Lbond9: I am added a more difficult sample problem.

by Julia Logan

editing claimed by Leila Bond

==Definition==

===A Mathematical Model===
In order to calculate net force, all EXTERNAL forces acting on a system are added together. The mathematical definition is <center><math> Fnet = F1 + F2 + F3... </math></center>
Additionally,
<center><math> Fnet = ma </math> 
where m=mass of the object, and a = acceleration of the object.</center>
This is a result of Newton's Second Law of motion. If there is a nonzero net force acting on an object, that object is accelerating (not traveling at a constant velocity). Interestingly, there is zero net force acting on an object if its velocity is constant. This seems counter-intuitive (surely something is causing the object to move!) but makes sense in the context of Newton's Second Law. The forces are balanced (sum to zero) if there is no acceleration, despite any movement that may be happening.

===A Computational Model===

Net force is an essential component of the Momentum Principle! We can use the Momentum Principle in vpython to update the position of a moving object. But first, we have to find net force.
[[File:netforce.png|200px|thumb|left|Tracing the path of a ball/spring model in vpython using net force and the momentum principle.]]

#1 Fspring = -k*s
#2 Fgravmag = mball * g
#3 Fgrav = Fgravmag * vector(0,-1,0)
#4 Fnet = Fspring+Fgrav
#5 pball = pball + Fnet * deltat
#6 vball = pball / mball
#7 ball.pos=ball.pos+vball*deltat

Here, the spring force and the gravitational force are found using formulas (lines 1-3). Then, they are added together to get the net force on the object (in this case a ball, line 4). The net force is then used in the update form of the momentum principle (line 5). In line 6 the velocity is updated, and line 7 the position is updated. Without net force calculations, tracing an object's path would be impossible.
 
 
 
 
 

=Simple Example=
When calculating net force, it is most useful to construct a free body diagram. A free body diagram is a physical representation of the external forces applied to a system. Often, arrows are used to represent forces. In this example, forces are displayed acting on a box.

[[File:forcediagram.gif]]

The first two boxes' net force can be easily calculated by adding the two forces acting on them, respectively. With down being in the negative y direction, for the first box we have: 

<math> Fnet = (0, 1200, 0) N + (0, -800, 0) N </math> 
<math> Fnet = (0, 400, 0) N </math> 

And the second box: 

<math> Fnet = (0, 600, 0) N + (0, -800, 0) N </math> 
<math> Fnet = (0, -200, 0) N </math> 

The third box has both x-component forces and y-component forces. It is important to separate these in solving for the net force. 
y-components: 
<math> Fnet,y = (0, 50, 0) N + (0, -50, 0) N </math> 
<math> Fnet,y = (0, 0, 0) N </math> 
x-components: 
<math> Fnet,x = (-20, 0, 0) N + (0, 0, 0) N </math> 
Put them together: 
<math> Fnet = (-20, 0, 0) N </math> 

=More Complicated Example=
There is a box, small enough to represented as a point, sitting on a slope inclined twenty degrees with respect to the horizontal. If its mass is 10 kg, what does the magnitude of the force of static friction (pointing up the hill) have to be for net force to be zero? In that case, what is the magnitude of the normal force? (All forces are measured in newtons, and the acceleration due to gravity <math> = g = 9.8</math> <math>m/(s^2) </math>).

Let <math> f </math> = force of friction, <math> W </math> = weight of the object, and <math> N = </math> normal force. (The pictures are not to scale.)

[[File:Net_force_wiki_1.PNG]]

First, we have to identify our coordinate axes. We could have the typical horizontal x-axis and vertical y-axis (and we know where to put <math>θ</math> using similar triangles):

[[File:Net_force_wiki_2.png]]

But, that leaves us with two forces that have to be decomposed into x- and y- components. It makes more sense to draw the axes rotated twenty degrees counterclockwise, like this:

[[File:Net_force_wiki_3.png]]

<math> W </math> is easy to find, since it's just mass times acceleration due to gravity, both of which are known quantities.

<math> W = mg = (10</math> <math>kg)*(9.8</math> <math>m/(s^2)) = 98</math> <math>newtons </math>

Now we are ready to solve for the frictional force. It acts in the positive x direction, and we know that the net force in the x direction has to be zero, so we have to identify the other forces that act in the positive or negative x direction. In this case, it's only a component of the weight, which points in the negative x direction. Using simple trigonometry, we find that that is

<math> -W*sin(θ) </math>

So we can write our equilibrium equation like this:

<math> Fnetx = f - W*sin(θ) = 0 </math>

Then, all we have to do is solve for <math> f </math>, since <math> W </math> and <math> θ </math> are known quantities.

<math> f = W*sin(θ) = (98</math> N<math>)*sin(20°) = 33.51797405</math> N, which is about equal to <math>33.5</math> N.

Now we have to solve for the normal force. It acts in the positive y direction, and we know that the net force in the y direction has to be zero, so we have to identify the other forces that act in the positive or negative y direction. In this case, the only one is the other component of the weight, which points in the negative y direction. Using simple trigonometry, we find that that is

<math> -W*cos(θ) </math>

So we can write our equilibrium equation like this:

<math> Fnety = N - W*cos(θ) = 0 </math>

Then, all we have to do is solve for <math> N </math>, since <math> W </math> and <math> θ </math> are known quantities.

<math> N = W*cos(θ) = (98</math> N<math>)*cos(20°) = 92.08987684</math> N, which is about equal to <math>92.1</math> N.

=Connectedness=
Net force is one of the building blocks of Intro Physics, and I would assume all of physics. It's really important for all motion-related topics, specifically [[Curving Motion]]. A net force due to the gravitational pull of the Sun in the perpendicular direction is how the Earth revolves around the Sun -- why we have days and nights and years! We can see from the derivative form of the Momentum Principle that any change in momentum is due to a nonzero net force acting on a system. All changes in motion can be attributed to a net force acting in some direction. 

