Physics Book - User contributions [en]

Relative Velocity

2017-04-10T03:15:40Z

Rajpatel486:

Claimed by Lily Masters (Fall 2016)

Edited by Raj Patel (Spring 2017)

The motion of an object looks different based on the line of sight. This is known as a reference frame.

==Reference Frame==

Reference frames can be used to change how problems are seen.

[[File:Wikipage_pic.PNG]]

A car moving left to one person can also be moving right to another person on the other side of the road. A frame of reference like this is known as an observational frame of reference. Differences in reference frames can result in problems varying slightly from person to person. On a coordinate axis, one reference frame may show direction to the left as moving along the negative x-axis while another may show that direction as moving along the positive x-axis.

==Relative Velocity==

When an object is moving in a medium that is also moving, its velocity may be different depending on the location of the observer. For example, consider a boat moving through a flowing river. If the observer is aboard the boat, the velocity will be different than if the observer was standing by the side of the river. This can be more easily described through vector addition with one reference frame considered an intermediate reference frame:

<math>\vec{v}_{AC} = \vec{v}_{AB} + \vec{v}_{BC}</math>

This means that the velocity of A with respect to C is equal to the sum of the velocity of A with respect to B and the velocity of B with respect to C. In this case, B is the intermediate reference frame.

==Examples==

===Airplane in Wind===

[[File:planewind.gif]]

An airplane is flying with a velocity of <math>\vec{v}_{PA}</math> relative to the air. The wind is moving with a velocity of <math>\vec{v}_{AG}</math> relative to an observer on the ground. The velocity of the plane relative to the ground can be found using vector addition:

<math>\vec{v}_{PG} = \vec{v}_{PA} + \vec{v}_{AG}</math>

Suppose the plane is moving with a velocity of <math>\left \langle {150,20,0} \right \rangle</math> km/h relative to the air. The wind is moving with a velocity of <math>\left \langle {-25,0,-10} \right \rangle</math> km/h relative to the ground. What is the velocity of the plane relative to the ground?

Answer:

<math>\vec{v}_{PG} = \left \langle {150,20,0} \right \rangle + \left \langle {-25,0,-10} \right \rangle</math>

<math>\vec{v}_{PG} = \left \langle {125,20,-10} \right \rangle</math>

===Boat in Current===

[[File:boatc4.gif]]

A boat is moving straight across a river with a velocity of <math>\vec{v}_{BW}</math> relative to the water. The river has a current flowing perpendicular to the boat which has a velocity of <math>\vec{v}_{WE}</math> relative to the earth. The velocity of the boat relative to the Earth can be found using vector addition and the bearing of the boat can be found using trig relations:

<math>\vec{v}_{BE} = \vec{v}_{BW} + \vec{v}_{WE}</math>

<math>\Theta = \arctan \frac{\left \Vert \vec{v}_{WE} \right \|}{\left \Vert \vec{v}_{BW} \right \|}</math>

Suppose the boat is moving straight across the river with a velocity of 37 m/s relative to the water and the current is moving downstream and perpendicular to the boat with a velocity of 4 m/s relative to the earth. What is the velocity of the boat relative to the earth and what is its bearing?

Answer:

<math>\vec{v}_{BE} = \left \langle {37,0,0} \right \rangle + \left \langle {0,-4,0} \right \rangle</math>

<math>\vec{v}_{BE} = \left \langle {37,-4,0} \right \rangle</math>

<math>\Theta = \arctan \frac{4}{37}</math>

<math>\Theta = 6.17018^\circ</math>

== See also ==
*[[Velocity]]
*[[Speed and Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]

===External links===
[http://hyperphysics.phy-astr.gsu.edu/hbase/relmot.html#c1 HyperPhysics: Relative Motion]

==References==
[http://hyperphysics.phy-astr.gsu.edu/hbase/relmot.html#c1 HyperPhysics: Relative Motion]

[https://commons.wikimedia.org/wiki/File:Wikipage_pic.PNG Example from Frame of Reference]

[[Category:Velocity and Momentum]]

Relative Velocity

2017-04-10T02:59:48Z

Rajpatel486:

Claimed by Lily Masters (Fall 2016)

Edited by Raj Patel (Spring 2017)

The motion of an object looks different based on the line of sight. This is known as a reference frame.

==Reference Frame==

Reference frames can be used to change how problems are seen.

[[File:Wikipage_pic.PNG]]

A car moving left to one person can also be moving right to another person on the other side of the road. Differences in reference frames can result in problems varying slightly from person to person.

==Relative Velocity==

When an object is moving in a medium that is also moving, its velocity may be different depending on the location of the observer. For example, consider a boat moving through a flowing river. If the observer is aboard the boat, the velocity will be different than if the observer was standing by the side of the river. This can be more easily described through vector addition with one reference frame considered an intermediate reference frame:

<math>\vec{v}_{AC} = \vec{v}_{AB} + \vec{v}_{BC}</math>

This means that the velocity of A with respect to C is equal to the sum of the velocity of A with respect to B and the velocity of B with respect to C. In this case, B is the intermediate reference frame.

