File:Springbox.png

2015-12-01T23:29:07Z

Akerrison3:

File:Spring in box.png

2015-12-01T23:28:05Z

Akerrison3:

Point Particle Systems

2015-12-01T23:27:11Z

Akerrison3: /* Jumper Model */

This topic has been claimed akerrison3.

==The Main Idea==

The point particle method of measuring changes in energy simplifies the system of interest down to a single point, or focuses on its center of mass. Therefore, the only energy changing in the system is translational kinetic energy. Translational kinetic energy is the energy that comes from an object moving from one location to another. This can then be used in the extended system of the object, which includes all energy transfers.

[[File:Cow_point.png|400 px]] Center of Mass of a Cow as a Point

===A Mathematical Model===

Translational kinetic energy is equal to [[File:Translational_kinetic_energy.png|50 px]], where '''M''' is mass and '''v''' is the velocity of the center of mass.

The change in translational kinetic energy is equal to [[File:Change_in_trans.png|50 px]], where '''F''' is the net force acting on the object and '''delta r''' is the change in position of the object center of mass.

In the point particle system, total change in energy is equal to the total change in kinetic energy. Because of the energy principle, [[File:Energy_work.png|70 px]], where '''delta E''' is change in total energy and '''W''' is work, the change in translational kinetic energy is equal to work. Remember, work is equal to [[File:Change_in_trans.png|50 px]] as well.

==Examples==

===Jumper Model===

A person jumps straight up in the air from a crouching position. Their center of mass moves '''h''', or 2 m. Their total mass, '''m''' is equal to 60 kg. Find the velocity of the center of mass of the jumper. When the jumper jumps, the normal force of the ground is equal to 2x the force of gravity.

[[File:Jumper.png|250 px]]

Imagine the jumper's center of mass as a point, and it moves up 2 m.

Remember, [[File:K_trans_1.png|100 px]] and [[File:Change_k_trans_1.png|100 px]].
We need to find '''Fnet'''. The only forces acting on the jumper are the gravitational force of the Earth and the normal force. Therefore, '''Fnet = Fn-Fg'''.
'''Fg = Mg''', therefore '''Fn = 2Mg'''.

Steps:

[[File:Change_k_trans_1.png|130 px]]

[[File:Step_1.png|230 px]]

[[File:Step_2.png|200 px]]

[[File:Step3.png|250 px]]

When worked out, the '''v = 6.26 m/s'''.

The final translational kinetic energy can be used for further calculations if one was to calculate the total change in energy of the real system, including perhaps the thermal energy of the body when jumping increasing, or the rotational kinetic energy of the arms moving.

===Yo-Yo Example===

You pull up on a string the distance '''d''', 0.2 m, with a force, '''F''', 0.3 N. The yo-yo falls a distance '''h''', 0.35 m. The mass of the yo-yo, '''m''', is 0.05 kg. What is the change in translational kinetic energy?

[[File:Yo-yoo.png|150 px]] [[File:Yoyoimage.jpg]]

For this example, the '''Fnet''' is equal to the force of your hand and the gravitational force of the earth. '''Delta r''' is equal to the movement of the yo-yo down, '''h'''.

Steps:

[[File:Yoyo_steps.png|300 px]]

This information could be used to solve for the extended system, which would include the work done by your hand and the earth, as well as rotational kinetic energy.

===Spring in a Box Example===

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

I think it is interesting how physicists have simplified the process of finding changes of energy in a system in order to make approximations and calculate more complicated changes in energy. For me, it really helped me to understand exactly what translational kinetic energy is and how it applies to the entire system.

#How is it connected to your major?

My major is industrial engineering, and although I do not think this topic applies directly to my major, it applies to simplifying and making a more efficient and easy way to calculate the changes of energy in a system. That is the goal of industrial engineering, so in that way, I really enjoy this method of finding changes in energy.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." Matter & Interactions. N.p.: n.p., n.d. N. pag. Print.

[[Category: Energy]]

Point Particle Systems

2015-12-01T23:26:09Z

Akerrison3: /* Examples */

This topic has been claimed akerrison3.

==The Main Idea==

The point particle method of measuring changes in energy simplifies the system of interest down to a single point, or focuses on its center of mass. Therefore, the only energy changing in the system is translational kinetic energy. Translational kinetic energy is the energy that comes from an object moving from one location to another. This can then be used in the extended system of the object, which includes all energy transfers.

[[File:Cow_point.png|400 px]] Center of Mass of a Cow as a Point

===A Mathematical Model===

Translational kinetic energy is equal to [[File:Translational_kinetic_energy.png|50 px]], where '''M''' is mass and '''v''' is the velocity of the center of mass.