<math> dP/dt=Fnet </math>

=History=

Some of the earliest records of humans' musings about force come from Aristotle. Aristotle observed the natural world and made assumptions and equations based on what he saw. He described all motion as being either "natural"--circular and infinite OR finite, up and down, in a straight line--or "violent." Aristotle had issues with projectile motion as he could not reconcile the continuing movement of the object with the lack of force being applied. He ended up concluding that the air provides a simultaneous resistant and accelerating force to the object. 

These ideas were challenged by Renaissance men such as John Philoponus, John Buridan, and Oresme, with a clear understanding of the conservation of linear momentum not arriving to the world until Descartes. The most famous face we associate with forces in Physics is Sir Isaac Newton, and he certainly played a huge role in the understanding of net force and momentum. However, he initially believed in the idea of impetus, that a projectile has a certain internal force that keeps it moving, and also the idea of transfer, that objects give up parts of their force during a collision. Though he was wrong, these ideas are not at all silly--in fact they seem quite logical--and he later corrected them after a series of experiments. Thus, the second law of motion was established and with it the relationship between force and motion.

== See also ==
These other wiki pages might help: 
[[Momentum Principle]] 
[[Conservation of Momentum]] 
[[Newton's Laws and Linear Momentum]]

===External links===
[http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Determining-the-Net-Force Physics Classroom: Net Force]
[http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Drawing-Free-Body-Diagrams Physics Classroom: Drawing Free Body Diagrams]

==References==

Cardenas, Richard. "What is Net Force? - Definition, Magnitude & Equations." Web. 30 Nov 2015. http://study.com/academy/lesson/what-is-net-force-definition-magnitude-equations.html 

"Net Force." Wikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc. Web. 30 Nov 2015. https://en.wikipedia.org/wiki/Net_force 

The Physics Classroom. "Determining the Net Force." Web. 30 Nov 2015. http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Determining-the-Net-Force 

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. Modern Mechanics. Hoboken, NJ: Wiley, 2011. Print. 

Stinner, Arthur. "The story of force: from Aristotle to Einstein." Physics Education. 1994. Web. 30 Nov 2015. http://www.arthurstinner.com/stinner/pdfs/1994-storyofforce.pdf 
[[Category:Which Category did you place this in?]]

File:Net force wiki 3.png

2016-04-12T18:45:00Z

Lbond9: Net force more difficult example, picture 3

Net force more difficult example, picture 3

Net Force

2016-04-12T18:28:21Z

Lbond9: I am in the process of adding a more difficult sample problem.

by Julia Logan

editing claimed by Leila Bond

==Definition==

===A Mathematical Model===
In order to calculate net force, all EXTERNAL forces acting on a system are added together. The mathematical definition is <center><math> Fnet = F1 + F2 + F3... </math></center>
Additionally,
<center><math> Fnet = ma </math> 
where m=mass of the object, and a = acceleration of the object.</center>
This is a result of Newton's Second Law of motion. If there is a nonzero net force acting on an object, that object is accelerating (not traveling at a constant velocity). Interestingly, there is zero net force acting on an object if its velocity is constant. This seems counter-intuitive (surely something is causing the object to move!) but makes sense in the context of Newton's Second Law. The forces are balanced (sum to zero) if there is no acceleration, despite any movement that may be happening.

===A Computational Model===

Net force is an essential component of the Momentum Principle! We can use the Momentum Principle in vpython to update the position of a moving object. But first, we have to find net force.
[[File:netforce.png|200px|thumb|left|Tracing the path of a ball/spring model in vpython using net force and the momentum principle.]]

#1 Fspring = -k*s
#2 Fgravmag = mball * g
#3 Fgrav = Fgravmag * vector(0,-1,0)
#4 Fnet = Fspring+Fgrav
#5 pball = pball + Fnet * deltat
#6 vball = pball / mball
#7 ball.pos=ball.pos+vball*deltat

Here, the spring force and the gravitational force are found using formulas (lines 1-3). Then, they are added together to get the net force on the object (in this case a ball, line 4). The net force is then used in the update form of the momentum principle (line 5). In line 6 the velocity is updated, and line 7 the position is updated. Without net force calculations, tracing an object's path would be impossible.
 
 
 
 
 

=Simple Example=
When calculating net force, it is most useful to construct a free body diagram. A free body diagram is a physical representation of the external forces applied to a system. Often, arrows are used to represent forces. In this example, forces are displayed acting on a box.

[[File:forcediagram.gif]]

The first two boxes' net force can be easily calculated by adding the two forces acting on them, respectively. With down being in the negative y direction, for the first box we have: 

<math> Fnet = (0, 1200, 0) N + (0, -800, 0) N </math> 
<math> Fnet = (0, 400, 0) N </math> 

And the second box: 

<math> Fnet = (0, 600, 0) N + (0, -800, 0) N </math> 
<math> Fnet = (0, -200, 0) N </math> 

The third box has both x-component forces and y-component forces. It is important to separate these in solving for the net force. 
y-components: 
<math> Fnet,y = (0, 50, 0) N + (0, -50, 0) N </math> 
<math> Fnet,y = (0, 0, 0) N </math> 
x-components: 
<math> Fnet,x = (-20, 0, 0) N + (0, 0, 0) N </math> 
Put them together: 
<math> Fnet = (-20, 0, 0) N </math> 

=More Complicated Example=
There is a box, small enough to represented as a point, sitting on a slope inclined twenty degrees with respect to the horizontal. If its mass is 10 kg, what does the magnitude of the force of static friction (pointing up the hill) have to be for net force to be zero? In that case, what is the magnitude of the normal force? (All forces are measured in newtons, and the acceleration due to gravity <math> = g = 9.8</math> <math>m/(s^2) </math>).