==Examples==

===Airplane in Wind===

[[File:planewind.gif]]

An airplane is flying with a velocity of <math>\vec{v}_{PA}</math> relative to the air. The wind is moving with a velocity of <math>\vec{v}_{AG}</math> relative to an observer on the ground. The velocity of the plane relative to the ground can be found using vector addition:

<math>\vec{v}_{PG} = \vec{v}_{PA} + \vec{v}_{AG}</math>

Suppose the plane is moving with a velocity of <math>\left \langle {150,20,0} \right \rangle</math> km/h relative to the air. The wind is moving with a velocity of <math>\left \langle {-25,0,-10} \right \rangle</math> km/h relative to the ground. What is the velocity of the plane relative to the ground?

Answer:

<math>\vec{v}_{PG} = \left \langle {150,20,0} \right \rangle + \left \langle {-25,0,-10} \right \rangle</math>

<math>\vec{v}_{PG} = \left \langle {125,20,-10} \right \rangle</math>

===Boat in Current===

[[File:boatc4.gif]]

A boat is moving straight across a river with a velocity of <math>\vec{v}_{BW}</math> relative to the water. The river has a current flowing perpendicular to the boat which has a velocity of <math>\vec{v}_{WE}</math> relative to the earth. The velocity of the boat relative to the Earth can be found using vector addition and the bearing of the boat can be found using trig relations:

<math>\vec{v}_{BE} = \vec{v}_{BW} + \vec{v}_{WE}</math>

<math>\Theta = \arctan \frac{\left \Vert \vec{v}_{WE} \right \|}{\left \Vert \vec{v}_{BW} \right \|}</math>

Suppose the boat is moving straight across the river with a velocity of 37 m/s relative to the water and the current is moving downstream and perpendicular to the boat with a velocity of 4 m/s relative to the earth. What is the velocity of the boat relative to the earth and what is its bearing?

Answer:

<math>\vec{v}_{BE} = \left \langle {37,0,0} \right \rangle + \left \langle {0,-4,0} \right \rangle</math>

<math>\vec{v}_{BE} = \left \langle {37,-4,0} \right \rangle</math>

<math>\Theta = \arctan \frac{4}{37}</math>

<math>\Theta = 6.17018^\circ</math>

== See also ==
*[[Velocity]]
*[[Speed and Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]

===External links===
[http://hyperphysics.phy-astr.gsu.edu/hbase/relmot.html#c1 HyperPhysics: Relative Motion]

==References==
[http://hyperphysics.phy-astr.gsu.edu/hbase/relmot.html#c1 HyperPhysics: Relative Motion]

[https://commons.wikimedia.org/wiki/File:Wikipage_pic.PNG Example from Frame of Reference]

[[Category:Velocity and Momentum]]

Relative Velocity

2017-04-10T02:58:50Z

Rajpatel486:

Claimed by Lily Masters (Fall 2016)

Edited by Raj Patel (Spring 2017)

The motion of an object looks different based on the line of sight. This is known as a reference frame.

==Reference Frame==

Reference frames can be used to change how problems are seen.

[[File:Wikipage_pic.PNG]]

A car moving left to one person can also be moving right to another person on the other side of the road. Differences in reference frames can result in problems varying slightly from person to person.

==Relative Velocity==

When an object is moving in a medium that is also moving, its velocity may be different depending on the location of the observer. For example, consider a boat moving through a flowing river. If the observer is aboard the boat, the velocity will be different than if the observer was standing by the side of the river. This can be more easily described through vector addition with one reference frame considered an intermediate reference frame:

<math>\vec{v}_{AC} = \vec{v}_{AB} + \vec{v}_{BC}</math>

This means that the velocity of A with respect to C is equal to the sum of the velocity of A with respect to B and the velocity of B with respect to C. In this case, B is the intermediate reference frame.

==Examples==

===Airplane in Wind===

[[File:planewind.gif]]

An airplane is flying with a velocity of <math>\vec{v}_{PA}</math> relative to the air. The wind is moving with a velocity of <math>\vec{v}_{AG}</math> relative to an observer on the ground. The velocity of the plane relative to the ground can be found using vector addition:

<math>\vec{v}_{PG} = \vec{v}_{PA} + \vec{v}_{AG}</math>

Suppose the plane is moving with a velocity of <math>\left \langle {150,20,0} \right \rangle</math> km/h relative to the air. The wind is moving with a velocity of <math>\left \langle {-25,0,-10} \right \rangle</math> km/h relative to the ground. What is the velocity of the plane relative to the ground?