The change in translational kinetic energy is equal to [[File:Change_in_trans.png|50 px]], where '''F''' is the net force acting on the object and '''delta r''' is the change in position of the object center of mass.

In the point particle system, total change in energy is equal to the total change in kinetic energy. Because of the energy principle, [[File:Energy_work.png|70 px]], where '''delta E''' is change in total energy and '''W''' is work, the change in translational kinetic energy is equal to work. Remember, work is equal to [[File:Change_in_trans.png|50 px]] as well.

==Examples==

===Jumper Model===

A person jumps straight up in the air from a crouching position. Their center of mass moves '''h''', or 2 meters. Their total mass, '''m''' is equal to 60 kg. Find the velocity of the center of mass of the jumper. When the jumper jumps, the normal force of the ground is equal to 2x the force of gravity.

[[File:Jumper.png|250 px]]

Imagine the jumper's center of mass as a point, and it moves up 2 meters.

Remember, [[File:K_trans_1.png|100 px]] and [[File:Change_k_trans_1.png|100 px]].
We need to find '''Fnet'''. The only forces acting on the jumper are the gravitational force of the Earth and the normal force. Therefore, '''Fnet = Fn-Fg'''.
'''Fg = Mg''', therefore '''Fn = 2Mg'''.

Steps:

[[File:Change_k_trans_1.png|130 px]]

[[File:Step_1.png|230 px]]

[[File:Step_2.png|200 px]]

[[File:Step3.png|250 px]]

When worked out, the '''v = 6.26 m/s'''.

The final translational kinetic energy can be used for further calculations if one was to calculate the total change in energy of the real system, including perhaps the thermal energy of the body when jumping increasing, or the rotational kinetic energy of the arms moving.

===Yo-Yo Example===

You pull up on a string the distance '''d''', 0.2 m, with a force, '''F''', 0.3 N. The yo-yo falls a distance '''h''', 0.35 m. The mass of the yo-yo, '''m''', is 0.05 kg. What is the change in translational kinetic energy?

[[File:Yo-yoo.png|150 px]] [[File:Yoyoimage.jpg]]

For this example, the '''Fnet''' is equal to the force of your hand and the gravitational force of the earth. '''Delta r''' is equal to the movement of the yo-yo down, '''h'''.

Steps:

[[File:Yoyo_steps.png|300 px]]

This information could be used to solve for the extended system, which would include the work done by your hand and the earth, as well as rotational kinetic energy.

===Spring in a Box Example===

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

I think it is interesting how physicists have simplified the process of finding changes of energy in a system in order to make approximations and calculate more complicated changes in energy. For me, it really helped me to understand exactly what translational kinetic energy is and how it applies to the entire system.

#How is it connected to your major?

My major is industrial engineering, and although I do not think this topic applies directly to my major, it applies to simplifying and making a more efficient and easy way to calculate the changes of energy in a system. That is the goal of industrial engineering, so in that way, I really enjoy this method of finding changes in energy.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." Matter & Interactions. N.p.: n.p., n.d. N. pag. Print.

[[Category: Energy]]

File:Yoyoimage.jpg

2015-12-01T23:24:58Z

Akerrison3:

Point Particle Systems

2015-12-01T23:19:50Z

Akerrison3: /* Yo-Yo Example */

This topic has been claimed akerrison3.

==The Main Idea==

The point particle method of measuring changes in energy simplifies the system of interest down to a single point, or focuses on its center of mass. Therefore, the only energy changing in the system is translational kinetic energy. Translational kinetic energy is the energy that comes from an object moving from one location to another. This can then be used in the extended system of the object, which includes all energy transfers.

[[File:Cow_point.png|400 px]] Center of Mass of a Cow as a Point

===A Mathematical Model===

Translational kinetic energy is equal to [[File:Translational_kinetic_energy.png|50 px]], where '''M''' is mass and '''v''' is the velocity of the center of mass.

The change in translational kinetic energy is equal to [[File:Change_in_trans.png|50 px]], where '''F''' is the net force acting on the object and '''delta r''' is the change in position of the object center of mass.

In the point particle system, total change in energy is equal to the total change in kinetic energy. Because of the energy principle, [[File:Energy_work.png|70 px]], where '''delta E''' is change in total energy and '''W''' is work, the change in translational kinetic energy is equal to work. Remember, work is equal to [[File:Change_in_trans.png|50 px]] as well.