Let <math> f </math> = force of friction, <math> W </math> = weight of the object, and <math> N = </math> normal force. (The pictures are not to scale.)

[[File:Net_force_wiki_1.PNG]]

First, we have to identify our coordinate axes. We could have the typical horizontal x-axis and vertical y-axis (and we know where to put <math>θ</math> using similar triangles):

[[File:Net_force_wiki_2.PNG]]

But, that leaves us with two forces that have to be decomposed into x- and y- components. It makes more sense to draw the axes rotated twenty degrees counterclockwise, like this:

(picture3)

<math> W </math> is easy to find, since it's just mass times acceleration due to gravity, both of which are known quantities.

<math> W = mg = (10</math> <math>kg)*(9.8</math> <math>m/(s^2)) = 98</math> <math>newtons </math>

Now we are ready to solve for the frictional force. It acts in the positive x direction, and we know that the net force in the x direction has to be zero, so we have to identify the other forces that act in the positive or negative x direction. In this case, it's only a component of the weight, which points in the negative x direction. Using simple trigonometry, we find that that is

<math> -W*sin(θ) </math>

So we can write our equilibrium equation like this:

<math> Fnetx = f - W*sin(θ) = 0 </math>

Then, all we have to do is solve for <math> f </math>, since <math> W </math> and <math> θ </math> are known quantities.

<math> f = W*sin(θ) = (98</math> N<math>)*sin(20°) = 33.51797405</math> N, which is about equal to <math>33.5</math> N.

Now we have to solve for the normal force. It acts in the positive y direction, and we know that the net force in the y direction has to be zero, so we have to identify the other forces that act in the positive or negative y direction. In this case, the only one is the other component of the weight, which points in the negative y direction. Using simple trigonometry, we find that that is

<math> -W*cos(θ) </math>

So we can write our equilibrium equation like this:

<math> Fnety = N - W*cos(θ) = 0 </math>

Then, all we have to do is solve for <math> N </math>, since <math> W </math> and <math> θ </math> are known quantities.

<math> N = W*cos(θ) = (98</math> N<math>)*cos(20°) = 92.08987684</math> N, which is about equal to <math>92.1</math> N.

=Connectedness=
Net force is one of the building blocks of Intro Physics, and I would assume all of physics. It's really important for all motion-related topics, specifically [[Curving Motion]]. A net force due to the gravitational pull of the Sun in the perpendicular direction is how the Earth revolves around the Sun -- why we have days and nights and years! We can see from the derivative form of the Momentum Principle that any change in momentum is due to a nonzero net force acting on a system. All changes in motion can be attributed to a net force acting in some direction. 

<math> dP/dt=Fnet </math>

=History=

Some of the earliest records of humans' musings about force come from Aristotle. Aristotle observed the natural world and made assumptions and equations based on what he saw. He described all motion as being either "natural"--circular and infinite OR finite, up and down, in a straight line--or "violent." Aristotle had issues with projectile motion as he could not reconcile the continuing movement of the object with the lack of force being applied. He ended up concluding that the air provides a simultaneous resistant and accelerating force to the object. 

These ideas were challenged by Renaissance men such as John Philoponus, John Buridan, and Oresme, with a clear understanding of the conservation of linear momentum not arriving to the world until Descartes. The most famous face we associate with forces in Physics is Sir Isaac Newton, and he certainly played a huge role in the understanding of net force and momentum. However, he initially believed in the idea of impetus, that a projectile has a certain internal force that keeps it moving, and also the idea of transfer, that objects give up parts of their force during a collision. Though he was wrong, these ideas are not at all silly--in fact they seem quite logical--and he later corrected them after a series of experiments. Thus, the second law of motion was established and with it the relationship between force and motion.

== See also ==
These other wiki pages might help: 
[[Momentum Principle]] 
[[Conservation of Momentum]] 
[[Newton's Laws and Linear Momentum]]

===External links===
[http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Determining-the-Net-Force Physics Classroom: Net Force]
[http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Drawing-Free-Body-Diagrams Physics Classroom: Drawing Free Body Diagrams]

==References==

Cardenas, Richard. "What is Net Force? - Definition, Magnitude & Equations." Web. 30 Nov 2015. http://study.com/academy/lesson/what-is-net-force-definition-magnitude-equations.html 

"Net Force." Wikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc. Web. 30 Nov 2015. https://en.wikipedia.org/wiki/Net_force 

The Physics Classroom. "Determining the Net Force." Web. 30 Nov 2015. http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Determining-the-Net-Force 

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. Modern Mechanics. Hoboken, NJ: Wiley, 2011. Print. 

Stinner, Arthur. "The story of force: from Aristotle to Einstein." Physics Education. 1994. Web. 30 Nov 2015. http://www.arthurstinner.com/stinner/pdfs/1994-storyofforce.pdf 
[[Category:Which Category did you place this in?]]

File:Net force wiki 2.png

2016-04-12T18:24:19Z

Lbond9: Net force more difficult example, picture 2

Net force more difficult example, picture 2

File:Net force wiki 1.PNG

2016-04-12T18:22:42Z

Lbond9: Net force more difficult example, picture 1

Net force more difficult example, picture 1

Net Force

2016-04-12T18:12:26Z

Lbond9: I am in the process of adding a more difficult sample problem.

by Julia Logan

editing claimed by Leila Bond

==Definition==

===A Mathematical Model===
In order to calculate net force, all EXTERNAL forces acting on a system are added together. The mathematical definition is <center><math> Fnet = F1 + F2 + F3... </math></center>
Additionally,
<center><math> Fnet = ma </math> 
where m=mass of the object, and a = acceleration of the object.</center>
This is a result of Newton's Second Law of motion. If there is a nonzero net force acting on an object, that object is accelerating (not traveling at a constant velocity). Interestingly, there is zero net force acting on an object if its velocity is constant. This seems counter-intuitive (surely something is causing the object to move!) but makes sense in the context of Newton's Second Law. The forces are balanced (sum to zero) if there is no acceleration, despite any movement that may be happening.