Answer:

<math>\vec{v}_{PG} = \left \langle {150,20,0} \right \rangle + \left \langle {-25,0,-10} \right \rangle</math>

<math>\vec{v}_{PG} = \left \langle {125,20,-10} \right \rangle</math>

===Boat in Current===

[[File:boatc4.gif]]

A boat is moving straight across a river with a velocity of <math>\vec{v}_{BW}</math> relative to the water. The river has a current flowing perpendicular to the boat which has a velocity of <math>\vec{v}_{WE}</math> relative to the earth. The velocity of the boat relative to the Earth can be found using vector addition and the bearing of the boat can be found using trig relations:

<math>\vec{v}_{BE} = \vec{v}_{BW} + \vec{v}_{WE}</math>

<math>\Theta = \arctan \frac{\left \Vert \vec{v}_{WE} \right \|}{\left \Vert \vec{v}_{BW} \right \|}</math>

Suppose the boat is moving straight across the river with a velocity of 37 m/s relative to the water and the current is moving downstream and perpendicular to the boat with a velocity of 4 m/s relative to the earth. What is the velocity of the boat relative to the earth and what is its bearing?

Answer:

<math>\vec{v}_{BE} = \left \langle {37,0,0} \right \rangle + \left \langle {0,-4,0} \right \rangle</math>

<math>\vec{v}_{BE} = \left \langle {37,-4,0} \right \rangle</math>

<math>\Theta = \arctan \frac{4}{37}</math>

<math>\Theta = 6.17018^\circ</math>

== See also ==
*[[Velocity]]
*[[Speed and Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]

===External links===
[http://hyperphysics.phy-astr.gsu.edu/hbase/relmot.html#c1 HyperPhysics: Relative Motion]

==References==
[http://hyperphysics.phy-astr.gsu.edu/hbase/relmot.html#c1 HyperPhysics: Relative Motion]

[https://en.wikipedia.org/wiki/Frame_of_reference#Additional_example Example from Frame of Reference]

[[Category:Velocity and Momentum]]

Relative Velocity

2017-04-10T02:52:30Z

Rajpatel486:

Claimed by Lily Masters (Fall 2016)

Edited by Raj Patel (Spring 2017)

The motion of an object looks different based on the line of sight. This is known as a reference frame.

==Reference Frame==

Reference frames can be used to change how problems are seen.

[[File:Wikipage_pic.PNG]]

A car moving left to one person can also be moving right to another person on the other side of the road. Differences in reference frames can result in problems varying slightly from person to person.

==Relative Velocity==

When an object is moving in a medium that is also moving, its velocity may be different depending on the location of the observer. For example, consider a boat moving through a flowing river. If the observer is aboard the boat, the velocity will be different than if the observer was standing by the side of the river. This can be more easily described through vector addition with one reference frame considered an intermediate reference frame:

<math>\vec{v}_{AC} = \vec{v}_{AB} + \vec{v}_{BC}</math>

This means that the velocity of A with respect to C is equal to the sum of the velocity of A with respect to B and the velocity of B with respect to C. In this case, B is the intermediate reference frame.

==Examples==

===Airplane in Wind===

[[File:planewind.gif]]

An airplane is flying with a velocity of <math>\vec{v}_{PA}</math> relative to the air. The wind is moving with a velocity of <math>\vec{v}_{AG}</math> relative to an observer on the ground. The velocity of the plane relative to the ground can be found using vector addition:

<math>\vec{v}_{PG} = \vec{v}_{PA} + \vec{v}_{AG}</math>

Suppose the plane is moving with a velocity of <math>\left \langle {150,20,0} \right \rangle</math> km/h relative to the air. The wind is moving with a velocity of <math>\left \langle {-25,0,-10} \right \rangle</math> km/h relative to the ground. What is the velocity of the plane relative to the ground?

Answer:

<math>\vec{v}_{PG} = \left \langle {150,20,0} \right \rangle + \left \langle {-25,0,-10} \right \rangle</math>

<math>\vec{v}_{PG} = \left \langle {125,20,-10} \right \rangle</math>

===Boat in Current===

[[File:boatc4.gif]]

A boat is moving straight across a river with a velocity of <math>\vec{v}_{BW}</math> relative to the water. The river has a current flowing perpendicular to the boat which has a velocity of <math>\vec{v}_{WE}</math> relative to the earth. The velocity of the boat relative to the Earth can be found using vector addition and the bearing of the boat can be found using trig relations:

<math>\vec{v}_{BE} = \vec{v}_{BW} + \vec{v}_{WE}</math>

<math>\Theta = \arctan \frac{\left \Vert \vec{v}_{WE} \right \|}{\left \Vert \vec{v}_{BW} \right \|}</math>

Suppose the boat is moving straight across the river with a velocity of 37 m/s relative to the water and the current is moving downstream and perpendicular to the boat with a velocity of 4 m/s relative to the earth. What is the velocity of the boat relative to the earth and what is its bearing?