==Examples==

===Jumper Model===

A person jumps straight up in the air from a crouching position. Their center of mass moves '''h''', or 2 meters. Their total mass, '''m''' is equal to 60 kg. Find the velocity of the center of mass of the jumper. When the jumper jumps, the normal force of the ground is equal to 2x the force of gravity.

[[File:Jumper.png|250 px]]

Imagine the jumper's center of mass as a point, and it moves up 2 meters.

Remember, [[File:K_trans_1.png|100 px]] and [[File:Change_k_trans_1.png|100 px]].
We need to find '''Fnet'''. The only forces acting on the jumper are the gravitational force of the Earth and the normal force. Therefore, '''Fnet = Fn-Fg'''.
'''Fg = Mg''', therefore '''Fn = 2Mg'''.

Steps:

1) [[File:Change_k_trans_1.png|130 px]]

2) [[File:Step_1.png|230 px]]

3) [[File:Step_2.png|200 px]]

4) [[File:Step3.png|250 px]]

When worked out, the '''v = 6.26 m/s'''.

The final translational kinetic energy can be used for further calculations if one was to calculate the total change in energy of the real system, including perhaps the thermal energy of the body when jumping increasing, or the rotational kinetic energy of the arms moving.

===Yo-Yo Example===

You pull up on a string the distance '''d''', 0.2 m, with a force, '''F''', 0.3 N. The yo-yo falls a distance '''h''', 0.35 m. The mass of the yo-yo, '''m''', is 0.05 kg. What is the change in translational kinetic energy?

[[File:Yo-yoo.png|150 px]]

For this example, the '''Fnet''' is equal to the force of your hand and the gravitational force of the earth. '''Delta r''' is equal to the movement of the yo-yo down, '''h'''.

Steps:

[[File:Yoyo_steps.png|300 px]]

This information could be used to solve for the extended system, which would include the work done by your hand and the earth, as well as rotational kinetic energy.

===Spring in a Box Example===

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

I think it is interesting how physicists have simplified the process of finding changes of energy in a system in order to make approximations and calculate more complicated changes in energy. For me, it really helped me to understand exactly what translational kinetic energy is and how it applies to the entire system.

#How is it connected to your major?

My major is industrial engineering, and although I do not think this topic applies directly to my major, it applies to simplifying and making a more efficient and easy way to calculate the changes of energy in a system. That is the goal of industrial engineering, so in that way, I really enjoy this method of finding changes in energy.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." Matter & Interactions. N.p.: n.p., n.d. N. pag. Print.

[[Category: Energy]]

Point Particle Systems

2015-12-01T20:10:15Z

Akerrison3: /* Yo-Yo Example */

This topic has been claimed akerrison3.

==The Main Idea==

The point particle method of measuring changes in energy simplifies the system of interest down to a single point, or focuses on its center of mass. Therefore, the only energy changing in the system is translational kinetic energy. Translational kinetic energy is the energy that comes from an object moving from one location to another. This can then be used in the extended system of the object, which includes all energy transfers.

[[File:Cow_point.png|400 px]] Center of Mass of a Cow as a Point

===A Mathematical Model===

Translational kinetic energy is equal to [[File:Translational_kinetic_energy.png|50 px]], where '''M''' is mass and '''v''' is the velocity of the center of mass.

The change in translational kinetic energy is equal to [[File:Change_in_trans.png|50 px]], where '''F''' is the net force acting on the object and '''delta r''' is the change in position of the object center of mass.

In the point particle system, total change in energy is equal to the total change in kinetic energy. Because of the energy principle, [[File:Energy_work.png|70 px]], where '''delta E''' is change in total energy and '''W''' is work, the change in translational kinetic energy is equal to work. Remember, work is equal to [[File:Change_in_trans.png|50 px]] as well.

==Examples==

===Jumper Model===

A person jumps straight up in the air from a crouching position. Their center of mass moves '''h''', or 2 meters. Their total mass, '''m''' is equal to 60 kg. Find the velocity of the center of mass of the jumper. When the jumper jumps, the normal force of the ground is equal to 2x the force of gravity.

[[File:Jumper.png|250 px]]

Imagine the jumper's center of mass as a point, and it moves up 2 meters.

Remember, [[File:K_trans_1.png|100 px]] and [[File:Change_k_trans_1.png|100 px]].
We need to find '''Fnet'''. The only forces acting on the jumper are the gravitational force of the Earth and the normal force. Therefore, '''Fnet = Fn-Fg'''.
'''Fg = Mg''', therefore '''Fn = 2Mg'''.