===A Computational Model===

Net force is an essential component of the Momentum Principle! We can use the Momentum Principle in vpython to update the position of a moving object. But first, we have to find net force.
[[File:netforce.png|200px|thumb|left|Tracing the path of a ball/spring model in vpython using net force and the momentum principle.]]

#1 Fspring = -k*s
#2 Fgravmag = mball * g
#3 Fgrav = Fgravmag * vector(0,-1,0)
#4 Fnet = Fspring+Fgrav
#5 pball = pball + Fnet * deltat
#6 vball = pball / mball
#7 ball.pos=ball.pos+vball*deltat

Here, the spring force and the gravitational force are found using formulas (lines 1-3). Then, they are added together to get the net force on the object (in this case a ball, line 4). The net force is then used in the update form of the momentum principle (line 5). In line 6 the velocity is updated, and line 7 the position is updated. Without net force calculations, tracing an object's path would be impossible.
 
 
 
 
 

=Simple Example=
When calculating net force, it is most useful to construct a free body diagram. A free body diagram is a physical representation of the external forces applied to a system. Often, arrows are used to represent forces. In this example, forces are displayed acting on a box.

[[File:forcediagram.gif]]

The first two boxes' net force can be easily calculated by adding the two forces acting on them, respectively. With down being in the negative y direction, for the first box we have: 

<math> Fnet = (0, 1200, 0) N + (0, -800, 0) N </math> 
<math> Fnet = (0, 400, 0) N </math> 

And the second box: 

<math> Fnet = (0, 600, 0) N + (0, -800, 0) N </math> 
<math> Fnet = (0, -200, 0) N </math> 

The third box has both x-component forces and y-component forces. It is important to separate these in solving for the net force. 
y-components: 
<math> Fnet,y = (0, 50, 0) N + (0, -50, 0) N </math> 
<math> Fnet,y = (0, 0, 0) N </math> 
x-components: 
<math> Fnet,x = (-20, 0, 0) N + (0, 0, 0) N </math> 
Put them together: 
<math> Fnet = (-20, 0, 0) N </math> 

=More Complicated Example=
There is a box, small enough to represented as a point, sitting on a slope inclined twenty degrees with respect to the horizontal. If its mass is 10 kg, what does the magnitude of the force of static friction (pointing up the hill) have to be for net force to be zero? In that case, what is the magnitude of the normal force? (All forces are measured in newtons, and the acceleration due to gravity <math> = g = 9.8</math> <math>m/(s^2) </math>).

Let <math> f </math> = force of friction, <math> W </math> = weight of the object, and <math> N = </math> normal force.

(there will be a picture here)

First, we have to identify our coordinate axes. We could have the typical horizontal x-axis and vertical y-axis (and we know where to put <math>θ</math> using similar triangles):

(picture)

But, that leaves us with two forces that have to be decomposed into x- and y- components. It makes more sense to draw the axes rotated twenty degrees counterclockwise, like this:

(picture)

<math> W </math> is easy to find, since it's just mass times acceleration due to gravity, both of which are known quantities.

<math> W = mg = (10</math> <math>kg)*(9.8</math> <math>m/(s^2)) = 98</math> <math>newtons </math>

Now we are ready to solve for the frictional force. It acts in the positive x direction, and we know that the net force in the x direction has to be zero, so we have to identify the other forces that act in the positive or negative x direction. In this case, it's only a component of the weight, which points in the negative x direction. Using simple trigonometry, we find that that is

<math> -W*sin(θ) </math>

So we can write our equilibrium equation like this:

<math> Fnetx = f - W*sin(θ) = 0 </math>

Then, all we have to do is solve for <math> f </math>, since <math> W </math> and <math> θ </math> are known quantities.

<math> f = W*sin(θ) = (98</math> N<math>)*sin(20°) = 33.51797405</math> N, which is about equal to <math>33.5</math> N.

Now we have to solve for the normal force. It acts in the positive y direction, and we know that the net force in the y direction has to be zero, so we have to identify the other forces that act in the positive or negative y direction. In this case, the only one is the other component of the weight, which points in the negative y direction. Using simple trigonometry, we find that that is

<math> -W*cos(θ) </math>

So we can write our equilibrium equation like this:

<math> Fnety = N - W*cos(θ) = 0 </math>

Then, all we have to do is solve for <math> N </math>, since <math> W </math> and <math> θ </math> are known quantities.

<math> N = W*cos(θ) = (98</math> N<math>)*cos(20°) = 92.08987684</math> N, which is about equal to <math>92.1</math> N.

=Connectedness=
Net force is one of the building blocks of Intro Physics, and I would assume all of physics. It's really important for all motion-related topics, specifically [[Curving Motion]]. A net force due to the gravitational pull of the Sun in the perpendicular direction is how the Earth revolves around the Sun -- why we have days and nights and years! We can see from the derivative form of the Momentum Principle that any change in momentum is due to a nonzero net force acting on a system. All changes in motion can be attributed to a net force acting in some direction. 

<math> dP/dt=Fnet </math>

=History=

Some of the earliest records of humans' musings about force come from Aristotle. Aristotle observed the natural world and made assumptions and equations based on what he saw. He described all motion as being either "natural"--circular and infinite OR finite, up and down, in a straight line--or "violent." Aristotle had issues with projectile motion as he could not reconcile the continuing movement of the object with the lack of force being applied. He ended up concluding that the air provides a simultaneous resistant and accelerating force to the object. 