Answer:

<math>\vec{v}_{BE} = \left \langle {37,0,0} \right \rangle + \left \langle {0,-4,0} \right \rangle</math>

<math>\vec{v}_{BE} = \left \langle {37,-4,0} \right \rangle</math>

<math>\Theta = \arctan \frac{4}{37}</math>

<math>\Theta = 6.17018^\circ</math>

== See also ==
*[[Velocity]]
*[[Speed and Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]

===External links===
[http://hyperphysics.phy-astr.gsu.edu/hbase/relmot.html#c1 HyperPhysics: Relative Motion]

==References==
[http://hyperphysics.phy-astr.gsu.edu/hbase/relmot.html#c1 HyperPhysics: Relative Motion]

[[Category:Velocity and Momentum]]

Relative Velocity

2017-04-10T01:49:18Z

Rajpatel486:

Claimed by Lily Masters (Fall 2016)

Edited by Raj Patel (Spring 2017)

The motion of an object looks different based on the line of sight. This is known as a reference frame.

==Relative Velocity==

When an object is moving in a medium that is also moving, its velocity may be different depending on the location of the observer. For example, consider a boat moving through a flowing river. If the observer is aboard the boat, the velocity will be different than if the observer was standing by the side of the river. This can be more easily described through vector addition with one reference frame considered an intermediate reference frame:

<math>\vec{v}_{AC} = \vec{v}_{AB} + \vec{v}_{BC}</math>

This means that the velocity of A with respect to C is equal to the sum of the velocity of A with respect to B and the velocity of B with respect to C. In this case, B is the intermediate reference frame.

==Examples==

===Airplane in Wind===

[[File:planewind.gif]]

An airplane is flying with a velocity of <math>\vec{v}_{PA}</math> relative to the air. The wind is moving with a velocity of <math>\vec{v}_{AG}</math> relative to an observer on the ground. The velocity of the plane relative to the ground can be found using vector addition:

<math>\vec{v}_{PG} = \vec{v}_{PA} + \vec{v}_{AG}</math>

Suppose the plane is moving with a velocity of <math>\left \langle {150,20,0} \right \rangle</math> km/h relative to the air. The wind is moving with a velocity of <math>\left \langle {-25,0,-10} \right \rangle</math> km/h relative to the ground. What is the velocity of the plane relative to the ground?

Answer:

<math>\vec{v}_{PG} = \left \langle {150,20,0} \right \rangle + \left \langle {-25,0,-10} \right \rangle</math>

<math>\vec{v}_{PG} = \left \langle {125,20,-10} \right \rangle</math>

===Boat in Current===

[[File:boatc4.gif]]

A boat is moving straight across a river with a velocity of <math>\vec{v}_{BW}</math> relative to the water. The river has a current flowing perpendicular to the boat which has a velocity of <math>\vec{v}_{WE}</math> relative to the earth. The velocity of the boat relative to the Earth can be found using vector addition and the bearing of the boat can be found using trig relations:

<math>\vec{v}_{BE} = \vec{v}_{BW} + \vec{v}_{WE}</math>

<math>\Theta = \arctan \frac{\left \Vert \vec{v}_{WE} \right \|}{\left \Vert \vec{v}_{BW} \right \|}</math>

Suppose the boat is moving straight across the river with a velocity of 37 m/s relative to the water and the current is moving downstream and perpendicular to the boat with a velocity of 4 m/s relative to the earth. What is the velocity of the boat relative to the earth and what is its bearing?

Answer:

<math>\vec{v}_{BE} = \left \langle {37,0,0} \right \rangle + \left \langle {0,-4,0} \right \rangle</math>

<math>\vec{v}_{BE} = \left \langle {37,-4,0} \right \rangle</math>

<math>\Theta = \arctan \frac{4}{37}</math>

<math>\Theta = 6.17018^\circ</math>

== See also ==
*[[Velocity]]
*[[Speed and Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]

===External links===
[http://hyperphysics.phy-astr.gsu.edu/hbase/relmot.html#c1 HyperPhysics: Relative Motion]

==References==
[http://hyperphysics.phy-astr.gsu.edu/hbase/relmot.html#c1 HyperPhysics: Relative Motion]

[[Category:Velocity and Momentum]]

Relative Velocity

2017-04-10T01:31:11Z

Rajpatel486:

Claimed by Lily Masters (Fall 2016)

Edited by Raj Patel (Spring 2017)

The motion of an object may look different when viewed from a different reference frame. This can be described by defining the relative velocity of the reference frame.

==Relative Velocity==

When an object is moving in a medium that is also moving, its velocity may be different depending on the location of the observer. For example, consider a boat moving through a flowing river. If the observer is aboard the boat, the velocity will be different than if the observer was standing by the side of the river. This can be more easily described through vector addition with one reference frame considered an intermediate reference frame:

<math>\vec{v}_{AC} = \vec{v}_{AB} + \vec{v}_{BC}</math>

This means that the velocity of A with respect to C is equal to the sum of the velocity of A with respect to B and the velocity of B with respect to C. In this case, B is the intermediate reference frame.