Steps:

1) [[File:Change_k_trans_1.png|130 px]]

2) [[File:Step_1.png|230 px]]

3) [[File:Step_2.png|200 px]]

4) [[File:Step3.png|250 px]]

When worked out, the '''v = 6.26 m/s'''.

The final translational kinetic energy can be used for further calculations if one was to calculate the total change in energy of the real system, including perhaps the thermal energy of the body when jumping increasing, or the rotational kinetic energy of the arms moving.

===Yo-Yo Example===

You pull up on a string the distance '''d''', 0.2 m, with a force, '''F''', 0.3 N. The yo-yo falls a distance '''h''', 0.35 m. The mass of the yo-yo, '''m''', is 0.05 kg. What is the change in translational kinetic energy?

[[File:Yo-yoo.png|150 px]]

For this example, the '''Fnet''' is equal to the force of your hand and the gravitational force of the earth. '''Delta r''' is equal to the movement of the yo-yo down, '''h'''.

Steps:

[[File:Yoyo_steps.png|300 px]]

If the extended system was

===Spring in a Box Example===

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

I think it is interesting how physicists have simplified the process of finding changes of energy in a system in order to make approximations and calculate more complicated changes in energy. For me, it really helped me to understand exactly what translational kinetic energy is and how it applies to the entire system.

#How is it connected to your major?

My major is industrial engineering, and although I do not think this topic applies directly to my major, it applies to simplifying and making a more efficient and easy way to calculate the changes of energy in a system. That is the goal of industrial engineering, so in that way, I really enjoy this method of finding changes in energy.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." Matter & Interactions. N.p.: n.p., n.d. N. pag. Print.

[[Category: Energy]]

Point Particle Systems

2015-12-01T20:09:49Z

Akerrison3: /* Yo-Yo Example */

This topic has been claimed akerrison3.

==The Main Idea==

The point particle method of measuring changes in energy simplifies the system of interest down to a single point, or focuses on its center of mass. Therefore, the only energy changing in the system is translational kinetic energy. Translational kinetic energy is the energy that comes from an object moving from one location to another. This can then be used in the extended system of the object, which includes all energy transfers.

[[File:Cow_point.png|400 px]] Center of Mass of a Cow as a Point

===A Mathematical Model===

Translational kinetic energy is equal to [[File:Translational_kinetic_energy.png|50 px]], where '''M''' is mass and '''v''' is the velocity of the center of mass.

The change in translational kinetic energy is equal to [[File:Change_in_trans.png|50 px]], where '''F''' is the net force acting on the object and '''delta r''' is the change in position of the object center of mass.

In the point particle system, total change in energy is equal to the total change in kinetic energy. Because of the energy principle, [[File:Energy_work.png|70 px]], where '''delta E''' is change in total energy and '''W''' is work, the change in translational kinetic energy is equal to work. Remember, work is equal to [[File:Change_in_trans.png|50 px]] as well.

==Examples==

===Jumper Model===

A person jumps straight up in the air from a crouching position. Their center of mass moves '''h''', or 2 meters. Their total mass, '''m''' is equal to 60 kg. Find the velocity of the center of mass of the jumper. When the jumper jumps, the normal force of the ground is equal to 2x the force of gravity.

[[File:Jumper.png|250 px]]

Imagine the jumper's center of mass as a point, and it moves up 2 meters.

Remember, [[File:K_trans_1.png|100 px]] and [[File:Change_k_trans_1.png|100 px]].
We need to find '''Fnet'''. The only forces acting on the jumper are the gravitational force of the Earth and the normal force. Therefore, '''Fnet = Fn-Fg'''.
'''Fg = Mg''', therefore '''Fn = 2Mg'''.

Steps:

1) [[File:Change_k_trans_1.png|130 px]]

2) [[File:Step_1.png|230 px]]

3) [[File:Step_2.png|200 px]]

4) [[File:Step3.png|250 px]]

When worked out, the '''v = 6.26 m/s'''.

The final translational kinetic energy can be used for further calculations if one was to calculate the total change in energy of the real system, including perhaps the thermal energy of the body when jumping increasing, or the rotational kinetic energy of the arms moving.

===Yo-Yo Example===

You pull up on a string the distance '''d''', 0.2 m, with a force, '''F''', 0.3 N. The yo-yo falls a distance '''h''', 0.35 m. The mass of the yo-yo, '''m''', is 0.05 kg. What is the change in translational kinetic energy?

[[File:Yo-yoo.png|150 px]]

For this example, the '''Fnet''' is equal to the force of your hand and the gravitational force of the earth. '''Delta r''' is equal to the movement of the yo-yo down, '''h'''.

Steps:

[[File:Yoyo_steps.png|200 px]]

If the extended system was

===Spring in a Box Example===

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

I think it is interesting how physicists have simplified the process of finding changes of energy in a system in order to make approximations and calculate more complicated changes in energy. For me, it really helped me to understand exactly what translational kinetic energy is and how it applies to the entire system.

#How is it connected to your major?

My major is industrial engineering, and although I do not think this topic applies directly to my major, it applies to simplifying and making a more efficient and easy way to calculate the changes of energy in a system. That is the goal of industrial engineering, so in that way, I really enjoy this method of finding changes in energy.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." Matter & Interactions. N.p.: n.p., n.d. N. pag. Print.

[[Category: Energy]]

Point Particle Systems

2015-12-01T20:09:25Z

Akerrison3: /* Yo-Yo Example */

This topic has been claimed akerrison3.

==The Main Idea==

The point particle method of measuring changes in energy simplifies the system of interest down to a single point, or focuses on its center of mass. Therefore, the only energy changing in the system is translational kinetic energy. Translational kinetic energy is the energy that comes from an object moving from one location to another. This can then be used in the extended system of the object, which includes all energy transfers.

[[File:Cow_point.png|400 px]] Center of Mass of a Cow as a Point

===A Mathematical Model===

Translational kinetic energy is equal to [[File:Translational_kinetic_energy.png|50 px]], where '''M''' is mass and '''v''' is the velocity of the center of mass.

The change in translational kinetic energy is equal to [[File:Change_in_trans.png|50 px]], where '''F''' is the net force acting on the object and '''delta r''' is the change in position of the object center of mass.

In the point particle system, total change in energy is equal to the total change in kinetic energy. Because of the energy principle, [[File:Energy_work.png|70 px]], where '''delta E''' is change in total energy and '''W''' is work, the change in translational kinetic energy is equal to work. Remember, work is equal to [[File:Change_in_trans.png|50 px]] as well.

==Examples==

===Jumper Model===

A person jumps straight up in the air from a crouching position. Their center of mass moves '''h''', or 2 meters. Their total mass, '''m''' is equal to 60 kg. Find the velocity of the center of mass of the jumper. When the jumper jumps, the normal force of the ground is equal to 2x the force of gravity.

[[File:Jumper.png|250 px]]

Imagine the jumper's center of mass as a point, and it moves up 2 meters.

Remember, [[File:K_trans_1.png|100 px]] and [[File:Change_k_trans_1.png|100 px]].
We need to find '''Fnet'''. The only forces acting on the jumper are the gravitational force of the Earth and the normal force. Therefore, '''Fnet = Fn-Fg'''.
'''Fg = Mg''', therefore '''Fn = 2Mg'''.

Steps:

1) [[File:Change_k_trans_1.png|130 px]]

2) [[File:Step_1.png|230 px]]

3) [[File:Step_2.png|200 px]]

4) [[File:Step3.png|250 px]]

When worked out, the '''v = 6.26 m/s'''.

The final translational kinetic energy can be used for further calculations if one was to calculate the total change in energy of the real system, including perhaps the thermal energy of the body when jumping increasing, or the rotational kinetic energy of the arms moving.

===Yo-Yo Example===

You pull up on a string the distance '''d''', 0.2 m, with a force, '''F''', 0.3 N. The yo-yo falls a distance '''h''', 0.35 m. The mass of the yo-yo, '''m''', is 0.05 kg. What is the change in translational kinetic energy?

[[File:Yo-yoo.png|150 px]]

For this example, the '''Fnet''' is equal to the force of your hand and the gravitational force of the earth. '''Delta r''' is equal to the movement of the yo-yo down, '''h'''.

Steps:

[[File:Yoyo_steps.png]]

If the extended system was

===Spring in a Box Example===

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

I think it is interesting how physicists have simplified the process of finding changes of energy in a system in order to make approximations and calculate more complicated changes in energy. For me, it really helped me to understand exactly what translational kinetic energy is and how it applies to the entire system.

#How is it connected to your major?

My major is industrial engineering, and although I do not think this topic applies directly to my major, it applies to simplifying and making a more efficient and easy way to calculate the changes of energy in a system. That is the goal of industrial engineering, so in that way, I really enjoy this method of finding changes in energy.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." Matter & Interactions. N.p.: n.p., n.d. N. pag. Print.

[[Category: Energy]]

File:Jumper.png

2015-12-01T02:47:19Z

Akerrison3:

Point Particle Systems

2015-12-01T02:37:27Z

Akerrison3: /* The Main Idea */