These ideas were challenged by Renaissance men such as John Philoponus, John Buridan, and Oresme, with a clear understanding of the conservation of linear momentum not arriving to the world until Descartes. The most famous face we associate with forces in Physics is Sir Isaac Newton, and he certainly played a huge role in the understanding of net force and momentum. However, he initially believed in the idea of impetus, that a projectile has a certain internal force that keeps it moving, and also the idea of transfer, that objects give up parts of their force during a collision. Though he was wrong, these ideas are not at all silly--in fact they seem quite logical--and he later corrected them after a series of experiments. Thus, the second law of motion was established and with it the relationship between force and motion.

== See also ==
These other wiki pages might help: 
[[Momentum Principle]] 
[[Conservation of Momentum]] 
[[Newton's Laws and Linear Momentum]]

===External links===
[http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Determining-the-Net-Force Physics Classroom: Net Force]
[http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Drawing-Free-Body-Diagrams Physics Classroom: Drawing Free Body Diagrams]

==References==

Cardenas, Richard. "What is Net Force? - Definition, Magnitude & Equations." Web. 30 Nov 2015. http://study.com/academy/lesson/what-is-net-force-definition-magnitude-equations.html 

"Net Force." Wikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc. Web. 30 Nov 2015. https://en.wikipedia.org/wiki/Net_force 

The Physics Classroom. "Determining the Net Force." Web. 30 Nov 2015. http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Determining-the-Net-Force 

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. Modern Mechanics. Hoboken, NJ: Wiley, 2011. Print. 

Stinner, Arthur. "The story of force: from Aristotle to Einstein." Physics Education. 1994. Web. 30 Nov 2015. http://www.arthurstinner.com/stinner/pdfs/1994-storyofforce.pdf 
[[Category:Which Category did you place this in?]]

Net Force

2016-04-11T23:38:26Z

Lbond9: I am in the process of adding a more difficult sample problem.

by Julia Logan

editing claimed by Leila Bond

==Definition==

===A Mathematical Model===
In order to calculate net force, all EXTERNAL forces acting on a system are added together. The mathematical definition is <center><math> Fnet = F1 + F2 + F3... </math></center>
Additionally,
<center><math> Fnet = ma </math> 
where m=mass of the object, and a = acceleration of the object.</center>
This is a result of Newton's Second Law of motion. If there is a nonzero net force acting on an object, that object is accelerating (not traveling at a constant velocity). Interestingly, there is zero net force acting on an object if its velocity is constant. This seems counter-intuitive (surely something is causing the object to move!) but makes sense in the context of Newton's Second Law. The forces are balanced (sum to zero) if there is no acceleration, despite any movement that may be happening.

===A Computational Model===

Net force is an essential component of the Momentum Principle! We can use the Momentum Principle in vpython to update the position of a moving object. But first, we have to find net force.
[[File:netforce.png|200px|thumb|left|Tracing the path of a ball/spring model in vpython using net force and the momentum principle.]]

#1 Fspring = -k*s
#2 Fgravmag = mball * g
#3 Fgrav = Fgravmag * vector(0,-1,0)
#4 Fnet = Fspring+Fgrav
#5 pball = pball + Fnet * deltat
#6 vball = pball / mball
#7 ball.pos=ball.pos+vball*deltat

Here, the spring force and the gravitational force are found using formulas (lines 1-3). Then, they are added together to get the net force on the object (in this case a ball, line 4). The net force is then used in the update form of the momentum principle (line 5). In line 6 the velocity is updated, and line 7 the position is updated. Without net force calculations, tracing an object's path would be impossible.
 
 
 
 
 

=Simple Example=
When calculating net force, it is most useful to construct a free body diagram. A free body diagram is a physical representation of the external forces applied to a system. Often, arrows are used to represent forces. In this example, forces are displayed acting on a box.

[[File:forcediagram.gif]]

The first two boxes' net force can be easily calculated by adding the two forces acting on them, respectively. With down being in the negative y direction, for the first box we have: 

<math> Fnet = (0, 1200, 0) N + (0, -800, 0) N </math> 
<math> Fnet = (0, 400, 0) N </math> 

And the second box: 

<math> Fnet = (0, 600, 0) N + (0, -800, 0) N </math> 
<math> Fnet = (0, -200, 0) N </math> 

The third box has both x-component forces and y-component forces. It is important to separate these in solving for the net force. 
y-components: 
<math> Fnet,y = (0, 50, 0) N + (0, -50, 0) N </math> 
<math> Fnet,y = (0, 0, 0) N </math> 
x-components: 
<math> Fnet,x = (-20, 0, 0) N + (0, 0, 0) N </math> 
Put them together: 
<math> Fnet = (-20, 0, 0) N </math> 

=More Complicated Example=
There is a box, small enough to represented as a point, sitting on a slope inclined twenty degrees with respect to the horizontal. If its mass is 10 kg, what does the magnitude of the force of static friction (pointing up the hill) have to be for net force to be zero? In that case, what is the magnitude of the normal force? (All forces are measured in newtons, and the acceleration due to gravity <math> = g = 9.8</math> <math>m/(s^2) </math>).

Let <math> f </math> = force of friction, <math> W </math> = weight of the object, and <math> N = </math> normal force.

(there will be a picture here)

First, we have to identify our coordinate axes. We could have the typical horizontal x-axis and vertical y-axis:

(picture)

But, that leaves us with two forces that have to be decomposed into x- and y- components. It makes more sense to draw the axes rotated twenty degrees counterclockwise, like this:

(picture)

<math> W </math> is easy to find, since it's just mass times acceleration due to gravity, both of which are known quantities.

<math> W = mg = (10</math> <math>kg)*(9.8</math> <math>m/(s^2)) = 98</math> <math>newtons </math>

Now we are ready to solve for the frictional force. It acts in the positive x direction, and we know that the net force in the x direction has to be zero, so we have to identify the other forces that act in the positive or negative x direction. In this case, it's only a component of the weight, which points in the negative x direction. Using simple trigonometry, we find that that is

<math> -W*sin(θ) </math>

So we can write our equilibrium equation like this:

<math> Fnetx = f - W*sin(θ) = 0 </math>

Then, all we have to do is solve for <math> f </math>, since <math> W </math> and <math> θ </math> are known quantities.