==Examples==

===Airplane in Wind===

[[File:planewind.gif]]

An airplane is flying with a velocity of <math>\vec{v}_{PA}</math> relative to the air. The wind is moving with a velocity of <math>\vec{v}_{AG}</math> relative to an observer on the ground. The velocity of the plane relative to the ground can be found using vector addition:

<math>\vec{v}_{PG} = \vec{v}_{PA} + \vec{v}_{AG}</math>

Suppose the plane is moving with a velocity of <math>\left \langle {150,20,0} \right \rangle</math> km/h relative to the air. The wind is moving with a velocity of <math>\left \langle {-25,0,-10} \right \rangle</math> km/h relative to the ground. What is the velocity of the plane relative to the ground?

Answer:

<math>\vec{v}_{PG} = \left \langle {150,20,0} \right \rangle + \left \langle {-25,0,-10} \right \rangle</math>

<math>\vec{v}_{PG} = \left \langle {125,20,-10} \right \rangle</math>

===Boat in Current===

[[File:boatc4.gif]]

A boat is moving straight across a river with a velocity of <math>\vec{v}_{BW}</math> relative to the water. The river has a current flowing perpendicular to the boat which has a velocity of <math>\vec{v}_{WE}</math> relative to the earth. The velocity of the boat relative to the Earth can be found using vector addition and the bearing of the boat can be found using trig relations:

<math>\vec{v}_{BE} = \vec{v}_{BW} + \vec{v}_{WE}</math>

<math>\Theta = \arctan \frac{\left \Vert \vec{v}_{WE} \right \|}{\left \Vert \vec{v}_{BW} \right \|}</math>

Suppose the boat is moving straight across the river with a velocity of 37 m/s relative to the water and the current is moving downstream and perpendicular to the boat with a velocity of 4 m/s relative to the earth. What is the velocity of the boat relative to the earth and what is its bearing?

Answer:

<math>\vec{v}_{BE} = \left \langle {37,0,0} \right \rangle + \left \langle {0,-4,0} \right \rangle</math>

<math>\vec{v}_{BE} = \left \langle {37,-4,0} \right \rangle</math>

<math>\Theta = \arctan \frac{4}{37}</math>

<math>\Theta = 6.17018^\circ</math>

== See also ==
*[[Velocity]]
*[[Speed and Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]

===External links===
[http://hyperphysics.phy-astr.gsu.edu/hbase/relmot.html#c1 HyperPhysics: Relative Motion]

==References==
[http://hyperphysics.phy-astr.gsu.edu/hbase/relmot.html#c1 HyperPhysics: Relative Motion]

[[Category:Velocity and Momentum]]

Newton's First Law of Motion

2017-04-10T01:22:12Z

Rajpatel486:

'''Claimed by Vivekanand Rajasekar (Fall 2016)'''

'''Edited by Raj Patel (Spring 2017)'''

This topic covers Newton's First Law of Motion

==The Main Idea==

Newton's First law states that an object at rest will stay at rest and an object in motion will stay in motion with the same speed and direction unless acted upon by an unbalanced external force.

Also called the '''Law of Inertia''', the law states that it is the natural tendency for objects to remain on their current course.

===A Mathematical Model===

The first law states that if the Net Force acting on the object is zero, then there is no change in the velocity of the object. Velocity is a vector, which has both direction and magnitude, therefore if the Net Force is zero, neither the direction or magnitude can be changing.

This idea can be quantified in the following manner:
:<math>
\sum \mathbf{F} = 0\; \Leftrightarrow\; \frac{\mathrm{d} \mathbf{v} }{\mathrm{d}t} = 0.
</math>

However, there are two particular instances of the object that this law could apply to:

1) The object is at rest and will stay at rest (Magnitude of velocity = 0) unless a nonzero force acts upon it.

2) The object is in motion (Velocity does not equal zero) and will continue to be in motion with the same velocity, proceeding in the same straight line unless a nonzero force acts upon it.

===A Computational Model===
This model defines an object that is at rest. It has no external forces acting on it, therefore its velocity is not changing:

mass=9
NetForce=vector(0,0,0)
t=0
deltat=.1
position=vector(0,0,0)
velocity=vector(0,0,0)
while t<6:
velocity=(mass*velocity+NetForce*deltat)/mass
t=t+deltat
print("New Velocity: ",velocity)

This model defines an object that is moving, but has no external forces acting on it, therefore its velocity is not changing:

mass=9
NetForce=vector(0,0,0)
t=0
deltat=.1
position=vector(0,0,0)
velocity=vector(10,10,10)
while t<6:
velocity=(mass*velocity+NetForce*deltat)/mass
t=t+deltat
print("New Velocity: ",velocity)

This model defines an object that is at rest, but has some nonzero external force, therefore, it experiences a change in velocity:

mass=9
NetForce=vector(10,10,10)
t=0
deltat=.1
position=vector(0,0,0)
velocity=vector(0,0,0)
while t<6:
velocity=(mass*velocity+NetForce*deltat)/mass
t=t+deltat
print("New Velocity: ",velocity)

This model defines an object that is moving, but also has some nonzero external force, therefore, it experiences a change in velocity.

mass=9
NetForce=vector(10,10,10)
t=0
deltat=.1
position=vector(0,0,0)
velocity=vector(10,10,10)
while t<6:
velocity=(mass*velocity+NetForce*deltat)/mass
t=t+deltat
print("New Velocity: ",velocity)

==Examples==

===Simple===

Let's do some examples and critical thinking similar to the book:

Question 1: In order to move a box with constant speed and direction across a table what do you have to do?

Answer: You would have to push the box the entire time across the table. With the same magnitude and direction of course. But why doesn't it just keep on moving after one push you ask? Well the net force on the box must equal zero for the box to continue moving at the same speed and in the same direction. So with the outside forces acting on the object, you would have to keep pushing to cancel them out and keep the motion of the object constant.

Question 2: Is a change in position an indicator of interaction?

Answer: Sometimes yes and sometimes no. It depends. If the change in position is a result of constant speed and direction of an object then no, it is not an indicator of an unbalanced force. Further data (like velocity at each position) would be needed to decide if an object is experiencing an interaction from an outside force.

===Medium===

Question: A gymnast is holding himself perfectly still in the cross position. The angle between the wires supporting the rings is 12 degrees from the vertical on each side. If his mass is 75kg calculate the tension in each wire.

Solution: Because the gymnast's velocity is zero and is not changing, we know that the Net Force equals zero. We know that the vertical components of the force must equal zero, so 2T*cos(12)=75*9.8. When we solve for T, we get 391.48N. Recognizing that lack of movement implies no external forces and a net force of zero is vital to solving this problem.

===Difficult===

Question: Suppose there exists a car of mass 9000 kg that is moving at a constant speed of 90 m/s in the positive x direction. If you know that the wheels provide a force of 1000 N to the right, what is the frictional constant and the normal force?

Solutions: First off, we need to recognize that there is no change in velocity, since the question so clearly mentions the word '''constant.''' Therefore, the net force is zero. This means the net force in the horizontal and vertical directions is zero. If we begin with the vertical component, we know that the normal force must equal the gravitational force. If not, the car would be moving towards the ground. So 9.8*9000 = Normal Force. This means, the normal force equals 88200 N. Now, to find the frictional force, we know that we are providing a force of 1000 N to the right. That must mean that to make the net horizontal force zero, the frictional force must be 1000 N to the left. Now, frictional force = frictional constant*normal force. So, constant=friction force/normal force. Constant= 1.

==Connectedness==

This topic is connected to every aspect of life. Every time you get in a car or drop something on the floor or trip over a rock Newton's First Law is demonstrating itself to you. The connections of this topic to the real world is an endless list of possibilities.

*Some magicians often have "tricked" their audiences into believing their great powers when in reality, it is nothing more than the skillful manipulation of Newton's First Law. For example, when a magician pulls out a tablecloth from plates on the table and the plates maintain their initial state of rest without any change in their velocities, some people might be fooled into believing in magic. However, any admirer of Newton would know that this is simply a manipulation of Newton's First Law. The object (the plates) were not in motion, and because the tablecloth was pulled out in such a manner that it does not exert a force onto the plates, the plates do not change velocities.

*In space, there are small objects that are floating in a straight line. They are far enough from any large objects that no gravitational force exists to effect their motion. So, because there is no external force and the object was moving, it keeps on moving in a straight line indefinitely. Although modern astronomers would argue that the object would eventually come in contact with another object of great size that would exert a significant gravitational force onto this object, other astronomers could argue about the nature of the universe and the possibility that the object could be moving at the edge of the universe where it is moving at the same speed as the expansion of the universe and therefore could indeed move forever without any change in its velocity.

==History==

This theory was originally discovered by Galileo who conducted experiments on the concepts of inertia and acceleration due to gravity. Galileo studied the movement of balls on smooth and rough surfaces, developing the idea of friction. Isaac Newton further studied these concepts and ideas and presented his 3 Laws of Motion. The first of these 3 laws, as we know, stated that an object in motion will stay in motion with the same speed and direction until an unbalanced force acts on it. And with the absence of friction or other forces, an object will continue moving forever.

From the original Latin of Newton's ''Principia'':
''Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.''

Translated to English, this reads:
"Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed."

*Aristotle, the Greek who had an opinion on everything, believed that all objects have a natural place. Heavy objects wanted to be at rest on the Earth and light objects like smoke wanted to be at rest in the sky. He even went so far as to hypothesize that stars belonged only in the heavens. He thought that the natural state of objects was at rest and that nothing could keep moving forever without an external force. He did not believe that an object, without any external forces, could keep moving forever.

*Galileo, a more enlightened man, believed that although an outside force was needed to change the velocity of an object, no force was necessary to maintain its object. It could keep moving forever if nothing acted on it.