<math> f = W*sin(θ) = (98</math> N<math>)*sin(20°) = 33.51797405</math> N, which is about equal to <math>33.5</math> N.

Now we have to solve for the normal force. It acts in the positive y direction, and we know that the net force in the y direction has to be zero, so we have to identify the other forces that act in the positive or negative y direction. In this case, the only one is the other component of the weight, which points in the negative y direction. Using simple trigonometry, we find that that is

<math> -W*cos(θ) </math>

So we can write our equilibrium equation like this:

<math> Fnety = N - W*cos(θ) = 0 </math>

Then, all we have to do is solve for <math> N </math>, since <math> W </math> and <math> θ </math> are known quantities.

<math> N = W*cos(θ) = (98</math> N<math>)*cos(20°) = 92.08987684</math> N, which is about equal to <math>92.1</math> N.

=Connectedness=
Net force is one of the building blocks of Intro Physics, and I would assume all of physics. It's really important for all motion-related topics, specifically [[Curving Motion]]. A net force due to the gravitational pull of the Sun in the perpendicular direction is how the Earth revolves around the Sun -- why we have days and nights and years! We can see from the derivative form of the Momentum Principle that any change in momentum is due to a nonzero net force acting on a system. All changes in motion can be attributed to a net force acting in some direction. 

<math> dP/dt=Fnet </math>

=History=

Some of the earliest records of humans' musings about force come from Aristotle. Aristotle observed the natural world and made assumptions and equations based on what he saw. He described all motion as being either "natural"--circular and infinite OR finite, up and down, in a straight line--or "violent." Aristotle had issues with projectile motion as he could not reconcile the continuing movement of the object with the lack of force being applied. He ended up concluding that the air provides a simultaneous resistant and accelerating force to the object. 

These ideas were challenged by Renaissance men such as John Philoponus, John Buridan, and Oresme, with a clear understanding of the conservation of linear momentum not arriving to the world until Descartes. The most famous face we associate with forces in Physics is Sir Isaac Newton, and he certainly played a huge role in the understanding of net force and momentum. However, he initially believed in the idea of impetus, that a projectile has a certain internal force that keeps it moving, and also the idea of transfer, that objects give up parts of their force during a collision. Though he was wrong, these ideas are not at all silly--in fact they seem quite logical--and he later corrected them after a series of experiments. Thus, the second law of motion was established and with it the relationship between force and motion.

== See also ==
These other wiki pages might help: 
[[Momentum Principle]] 
[[Conservation of Momentum]] 
[[Newton's Laws and Linear Momentum]]

===External links===
[http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Determining-the-Net-Force Physics Classroom: Net Force]
[http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Drawing-Free-Body-Diagrams Physics Classroom: Drawing Free Body Diagrams]

==References==

Cardenas, Richard. "What is Net Force? - Definition, Magnitude & Equations." Web. 30 Nov 2015. http://study.com/academy/lesson/what-is-net-force-definition-magnitude-equations.html 

"Net Force." Wikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc. Web. 30 Nov 2015. https://en.wikipedia.org/wiki/Net_force 

The Physics Classroom. "Determining the Net Force." Web. 30 Nov 2015. http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Determining-the-Net-Force 

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. Modern Mechanics. Hoboken, NJ: Wiley, 2011. Print. 

Stinner, Arthur. "The story of force: from Aristotle to Einstein." Physics Education. 1994. Web. 30 Nov 2015. http://www.arthurstinner.com/stinner/pdfs/1994-storyofforce.pdf 
[[Category:Which Category did you place this in?]]

Net Force

2016-04-11T23:02:15Z

Lbond9: I'm in the process of making the more difficult sample question

by Julia Logan

editing claimed by Leila Bond

==Definition==

===A Mathematical Model===
In order to calculate net force, all EXTERNAL forces acting on a system are added together. The mathematical definition is <center><math> Fnet = F1 + F2 + F3... </math></center>
Additionally,
<center><math> Fnet = ma </math> 
where m=mass of the object, and a = acceleration of the object.</center>
This is a result of Newton's Second Law of motion. If there is a nonzero net force acting on an object, that object is accelerating (not traveling at a constant velocity). Interestingly, there is zero net force acting on an object if its velocity is constant. This seems counter-intuitive (surely something is causing the object to move!) but makes sense in the context of Newton's Second Law. The forces are balanced (sum to zero) if there is no acceleration, despite any movement that may be happening.

===A Computational Model===

Net force is an essential component of the Momentum Principle! We can use the Momentum Principle in vpython to update the position of a moving object. But first, we have to find net force.
[[File:netforce.png|200px|thumb|left|Tracing the path of a ball/spring model in vpython using net force and the momentum principle.]]

#1 Fspring = -k*s
#2 Fgravmag = mball * g
#3 Fgrav = Fgravmag * vector(0,-1,0)
#4 Fnet = Fspring+Fgrav
#5 pball = pball + Fnet * deltat
#6 vball = pball / mball
#7 ball.pos=ball.pos+vball*deltat

Here, the spring force and the gravitational force are found using formulas (lines 1-3). Then, they are added together to get the net force on the object (in this case a ball, line 4). The net force is then used in the update form of the momentum principle (line 5). In line 6 the velocity is updated, and line 7 the position is updated. Without net force calculations, tracing an object's path would be impossible.
 
 
 
 
 

=Simple Example=
When calculating net force, it is most useful to construct a free body diagram. A free body diagram is a physical representation of the external forces applied to a system. Often, arrows are used to represent forces. In this example, forces are displayed acting on a box.