*Newton, who formally stated the law in the fancy language of Latin and whose name is attached to the very law, actually did nothing more than simply restate the law of inertia which Galileo had already described. He even gave the appropriate credit to Galileo, but to this day, we refer to this law not as Galileo's First Law, but as Newton's.

==See Also==
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Kinds of Matter]]
*[[Detecting Interactions]]
*[[Fundamental Interactions]]
*[[System & Surroundings]]
*[[Gravitational Force]]

===Further reading or exploring===

Science of NFL Football: https://www.youtube.com/watch?v=08BFCZJDn9w

Real world application of Newton's First Law: https://www.youtube.com/watch?v=8zsE3mpZ6Hw

Everything you want to know about Newton's First Law of Motion: http://swift.sonoma.edu/education/newton/newton_1/html/newton1.html

===External links===

NASA can help you understand: https://www.grc.nasa.gov/www/k-12/airplane/newton1g.html

==References==

https://thescienceclassroom.wikispaces.com/Newton's+First+Law+of+Motion

http://teachertech.rice.edu/Participants/louviere/Newton/law1.html

Matter and Interactions: Modern Mechanics. Volume One. 4th Edition.

Page Created by: Brittney Vidal November 10, 2015 <-- For Credit

Page Edited by: Vivekanand Rajasekar November 27, 2015 <-- For Credit

Page Edited by: Raj Patel April 9, 2017 <-- Not For Credit

[[Interactions]]

Newton's First Law of Motion

2017-04-10T01:04:07Z

Rajpatel486:

'''Claimed by Raj Patel (Spring 2017)'''

This topic covers Newton's First Law of Motion

==The Main Idea==

Newton's First law states that an object at rest will stay at rest and an object in motion will stay in motion with the same speed and direction unless acted upon by an unbalanced external force.

Also called '''the Law of Inertia''', the law simply claims that there is a natural tendency of objects to keep on doing what they are doing.

===A Mathematical Model===

The first law states that if the Net Force acting on the object is zero, then there is no change in the velocity of the object. Velocity is a vector, which has both direction and magnitude, therefore if the Net Force is zero, neither the direction or magnitude can be changing.

This idea can be quantified in the following manner:
:<math>
\sum \mathbf{F} = 0\; \Leftrightarrow\; \frac{\mathrm{d} \mathbf{v} }{\mathrm{d}t} = 0.
</math>

However, there are two particular instances of the object that this law could apply to:

1) The object is at rest and will stay at rest (Magnitude of velocity = 0) unless a nonzero force acts upon it.

2) The object is in motion (Velocity does not equal zero) and will continue to be in motion with the same velocity, proceeding in the same straight line unless a nonzero force acts upon it.

===A Computational Model===
This model defines an object that is at rest. It has no external forces acting on it, therefore its velocity is not changing:

mass=9
NetForce=vector(0,0,0)
t=0
deltat=.1
position=vector(0,0,0)
velocity=vector(0,0,0)
while t<6:
velocity=(mass*velocity+NetForce*deltat)/mass
t=t+deltat
print("New Velocity: ",velocity)

This model defines an object that is moving, but has no external forces acting on it, therefore its velocity is not changing:

mass=9
NetForce=vector(0,0,0)
t=0
deltat=.1
position=vector(0,0,0)
velocity=vector(10,10,10)
while t<6:
velocity=(mass*velocity+NetForce*deltat)/mass
t=t+deltat
print("New Velocity: ",velocity)

This model defines an object that is at rest, but has some nonzero external force, therefore, it experiences a change in velocity:

mass=9
NetForce=vector(10,10,10)
t=0
deltat=.1
position=vector(0,0,0)
velocity=vector(0,0,0)
while t<6:
velocity=(mass*velocity+NetForce*deltat)/mass
t=t+deltat
print("New Velocity: ",velocity)

This model defines an object that is moving, but also has some nonzero external force, therefore, it experiences a change in velocity.

mass=9
NetForce=vector(10,10,10)
t=0
deltat=.1
position=vector(0,0,0)
velocity=vector(10,10,10)
while t<6:
velocity=(mass*velocity+NetForce*deltat)/mass
t=t+deltat
print("New Velocity: ",velocity)

==Examples==

===Simple===

Let's do some examples and critical thinking similar to the book:

Question 1: In order to move a box with constant speed and direction across a table what do you have to do?

Answer: You would have to push the box the entire time across the table. With the same magnitude and direction of course. But why doesn't it just keep on moving after one push you ask? Well the net force on the box must equal zero for the box to continue moving at the same speed and in the same direction. So with the outside forces acting on the object, you would have to keep pushing to cancel them out and keep the motion of the object constant.

Question 2: Is a change in position an indicator of interaction?

Answer: Sometimes yes and sometimes no. It depends. If the change in position is a result of constant speed and direction of an object then no, it is not an indicator of an unbalanced force. Further data (like velocity at each position) would be needed to decide if an object is experiencing an interaction from an outside force.

===Medium===

Question: A gymnast is holding himself perfectly still in the cross position. The angle between the wires supporting the rings is 12 degrees from the vertical on each side. If his mass is 75kg calculate the tension in each wire.

Solution: Because the gymnast's velocity is zero and is not changing, we know that the Net Force equals zero. We know that the vertical components of the force must equal zero, so 2Tcos(12)=75*9.8. When we solve for T, we get 391.48N. Recognizing that lack of movement implies no external forces and a net force of zero is vital to solving this problem.

===Difficult===

Question: Suppose there exists a car of mass 9000 kg that is moving at a constant speed of 90 m/s in the positive x direction. If you know that the wheels provide a force of 1000 N to the right, what is the frictional constant and the normal force?

Solutions: First off, we need to recognize that there is no change in velocity, since the question so clearly mentions the word '''constant.''' Therefore, the net force is zero. This means the net force in the horizontal and vertical directions is zero. If we begin with the vertical component, we know that the normal force must equal the gravitational force. If not, the car would be moving towards the ground. So 9.8*9000=Normal Force. This means, the normal force equals 88200 N. Now, to find the frictional force, we know that we are providing a force of 1000 N to the right. That must mean that to make the net horizontal force zero, the frictional force must be 1000 N to the left. Now, frictional force = frictional constant*normal force. So, constant=friction force/normal force. Constant= 1.

==Connectedness==

This topic is connected to every aspect of life. Every time you get in a car or drop something on the floor or trip over a rock Newton's First Law is demonstrating itself to you. The connections of this topic to the real world is an endless list of possibilities.

*Some magicians often have "tricked" their audiences into believing their great powers when in reality, it is nothing more than the skillful manipulation of Newton's First Law. For example, when a magician pulls out a tablecloth from plates on the table and the plates maintain their initial state of rest without any change in their velocities, some people might be fooled into believing in magic. However, any admirer of Newton would know that this is simply a manipulation of Newton's First Law. The object (the plates) were not in motion, and because the tablecloth was pulled out in such a manner that it does not exert a force onto the plates, the plates do not change velocities.

*In space, there are small objects that are floating in a straight line. They are far enough from any large objects that no gravitational force exists to effect their motion. So, because there is no external force and the object was moving, it keeps on moving in a straight line indefinitely. Although modern astronomers would argue that the object would eventually come in contact with another object of great size that would exert a significant gravitational force onto this object, other astronomers could argue about the nature of the universe and the possibility that the object could be moving at the edge of the universe where it is moving at the same speed as the expansion of the universe and therefore could indeed move forever without any change in its velocity.

==History==

This theory was originally discovered by Galileo who conducted experiments on the concepts of inertia and acceleration due to gravity. Galileo studied the movement of balls on smooth and rough surfaces, developing the idea of friction. Isaac Newton further studied these concepts and ideas and presented his 3 Laws of Motion. The first of these 3 laws, as we know, stated that an object in motion will stay in motion with the same speed and direction until an unbalanced force acts on it. And with the absence of friction or other forces, an object will continue moving forever.

From the original Latin of Newton's ''Principia'':
''Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.''

Translated to English, this reads:
"Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed."

*Aristotle, the Greek who had an opinion on everything, believed that all objects have a natural place. Heavy objects wanted to be at rest on the Earth and light objects like smoke wanted to be at rest in the sky. He even went so far as to hypothesize that stars belonged only in the heavens. He thought that the natural state of objects was at rest and that nothing could keep moving forever without an external force. He did not believe that an object, without any external forces, could keep moving forever.

*Galileo, a more enlightened man, believed that although an outside force was needed to change the velocity of an object, no force was necessary to maintain its object. It could keep moving forever if nothing acted on it.

*Newton, who formally stated the law in the fancy language of Latin and whose name is attached to the very law, actually did nothing more than simply restate the law of inertia which Galileo had already described. He even gave the appropriate credit to Galileo, but to this day, we refer to this law not as Galileo's First Law, but as Newton's.

==See Also==
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Kinds of Matter]]
*[[Detecting Interactions]]
*[[Fundamental Interactions]]
*[[System & Surroundings]]
*[[Gravitational Force]]

===Further reading or exploring===

Science of NFL Football: https://www.youtube.com/watch?v=08BFCZJDn9w

Real world application of Newton's First Law: https://www.youtube.com/watch?v=8zsE3mpZ6Hw

Everything you want to know about Newton's First Law of Motion: http://swift.sonoma.edu/education/newton/newton_1/html/newton1.html

===External links===

NASA can help you understand: https://www.grc.nasa.gov/www/k-12/airplane/newton1g.html

==References==

https://thescienceclassroom.wikispaces.com/Newton's+First+Law+of+Motion

http://teachertech.rice.edu/Participants/louviere/Newton/law1.html

Matter and Interactions: Modern Mechanics. Volume One. 4th Edition.

Page Created by: Brittney Vidal November 10, 2015 <-- For Credit

Page Edited by: Vivekanand Rajasekar November 27, 2015 <-- For Credit

[[Interactions]]