[[File:forcediagram.gif]]

The first two boxes' net force can be easily calculated by adding the two forces acting on them, respectively. With down being in the negative y direction, for the first box we have: 

<math> Fnet = (0, 1200, 0) N + (0, -800, 0) N </math> 
<math> Fnet = (0, 400, 0) N </math> 

And the second box: 

<math> Fnet = (0, 600, 0) N + (0, -800, 0) N </math> 
<math> Fnet = (0, -200, 0) N </math> 

The third box has both x-component forces and y-component forces. It is important to separate these in solving for the net force. 
y-components: 
<math> Fnet,y = (0, 50, 0) N + (0, -50, 0) N </math> 
<math> Fnet,y = (0, 0, 0) N </math> 
x-components: 
<math> Fnet,x = (-20, 0, 0) N + (0, 0, 0) N </math> 
Put them together: 
<math> Fnet = (-20, 0, 0) N </math> 

=More Complicated Example=
There is a box, small enough to represented as a point, sitting on a slope inclined twenty degrees with respect to the horizontal. If its mass is 10 kg, what does the magnitude of the force of static friction (pointing up the hill) have to be for net force to be zero? In that case, what is the magnitude of the normal force? (All forces are measured in newtons, and the acceleration due to gravity <math> = g = 9.8</math> <math>m/(s^2) </math>).

Let <math> f </math> = force of friction, <math> W </math> = weight of the object, and <math> N = </math> normal force.

(there will be a picture here)

First, we have to identify our coordinate axes. We could have the typical horizontal x-axis and vertical y-axis:

(picture)

But, that leaves us with two forces that have to be decomposed into x- and y- components. It makes more sense to draw the axes rotated twenty degrees counterclockwise, like this:

(picture)

<math> W </math> is easy to find, since it's just mass times acceleration due to gravity, both of which are known quantities.

<math> W = mg = (10</math> <math>kg)*(9.8</math> <math>m/(s^2)) = 98</math> <math>newtons </math>

Now we are ready to solve for the frictional force. It acts in the positive x direction, and we know that the net force in the x direction has to be zero, so we have to identify the other forces that act in the positive or negative x direction. In this case, it's only a component of the weight, which points in the negative x direction. Using simple trigonometry, we find that that is

<math> -W*sin(θ) </math>

So we can write our equilibrium equation like this:

<math> Fnetx = f - W*sin(θ) = 0 </math>

Then, all we have to do is solve for <math> f </math>, since <math> W </math> and <math> θ </math> are given quantities.

=Connectedness=
Net force is one of the building blocks of Intro Physics, and I would assume all of physics. It's really important for all motion-related topics, specifically [[Curving Motion]]. A net force due to the gravitational pull of the Sun in the perpendicular direction is how the Earth revolves around the Sun -- why we have days and nights and years! We can see from the derivative form of the Momentum Principle that any change in momentum is due to a nonzero net force acting on a system. All changes in motion can be attributed to a net force acting in some direction. 

<math> dP/dt=Fnet </math>

=History=

Some of the earliest records of humans' musings about force come from Aristotle. Aristotle observed the natural world and made assumptions and equations based on what he saw. He described all motion as being either "natural"--circular and infinite OR finite, up and down, in a straight line--or "violent." Aristotle had issues with projectile motion as he could not reconcile the continuing movement of the object with the lack of force being applied. He ended up concluding that the air provides a simultaneous resistant and accelerating force to the object. 

These ideas were challenged by Renaissance men such as John Philoponus, John Buridan, and Oresme, with a clear understanding of the conservation of linear momentum not arriving to the world until Descartes. The most famous face we associate with forces in Physics is Sir Isaac Newton, and he certainly played a huge role in the understanding of net force and momentum. However, he initially believed in the idea of impetus, that a projectile has a certain internal force that keeps it moving, and also the idea of transfer, that objects give up parts of their force during a collision. Though he was wrong, these ideas are not at all silly--in fact they seem quite logical--and he later corrected them after a series of experiments. Thus, the second law of motion was established and with it the relationship between force and motion.

== See also ==
These other wiki pages might help: 
[[Momentum Principle]] 
[[Conservation of Momentum]] 
[[Newton's Laws and Linear Momentum]]

===External links===
[http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Determining-the-Net-Force Physics Classroom: Net Force]
[http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Drawing-Free-Body-Diagrams Physics Classroom: Drawing Free Body Diagrams]

==References==

Cardenas, Richard. "What is Net Force? - Definition, Magnitude & Equations." Web. 30 Nov 2015. http://study.com/academy/lesson/what-is-net-force-definition-magnitude-equations.html 

"Net Force." Wikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc. Web. 30 Nov 2015. https://en.wikipedia.org/wiki/Net_force 

The Physics Classroom. "Determining the Net Force." Web. 30 Nov 2015. http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Determining-the-Net-Force 

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. Modern Mechanics. Hoboken, NJ: Wiley, 2011. Print. 

Stinner, Arthur. "The story of force: from Aristotle to Einstein." Physics Education. 1994. Web. 30 Nov 2015. http://www.arthurstinner.com/stinner/pdfs/1994-storyofforce.pdf 
[[Category:Which Category did you place this in?]]

Net Force

2016-04-11T22:08:17Z

Lbond9:

by Julia Logan

editing claimed by Leila Bond

==Definition==

===A Mathematical Model===
In order to calculate net force, all EXTERNAL forces acting on a system are added together. The mathematical definition is <center><math> Fnet = F1 + F2 + F3... </math></center>
Additionally,
<center><math> Fnet = ma </math> 
where m=mass of the object, and a = acceleration of the object.</center>
This is a result of Newton's Second Law of motion. If there is a nonzero net force acting on an object, that object is accelerating (not traveling at a constant velocity). Interestingly, there is zero net force acting on an object if its velocity is constant. This seems counter-intuitive (surely something is causing the object to move!) but makes sense in the context of Newton's Second Law. The forces are balanced (sum to zero) if there is no acceleration, despite any movement that may be happening.

===A Computational Model===

Net force is an essential component of the Momentum Principle! We can use the Momentum Principle in vpython to update the position of a moving object. But first, we have to find net force.
[[File:netforce.png|200px|thumb|left|Tracing the path of a ball/spring model in vpython using net force and the momentum principle.]]

#1 Fspring = -k*s
#2 Fgravmag = mball * g
#3 Fgrav = Fgravmag * vector(0,-1,0)
#4 Fnet = Fspring+Fgrav
#5 pball = pball + Fnet * deltat
#6 vball = pball / mball
#7 ball.pos=ball.pos+vball*deltat

Here, the spring force and the gravitational force are found using formulas (lines 1-3). Then, they are added together to get the net force on the object (in this case a ball, line 4). The net force is then used in the update form of the momentum principle (line 5). In line 6 the velocity is updated, and line 7 the position is updated. Without net force calculations, tracing an object's path would be impossible.
 
 
 
 
 

=Simple Example=
When calculating net force, it is most useful to construct a free body diagram. A free body diagram is a physical representation of the external forces applied to a system. Often, arrows are used to represent forces. In this example, forces are displayed acting on a box.

[[File:forcediagram.gif]]

The first two boxes' net force can be easily calculated by adding the two forces acting on them, respectively. With down being in the negative y direction, for the first box we have: 

<math> Fnet = (0, 1200, 0) N + (0, -800, 0) N </math> 
<math> Fnet = (0, 400, 0) N </math> 

And the second box: 

<math> Fnet = (0, 600, 0) N + (0, -800, 0) N </math> 
<math> Fnet = (0, -200, 0) N </math> 

The third box has both x-component forces and y-component forces. It is important to separate these in solving for the net force. 
y-components: 
<math> Fnet,y = (0, 50, 0) N + (0, -50, 0) N </math> 
<math> Fnet,y = (0, 0, 0) N </math> 
x-components: 
<math> Fnet,x = (-20, 0, 0) N + (0, 0, 0) N </math> 
Put them together: 
<math> Fnet = (-20, 0, 0) N </math> 

=More Complicated Example=
There is a box, small enough to represented as a point, sitting on a slope inclined twenty degrees with respect to the horizontal. If its mass is 10 kg, what does the magnitude of the force of static friction (pointing up the hill) have to be for net force to be zero? In that case, what is the magnitude of the normal force?

(there will be a picture here)

First, we have to identify our coordinate axes. We could have the typical horizontal x-axis and vertical y-axis:

(picture)

But, that leaves us with two forces that have to be decomposed into x- and y- components. It makes more sense to draw the axes rotated twenty degrees counterclockwise, like this:

(picture)

Now we are ready to solve for the frictional force. It acts in the positive x direction, and we know that the net force in the x direction has to be zero, so we have to identify the other forces that act in the positive or negative x direction. In this case, it's only a component of the weight, which points in the negative x direction. Using simple trigonometry, we find that that is

<math> -W*sin(θ) </math>

So we can write our equilibrium equation like this

=Connectedness=
Net force is one of the building blocks of Intro Physics, and I would assume all of physics. It's really important for all motion-related topics, specifically [[Curving Motion]]. A net force due to the gravitational pull of the Sun in the perpendicular direction is how the Earth revolves around the Sun -- why we have days and nights and years! We can see from the derivative form of the Momentum Principle that any change in momentum is due to a nonzero net force acting on a system. All changes in motion can be attributed to a net force acting in some direction. 

<math> dP/dt=Fnet </math>

=History=

Some of the earliest records of humans' musings about force come from Aristotle. Aristotle observed the natural world and made assumptions and equations based on what he saw. He described all motion as being either "natural"--circular and infinite OR finite, up and down, in a straight line--or "violent." Aristotle had issues with projectile motion as he could not reconcile the continuing movement of the object with the lack of force being applied. He ended up concluding that the air provides a simultaneous resistant and accelerating force to the object. 

These ideas were challenged by Renaissance men such as John Philoponus, John Buridan, and Oresme, with a clear understanding of the conservation of linear momentum not arriving to the world until Descartes. The most famous face we associate with forces in Physics is Sir Isaac Newton, and he certainly played a huge role in the understanding of net force and momentum. However, he initially believed in the idea of impetus, that a projectile has a certain internal force that keeps it moving, and also the idea of transfer, that objects give up parts of their force during a collision. Though he was wrong, these ideas are not at all silly--in fact they seem quite logical--and he later corrected them after a series of experiments. Thus, the second law of motion was established and with it the relationship between force and motion.

== See also ==
These other wiki pages might help: 
[[Momentum Principle]] 
[[Conservation of Momentum]] 
[[Newton's Laws and Linear Momentum]]

===External links===
[http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Determining-the-Net-Force Physics Classroom: Net Force]
[http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Drawing-Free-Body-Diagrams Physics Classroom: Drawing Free Body Diagrams]

==References==

Cardenas, Richard. "What is Net Force? - Definition, Magnitude & Equations." Web. 30 Nov 2015. http://study.com/academy/lesson/what-is-net-force-definition-magnitude-equations.html 

"Net Force." Wikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc. Web. 30 Nov 2015. https://en.wikipedia.org/wiki/Net_force 

The Physics Classroom. "Determining the Net Force." Web. 30 Nov 2015. http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Determining-the-Net-Force 

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. Modern Mechanics. Hoboken, NJ: Wiley, 2011. Print. 

Stinner, Arthur. "The story of force: from Aristotle to Einstein." Physics Education. 1994. Web. 30 Nov 2015. http://www.arthurstinner.com/stinner/pdfs/1994-storyofforce.pdf 
[[Category:Which Category did you place this in?]]

Net Force

2016-04-11T21:43:29Z

Lbond9: I am in the process of adding a more difficult sample problem and I fixed the format of some of the headings.

Net Force

2016-04-11T21:19:23Z

Lbond9: