Physics Book - User contributions [en]

Work and Energy for an Extended System

2015-12-04T07:09:26Z

Mlamarca3: /* External links */

"Work and Energy for an Extended System" in progress by Morgan LaMarca

==The Main Idea==

Unlike the point particle system where the only energy possible is translational kinetic energy, an extended object can rotate, vibrate, and change shape. Though the point particle system and the extended system both have the same total mass, and are both acted on by the same net force, the point particle system, has no rotational motion, vibrational motion, or internal energy because all of the forces act at the location of the point particle. In contrast, forces act at different locations on the mass in an extended system, thus causing them to rotate, vibrate and stretch. Because of these qualities, not every part of the system always moves in the same direction as the center of mass moves.

When calculating work done on an extended system, the displacement of every point where a force is applied must be considered separately, because it matters where each force is applied.

===A Mathematical Model===

Work and Energy for an Extended System:
[[File:Work and Energy for an Extended System.png]]

This equation assumes that each force is constant during the displacement. If each force is not constant during the displacement, the work of each force as an integral of <math>\vec{F}_{i}•d\vec{r}_{i}</math> must be calculated either analytically or numerically.

===A Computational Model===

'''A Jumping Kangaroo Modeled as an Extended Object:'''

If one were to model a jumping kangaroo as a point particle system, the change in translational kinetic energy could be derived. However in the real world, Kangaroos are not a point particle, but rather an extended system where energy changes occur in the legs and arms of the kangaroo relative to the center of mass. Chemical energy and thermal energy are just two more examples of energy changes that may occur in extended systems but not in point particle systems.

The work done on a point particle system is not the same as the work done on an extended system. Because forces are applied in many different locations on the mass in an extended system, sometimes these forces act through different distances than the displacement of the center of mass of the system, for different sections of the system move different distances. The following free-body diagram a modeled extended system illustrates how these individual forces may act at different locations:

[[File:Extended_System_Model.png]]

When considering all the possible changes in energy when a Kangaroo jumps, the energy equation for the Kangaroo modeled as an extended system (ignoring Q, or the transfer of energy due to a temperature difference between the Kangaroo and the surrounding air), should look like the following equation:
[[File:Improved_Energy_Equation_for_the_Extended_System_of_a_Kangaroo_Jumping.png]]

The change in relative kinetic energy and the change in internal energy do not appear in the energy equation for the point particle system because the point particle system only focuses on the translational motion of the center of mass point. The change in relative kinetic energy includes the rotation of the legs and the swinging of the upper body and tail of the Kangaroo. The change in internal energy includes the increase in thermal energy of the Kangaroo's body and the decrease in chemical energy that was previously chemically stored in the Kangaroo's body. This computational model of the jumping Kangaroo allows one to visualize how unlike the point particle system, the extended system changes shape due to the bending of the legs, arms, and torso of the Kangaroo during the jump.

==Example==
===A Yo-yo===

[[File:Yo-yo_as_an_extended_system.png]]

'''Solution'''
'''(a)'''

System: Point Particle

Surroundings: Hand and Earth

Initial State: Point particle with initial translational kinetic energy

Final State: Point particle with final translational kinetic energy

Energy Principle (keep in mind that point particle systems only have translational kinetic energy!)
[[File:Yo-yo_part_a_solution.png]]

'''Solution'''
'''(b)'''

[[File:Yo-yo_part_b_solution.png]]

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

This topic interests me because it involves calculating work in real systems present in the real world, unlike the point particle system which focuses more on calculating work on single atoms or idealized versions of objects modeled as a point particle. Being able to apply physics to real world situations is always so exciting for me.

2. How is it connected to your major?

I am a biology major. By learning how to calculate the work done on an extended system, for example a Kangaroo jumping, I am able to incorporate and consider chemical energy changes and thermal energy changes in the Kangaroo. Knowledge in how much energy a Kangaroo uses while jumping is just one example of how I am able to use physics to forward my knowledge in the biology field as well.

3. Is there an interesting industrial application?

This is a very interesting industrial application because knowing how to calculate the work done on an extended system such as a rocket, could forward our knowledge in rocket science and what is needed to travel further into space. Once we are able to quantify how much work must be done on a system to travel a certain distance at a safe, controlled speed, we have the potential to maybe one day reach Mars and other planets!

== See also ==

===Further reading===

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

For more information on Point Particle and Extended Systems please visit: http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:pp_vs_real

===External links===

Check out [http://www.physicsbook.gatech.edu/Point_Particle_Systems] to learn more about Point Particle Systems!

Also take a look at [http://www.physicsbook.gatech.edu/Real_Systems] to review more information on Extended (Real) Systems.

To learn more on how Kinetic Energy applies to everyday life: [http://classroom.synonym.com/kinetic-energy-potential-energy-apply-everyday-life-15430.html]

==References==

All images used on this page do not belong to me. All problem examples are from the Matter and Interactions Physics book referenced below.

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

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

Work and Energy for an Extended System

2015-12-04T07:08:04Z

Mlamarca3: /* Further reading */

"Work and Energy for an Extended System" in progress by Morgan LaMarca

==The Main Idea==

Unlike the point particle system where the only energy possible is translational kinetic energy, an extended object can rotate, vibrate, and change shape. Though the point particle system and the extended system both have the same total mass, and are both acted on by the same net force, the point particle system, has no rotational motion, vibrational motion, or internal energy because all of the forces act at the location of the point particle. In contrast, forces act at different locations on the mass in an extended system, thus causing them to rotate, vibrate and stretch. Because of these qualities, not every part of the system always moves in the same direction as the center of mass moves.

When calculating work done on an extended system, the displacement of every point where a force is applied must be considered separately, because it matters where each force is applied.

===A Mathematical Model===

Work and Energy for an Extended System:
[[File:Work and Energy for an Extended System.png]]

This equation assumes that each force is constant during the displacement. If each force is not constant during the displacement, the work of each force as an integral of <math>\vec{F}_{i}•d\vec{r}_{i}</math> must be calculated either analytically or numerically.

===A Computational Model===

'''A Jumping Kangaroo Modeled as an Extended Object:'''

If one were to model a jumping kangaroo as a point particle system, the change in translational kinetic energy could be derived. However in the real world, Kangaroos are not a point particle, but rather an extended system where energy changes occur in the legs and arms of the kangaroo relative to the center of mass. Chemical energy and thermal energy are just two more examples of energy changes that may occur in extended systems but not in point particle systems.

The work done on a point particle system is not the same as the work done on an extended system. Because forces are applied in many different locations on the mass in an extended system, sometimes these forces act through different distances than the displacement of the center of mass of the system, for different sections of the system move different distances. The following free-body diagram a modeled extended system illustrates how these individual forces may act at different locations:

[[File:Extended_System_Model.png]]

When considering all the possible changes in energy when a Kangaroo jumps, the energy equation for the Kangaroo modeled as an extended system (ignoring Q, or the transfer of energy due to a temperature difference between the Kangaroo and the surrounding air), should look like the following equation:
[[File:Improved_Energy_Equation_for_the_Extended_System_of_a_Kangaroo_Jumping.png]]

The change in relative kinetic energy and the change in internal energy do not appear in the energy equation for the point particle system because the point particle system only focuses on the translational motion of the center of mass point. The change in relative kinetic energy includes the rotation of the legs and the swinging of the upper body and tail of the Kangaroo. The change in internal energy includes the increase in thermal energy of the Kangaroo's body and the decrease in chemical energy that was previously chemically stored in the Kangaroo's body. This computational model of the jumping Kangaroo allows one to visualize how unlike the point particle system, the extended system changes shape due to the bending of the legs, arms, and torso of the Kangaroo during the jump.

==Example==
===A Yo-yo===

[[File:Yo-yo_as_an_extended_system.png]]

'''Solution'''
'''(a)'''

System: Point Particle

Surroundings: Hand and Earth

Initial State: Point particle with initial translational kinetic energy

Final State: Point particle with final translational kinetic energy

Energy Principle (keep in mind that point particle systems only have translational kinetic energy!)
[[File:Yo-yo_part_a_solution.png]]

'''Solution'''
'''(b)'''

[[File:Yo-yo_part_b_solution.png]]

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

This topic interests me because it involves calculating work in real systems present in the real world, unlike the point particle system which focuses more on calculating work on single atoms or idealized versions of objects modeled as a point particle. Being able to apply physics to real world situations is always so exciting for me.

2. How is it connected to your major?

I am a biology major. By learning how to calculate the work done on an extended system, for example a Kangaroo jumping, I am able to incorporate and consider chemical energy changes and thermal energy changes in the Kangaroo. Knowledge in how much energy a Kangaroo uses while jumping is just one example of how I am able to use physics to forward my knowledge in the biology field as well.

3. Is there an interesting industrial application?

This is a very interesting industrial application because knowing how to calculate the work done on an extended system such as a rocket, could forward our knowledge in rocket science and what is needed to travel further into space. Once we are able to quantify how much work must be done on a system to travel a certain distance at a safe, controlled speed, we have the potential to maybe one day reach Mars and other planets!

== See also ==

===Further reading===

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

For more information on Point Particle and Extended Systems please visit: http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:pp_vs_real

===External links===

Check out [http://www.physicsbook.gatech.edu/Point_Particle_Systems] to learn more about Point Particle Systems!

Also take a look at [http://www.physicsbook.gatech.edu/Real_Systems] to review more information on Extended (Real) Systems.

==References==

All images used on this page do not belong to me. All problem examples are from the Matter and Interactions Physics book referenced below.

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

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

Work and Energy for an Extended System

2015-12-04T07:04:03Z

Mlamarca3: /* Simple */

"Work and Energy for an Extended System" in progress by Morgan LaMarca

==The Main Idea==

Unlike the point particle system where the only energy possible is translational kinetic energy, an extended object can rotate, vibrate, and change shape. Though the point particle system and the extended system both have the same total mass, and are both acted on by the same net force, the point particle system, has no rotational motion, vibrational motion, or internal energy because all of the forces act at the location of the point particle. In contrast, forces act at different locations on the mass in an extended system, thus causing them to rotate, vibrate and stretch. Because of these qualities, not every part of the system always moves in the same direction as the center of mass moves.

When calculating work done on an extended system, the displacement of every point where a force is applied must be considered separately, because it matters where each force is applied.

===A Mathematical Model===

Work and Energy for an Extended System:
[[File:Work and Energy for an Extended System.png]]

This equation assumes that each force is constant during the displacement. If each force is not constant during the displacement, the work of each force as an integral of <math>\vec{F}_{i}•d\vec{r}_{i}</math> must be calculated either analytically or numerically.

===A Computational Model===

'''A Jumping Kangaroo Modeled as an Extended Object:'''

If one were to model a jumping kangaroo as a point particle system, the change in translational kinetic energy could be derived. However in the real world, Kangaroos are not a point particle, but rather an extended system where energy changes occur in the legs and arms of the kangaroo relative to the center of mass. Chemical energy and thermal energy are just two more examples of energy changes that may occur in extended systems but not in point particle systems.

The work done on a point particle system is not the same as the work done on an extended system. Because forces are applied in many different locations on the mass in an extended system, sometimes these forces act through different distances than the displacement of the center of mass of the system, for different sections of the system move different distances. The following free-body diagram a modeled extended system illustrates how these individual forces may act at different locations:

[[File:Extended_System_Model.png]]

When considering all the possible changes in energy when a Kangaroo jumps, the energy equation for the Kangaroo modeled as an extended system (ignoring Q, or the transfer of energy due to a temperature difference between the Kangaroo and the surrounding air), should look like the following equation:
[[File:Improved_Energy_Equation_for_the_Extended_System_of_a_Kangaroo_Jumping.png]]

The change in relative kinetic energy and the change in internal energy do not appear in the energy equation for the point particle system because the point particle system only focuses on the translational motion of the center of mass point. The change in relative kinetic energy includes the rotation of the legs and the swinging of the upper body and tail of the Kangaroo. The change in internal energy includes the increase in thermal energy of the Kangaroo's body and the decrease in chemical energy that was previously chemically stored in the Kangaroo's body. This computational model of the jumping Kangaroo allows one to visualize how unlike the point particle system, the extended system changes shape due to the bending of the legs, arms, and torso of the Kangaroo during the jump.

==Example==
===A Yo-yo===

[[File:Yo-yo_as_an_extended_system.png]]

'''Solution'''
'''(a)'''

System: Point Particle

Surroundings: Hand and Earth

Initial State: Point particle with initial translational kinetic energy

Final State: Point particle with final translational kinetic energy

Energy Principle (keep in mind that point particle systems only have translational kinetic energy!)
[[File:Yo-yo_part_a_solution.png]]

'''Solution'''
'''(b)'''

[[File:Yo-yo_part_b_solution.png]]

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

This topic interests me because it involves calculating work in real systems present in the real world, unlike the point particle system which focuses more on calculating work on single atoms or idealized versions of objects modeled as a point particle. Being able to apply physics to real world situations is always so exciting for me.

2. How is it connected to your major?

I am a biology major. By learning how to calculate the work done on an extended system, for example a Kangaroo jumping, I am able to incorporate and consider chemical energy changes and thermal energy changes in the Kangaroo. Knowledge in how much energy a Kangaroo uses while jumping is just one example of how I am able to use physics to forward my knowledge in the biology field as well.

3. Is there an interesting industrial application?

This is a very interesting industrial application because knowing how to calculate the work done on an extended system such as a rocket, could forward our knowledge in rocket science and what is needed to travel further into space. Once we are able to quantify how much work must be done on a system to travel a certain distance at a safe, controlled speed, we have the potential to maybe one day reach Mars and other planets!

== See also ==

===Further reading===

For more information on Point Particle and Extended Systems please visit: http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:pp_vs_real

===External links===

Check out [http://www.physicsbook.gatech.edu/Point_Particle_Systems] to learn more about Point Particle Systems!

Also take a look at [http://www.physicsbook.gatech.edu/Real_Systems] to review more information on Extended (Real) Systems.

==References==

All images used on this page do not belong to me. All problem examples are from the Matter and Interactions Physics book referenced below.

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

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

Work and Energy for an Extended System

2015-12-04T07:02:27Z

Mlamarca3: /* Simple */

"Work and Energy for an Extended System" in progress by Morgan LaMarca

==The Main Idea==

Unlike the point particle system where the only energy possible is translational kinetic energy, an extended object can rotate, vibrate, and change shape. Though the point particle system and the extended system both have the same total mass, and are both acted on by the same net force, the point particle system, has no rotational motion, vibrational motion, or internal energy because all of the forces act at the location of the point particle. In contrast, forces act at different locations on the mass in an extended system, thus causing them to rotate, vibrate and stretch. Because of these qualities, not every part of the system always moves in the same direction as the center of mass moves.

When calculating work done on an extended system, the displacement of every point where a force is applied must be considered separately, because it matters where each force is applied.

===A Mathematical Model===

Work and Energy for an Extended System:
[[File:Work and Energy for an Extended System.png]]

This equation assumes that each force is constant during the displacement. If each force is not constant during the displacement, the work of each force as an integral of <math>\vec{F}_{i}•d\vec{r}_{i}</math> must be calculated either analytically or numerically.

===A Computational Model===

'''A Jumping Kangaroo Modeled as an Extended Object:'''

If one were to model a jumping kangaroo as a point particle system, the change in translational kinetic energy could be derived. However in the real world, Kangaroos are not a point particle, but rather an extended system where energy changes occur in the legs and arms of the kangaroo relative to the center of mass. Chemical energy and thermal energy are just two more examples of energy changes that may occur in extended systems but not in point particle systems.

The work done on a point particle system is not the same as the work done on an extended system. Because forces are applied in many different locations on the mass in an extended system, sometimes these forces act through different distances than the displacement of the center of mass of the system, for different sections of the system move different distances. The following free-body diagram a modeled extended system illustrates how these individual forces may act at different locations:

[[File:Extended_System_Model.png]]

When considering all the possible changes in energy when a Kangaroo jumps, the energy equation for the Kangaroo modeled as an extended system (ignoring Q, or the transfer of energy due to a temperature difference between the Kangaroo and the surrounding air), should look like the following equation:
[[File:Improved_Energy_Equation_for_the_Extended_System_of_a_Kangaroo_Jumping.png]]

The change in relative kinetic energy and the change in internal energy do not appear in the energy equation for the point particle system because the point particle system only focuses on the translational motion of the center of mass point. The change in relative kinetic energy includes the rotation of the legs and the swinging of the upper body and tail of the Kangaroo. The change in internal energy includes the increase in thermal energy of the Kangaroo's body and the decrease in chemical energy that was previously chemically stored in the Kangaroo's body. This computational model of the jumping Kangaroo allows one to visualize how unlike the point particle system, the extended system changes shape due to the bending of the legs, arms, and torso of the Kangaroo during the jump.

==Example==
===Simple===
'''Example 1: A Yo-yo'''

[[File:Yo-yo_as_an_extended_system.png]]

'''Solution'''
'''(a)'''

System: Point Particle

Surroundings: Hand and Earth

Initial State: Point particle with initial translational kinetic energy

Final State: Point particle with final translational kinetic energy

Energy Principle (keep in mind that point particle systems only have translational kinetic energy!)
[[File:Yo-yo_part_a_solution.png]]

'''Solution'''
'''(b)'''

[[File:Yo-yo_part_b_solution.png]]

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

This topic interests me because it involves calculating work in real systems present in the real world, unlike the point particle system which focuses more on calculating work on single atoms or idealized versions of objects modeled as a point particle. Being able to apply physics to real world situations is always so exciting for me.

2. How is it connected to your major?

I am a biology major. By learning how to calculate the work done on an extended system, for example a Kangaroo jumping, I am able to incorporate and consider chemical energy changes and thermal energy changes in the Kangaroo. Knowledge in how much energy a Kangaroo uses while jumping is just one example of how I am able to use physics to forward my knowledge in the biology field as well.

3. Is there an interesting industrial application?

This is a very interesting industrial application because knowing how to calculate the work done on an extended system such as a rocket, could forward our knowledge in rocket science and what is needed to travel further into space. Once we are able to quantify how much work must be done on a system to travel a certain distance at a safe, controlled speed, we have the potential to maybe one day reach Mars and other planets!

== See also ==

===Further reading===

For more information on Point Particle and Extended Systems please visit: http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:pp_vs_real

===External links===

Check out [http://www.physicsbook.gatech.edu/Point_Particle_Systems] to learn more about Point Particle Systems!

Also take a look at [http://www.physicsbook.gatech.edu/Real_Systems] to review more information on Extended (Real) Systems.

==References==

All images used on this page do not belong to me. All problem examples are from the Matter and Interactions Physics book referenced below.

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

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

Work and Energy for an Extended System

2015-12-04T07:00:52Z

Mlamarca3: /* Simple */

"Work and Energy for an Extended System" in progress by Morgan LaMarca

==The Main Idea==

Unlike the point particle system where the only energy possible is translational kinetic energy, an extended object can rotate, vibrate, and change shape. Though the point particle system and the extended system both have the same total mass, and are both acted on by the same net force, the point particle system, has no rotational motion, vibrational motion, or internal energy because all of the forces act at the location of the point particle. In contrast, forces act at different locations on the mass in an extended system, thus causing them to rotate, vibrate and stretch. Because of these qualities, not every part of the system always moves in the same direction as the center of mass moves.

When calculating work done on an extended system, the displacement of every point where a force is applied must be considered separately, because it matters where each force is applied.

===A Mathematical Model===

Work and Energy for an Extended System:
[[File:Work and Energy for an Extended System.png]]

This equation assumes that each force is constant during the displacement. If each force is not constant during the displacement, the work of each force as an integral of <math>\vec{F}_{i}•d\vec{r}_{i}</math> must be calculated either analytically or numerically.

===A Computational Model===

'''A Jumping Kangaroo Modeled as an Extended Object:'''

If one were to model a jumping kangaroo as a point particle system, the change in translational kinetic energy could be derived. However in the real world, Kangaroos are not a point particle, but rather an extended system where energy changes occur in the legs and arms of the kangaroo relative to the center of mass. Chemical energy and thermal energy are just two more examples of energy changes that may occur in extended systems but not in point particle systems.

The work done on a point particle system is not the same as the work done on an extended system. Because forces are applied in many different locations on the mass in an extended system, sometimes these forces act through different distances than the displacement of the center of mass of the system, for different sections of the system move different distances. The following free-body diagram a modeled extended system illustrates how these individual forces may act at different locations:

[[File:Extended_System_Model.png]]

When considering all the possible changes in energy when a Kangaroo jumps, the energy equation for the Kangaroo modeled as an extended system (ignoring Q, or the transfer of energy due to a temperature difference between the Kangaroo and the surrounding air), should look like the following equation:
[[File:Improved_Energy_Equation_for_the_Extended_System_of_a_Kangaroo_Jumping.png]]

The change in relative kinetic energy and the change in internal energy do not appear in the energy equation for the point particle system because the point particle system only focuses on the translational motion of the center of mass point. The change in relative kinetic energy includes the rotation of the legs and the swinging of the upper body and tail of the Kangaroo. The change in internal energy includes the increase in thermal energy of the Kangaroo's body and the decrease in chemical energy that was previously chemically stored in the Kangaroo's body. This computational model of the jumping Kangaroo allows one to visualize how unlike the point particle system, the extended system changes shape due to the bending of the legs, arms, and torso of the Kangaroo during the jump.

==Example==
===Simple===
'''Example 1: A Yo-yo'''

[[File:Yo-yo_as_an_extended_system.png]][Chabay, Ruth W., and Bruce A. Sherwood. "9." Matter & Interactions. N.p.: n.p., n.d. N. pag. Print.](Chabay)

'''Solution'''
'''(a)'''

System: Point Particle

Surroundings: Hand and Earth

Initial State: Point particle with initial translational kinetic energy

Final State: Point particle with final translational kinetic energy

Energy Principle (keep in mind that point particle systems only have translational kinetic energy!)
[[File:Yo-yo_part_a_solution.png]]

'''Solution'''
'''(b)'''

[[File:Yo-yo_part_b_solution.png]]

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

This topic interests me because it involves calculating work in real systems present in the real world, unlike the point particle system which focuses more on calculating work on single atoms or idealized versions of objects modeled as a point particle. Being able to apply physics to real world situations is always so exciting for me.

2. How is it connected to your major?

I am a biology major. By learning how to calculate the work done on an extended system, for example a Kangaroo jumping, I am able to incorporate and consider chemical energy changes and thermal energy changes in the Kangaroo. Knowledge in how much energy a Kangaroo uses while jumping is just one example of how I am able to use physics to forward my knowledge in the biology field as well.

3. Is there an interesting industrial application?

This is a very interesting industrial application because knowing how to calculate the work done on an extended system such as a rocket, could forward our knowledge in rocket science and what is needed to travel further into space. Once we are able to quantify how much work must be done on a system to travel a certain distance at a safe, controlled speed, we have the potential to maybe one day reach Mars and other planets!

== See also ==

===Further reading===

For more information on Point Particle and Extended Systems please visit: http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:pp_vs_real

===External links===

Check out [http://www.physicsbook.gatech.edu/Point_Particle_Systems] to learn more about Point Particle Systems!

Also take a look at [http://www.physicsbook.gatech.edu/Real_Systems] to review more information on Extended (Real) Systems.

==References==

All images used on this page do not belong to me. All problem examples are from the Matter and Interactions Physics book referenced below.

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

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

Work and Energy for an Extended System

2015-12-04T07:00:11Z

Mlamarca3: /* References */

"Work and Energy for an Extended System" in progress by Morgan LaMarca

==The Main Idea==

Unlike the point particle system where the only energy possible is translational kinetic energy, an extended object can rotate, vibrate, and change shape. Though the point particle system and the extended system both have the same total mass, and are both acted on by the same net force, the point particle system, has no rotational motion, vibrational motion, or internal energy because all of the forces act at the location of the point particle. In contrast, forces act at different locations on the mass in an extended system, thus causing them to rotate, vibrate and stretch. Because of these qualities, not every part of the system always moves in the same direction as the center of mass moves.

When calculating work done on an extended system, the displacement of every point where a force is applied must be considered separately, because it matters where each force is applied.

===A Mathematical Model===

Work and Energy for an Extended System:
[[File:Work and Energy for an Extended System.png]]

This equation assumes that each force is constant during the displacement. If each force is not constant during the displacement, the work of each force as an integral of <math>\vec{F}_{i}•d\vec{r}_{i}</math> must be calculated either analytically or numerically.

===A Computational Model===

'''A Jumping Kangaroo Modeled as an Extended Object:'''

If one were to model a jumping kangaroo as a point particle system, the change in translational kinetic energy could be derived. However in the real world, Kangaroos are not a point particle, but rather an extended system where energy changes occur in the legs and arms of the kangaroo relative to the center of mass. Chemical energy and thermal energy are just two more examples of energy changes that may occur in extended systems but not in point particle systems.

The work done on a point particle system is not the same as the work done on an extended system. Because forces are applied in many different locations on the mass in an extended system, sometimes these forces act through different distances than the displacement of the center of mass of the system, for different sections of the system move different distances. The following free-body diagram a modeled extended system illustrates how these individual forces may act at different locations:

[[File:Extended_System_Model.png]]

When considering all the possible changes in energy when a Kangaroo jumps, the energy equation for the Kangaroo modeled as an extended system (ignoring Q, or the transfer of energy due to a temperature difference between the Kangaroo and the surrounding air), should look like the following equation:
[[File:Improved_Energy_Equation_for_the_Extended_System_of_a_Kangaroo_Jumping.png]]

The change in relative kinetic energy and the change in internal energy do not appear in the energy equation for the point particle system because the point particle system only focuses on the translational motion of the center of mass point. The change in relative kinetic energy includes the rotation of the legs and the swinging of the upper body and tail of the Kangaroo. The change in internal energy includes the increase in thermal energy of the Kangaroo's body and the decrease in chemical energy that was previously chemically stored in the Kangaroo's body. This computational model of the jumping Kangaroo allows one to visualize how unlike the point particle system, the extended system changes shape due to the bending of the legs, arms, and torso of the Kangaroo during the jump.

==Example==
===Simple===
'''Example 1: A Yo-yo'''

[[File:Yo-yo_as_an_extended_system.png]][http://www.example.com link title](Chabay)

'''Solution'''
'''(a)'''

System: Point Particle

Surroundings: Hand and Earth

Initial State: Point particle with initial translational kinetic energy

Final State: Point particle with final translational kinetic energy

Energy Principle (keep in mind that point particle systems only have translational kinetic energy!)
[[File:Yo-yo_part_a_solution.png]]

'''Solution'''
'''(b)'''

[[File:Yo-yo_part_b_solution.png]]

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

This topic interests me because it involves calculating work in real systems present in the real world, unlike the point particle system which focuses more on calculating work on single atoms or idealized versions of objects modeled as a point particle. Being able to apply physics to real world situations is always so exciting for me.

2. How is it connected to your major?

I am a biology major. By learning how to calculate the work done on an extended system, for example a Kangaroo jumping, I am able to incorporate and consider chemical energy changes and thermal energy changes in the Kangaroo. Knowledge in how much energy a Kangaroo uses while jumping is just one example of how I am able to use physics to forward my knowledge in the biology field as well.

3. Is there an interesting industrial application?

This is a very interesting industrial application because knowing how to calculate the work done on an extended system such as a rocket, could forward our knowledge in rocket science and what is needed to travel further into space. Once we are able to quantify how much work must be done on a system to travel a certain distance at a safe, controlled speed, we have the potential to maybe one day reach Mars and other planets!

== See also ==

===Further reading===

For more information on Point Particle and Extended Systems please visit: http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:pp_vs_real

===External links===

Check out [http://www.physicsbook.gatech.edu/Point_Particle_Systems] to learn more about Point Particle Systems!

Also take a look at [http://www.physicsbook.gatech.edu/Real_Systems] to review more information on Extended (Real) Systems.

==References==

All images used on this page do not belong to me. All problem examples are from the Matter and Interactions Physics book referenced below.

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

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

Work and Energy for an Extended System

2015-12-04T06:59:07Z

Mlamarca3: /* See also */

"Work and Energy for an Extended System" in progress by Morgan LaMarca

==The Main Idea==

Unlike the point particle system where the only energy possible is translational kinetic energy, an extended object can rotate, vibrate, and change shape. Though the point particle system and the extended system both have the same total mass, and are both acted on by the same net force, the point particle system, has no rotational motion, vibrational motion, or internal energy because all of the forces act at the location of the point particle. In contrast, forces act at different locations on the mass in an extended system, thus causing them to rotate, vibrate and stretch. Because of these qualities, not every part of the system always moves in the same direction as the center of mass moves.

When calculating work done on an extended system, the displacement of every point where a force is applied must be considered separately, because it matters where each force is applied.

===A Mathematical Model===

Work and Energy for an Extended System:
[[File:Work and Energy for an Extended System.png]]

This equation assumes that each force is constant during the displacement. If each force is not constant during the displacement, the work of each force as an integral of <math>\vec{F}_{i}•d\vec{r}_{i}</math> must be calculated either analytically or numerically.

===A Computational Model===

'''A Jumping Kangaroo Modeled as an Extended Object:'''

If one were to model a jumping kangaroo as a point particle system, the change in translational kinetic energy could be derived. However in the real world, Kangaroos are not a point particle, but rather an extended system where energy changes occur in the legs and arms of the kangaroo relative to the center of mass. Chemical energy and thermal energy are just two more examples of energy changes that may occur in extended systems but not in point particle systems.

The work done on a point particle system is not the same as the work done on an extended system. Because forces are applied in many different locations on the mass in an extended system, sometimes these forces act through different distances than the displacement of the center of mass of the system, for different sections of the system move different distances. The following free-body diagram a modeled extended system illustrates how these individual forces may act at different locations:

[[File:Extended_System_Model.png]]

When considering all the possible changes in energy when a Kangaroo jumps, the energy equation for the Kangaroo modeled as an extended system (ignoring Q, or the transfer of energy due to a temperature difference between the Kangaroo and the surrounding air), should look like the following equation:
[[File:Improved_Energy_Equation_for_the_Extended_System_of_a_Kangaroo_Jumping.png]]

The change in relative kinetic energy and the change in internal energy do not appear in the energy equation for the point particle system because the point particle system only focuses on the translational motion of the center of mass point. The change in relative kinetic energy includes the rotation of the legs and the swinging of the upper body and tail of the Kangaroo. The change in internal energy includes the increase in thermal energy of the Kangaroo's body and the decrease in chemical energy that was previously chemically stored in the Kangaroo's body. This computational model of the jumping Kangaroo allows one to visualize how unlike the point particle system, the extended system changes shape due to the bending of the legs, arms, and torso of the Kangaroo during the jump.

==Example==
===Simple===
'''Example 1: A Yo-yo'''

[[File:Yo-yo_as_an_extended_system.png]][http://www.example.com link title](Chabay)

'''Solution'''
'''(a)'''

System: Point Particle

Surroundings: Hand and Earth

Initial State: Point particle with initial translational kinetic energy

Final State: Point particle with final translational kinetic energy

Energy Principle (keep in mind that point particle systems only have translational kinetic energy!)
[[File:Yo-yo_part_a_solution.png]]

'''Solution'''
'''(b)'''

[[File:Yo-yo_part_b_solution.png]]

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

This topic interests me because it involves calculating work in real systems present in the real world, unlike the point particle system which focuses more on calculating work on single atoms or idealized versions of objects modeled as a point particle. Being able to apply physics to real world situations is always so exciting for me.

2. How is it connected to your major?

I am a biology major. By learning how to calculate the work done on an extended system, for example a Kangaroo jumping, I am able to incorporate and consider chemical energy changes and thermal energy changes in the Kangaroo. Knowledge in how much energy a Kangaroo uses while jumping is just one example of how I am able to use physics to forward my knowledge in the biology field as well.

3. Is there an interesting industrial application?

This is a very interesting industrial application because knowing how to calculate the work done on an extended system such as a rocket, could forward our knowledge in rocket science and what is needed to travel further into space. Once we are able to quantify how much work must be done on a system to travel a certain distance at a safe, controlled speed, we have the potential to maybe one day reach Mars and other planets!

== See also ==

===Further reading===

For more information on Point Particle and Extended Systems please visit: http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:pp_vs_real

===External links===

Check out [http://www.physicsbook.gatech.edu/Point_Particle_Systems] to learn more about Point Particle Systems!

Also take a look at [http://www.physicsbook.gatech.edu/Real_Systems] to review more information on Extended (Real) Systems.

==References==

All images used on this page do not belong to me. All problem examples are from the Matter and Interactions Physics book referenced below.
Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9

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

Work and Energy for an Extended System

2015-12-04T06:53:50Z

Mlamarca3: /* History */

"Work and Energy for an Extended System" in progress by Morgan LaMarca

==The Main Idea==

Unlike the point particle system where the only energy possible is translational kinetic energy, an extended object can rotate, vibrate, and change shape. Though the point particle system and the extended system both have the same total mass, and are both acted on by the same net force, the point particle system, has no rotational motion, vibrational motion, or internal energy because all of the forces act at the location of the point particle. In contrast, forces act at different locations on the mass in an extended system, thus causing them to rotate, vibrate and stretch. Because of these qualities, not every part of the system always moves in the same direction as the center of mass moves.

When calculating work done on an extended system, the displacement of every point where a force is applied must be considered separately, because it matters where each force is applied.

===A Mathematical Model===

Work and Energy for an Extended System:
[[File:Work and Energy for an Extended System.png]]

This equation assumes that each force is constant during the displacement. If each force is not constant during the displacement, the work of each force as an integral of <math>\vec{F}_{i}•d\vec{r}_{i}</math> must be calculated either analytically or numerically.

===A Computational Model===

'''A Jumping Kangaroo Modeled as an Extended Object:'''

If one were to model a jumping kangaroo as a point particle system, the change in translational kinetic energy could be derived. However in the real world, Kangaroos are not a point particle, but rather an extended system where energy changes occur in the legs and arms of the kangaroo relative to the center of mass. Chemical energy and thermal energy are just two more examples of energy changes that may occur in extended systems but not in point particle systems.

The work done on a point particle system is not the same as the work done on an extended system. Because forces are applied in many different locations on the mass in an extended system, sometimes these forces act through different distances than the displacement of the center of mass of the system, for different sections of the system move different distances. The following free-body diagram a modeled extended system illustrates how these individual forces may act at different locations:

[[File:Extended_System_Model.png]]

When considering all the possible changes in energy when a Kangaroo jumps, the energy equation for the Kangaroo modeled as an extended system (ignoring Q, or the transfer of energy due to a temperature difference between the Kangaroo and the surrounding air), should look like the following equation:
[[File:Improved_Energy_Equation_for_the_Extended_System_of_a_Kangaroo_Jumping.png]]

The change in relative kinetic energy and the change in internal energy do not appear in the energy equation for the point particle system because the point particle system only focuses on the translational motion of the center of mass point. The change in relative kinetic energy includes the rotation of the legs and the swinging of the upper body and tail of the Kangaroo. The change in internal energy includes the increase in thermal energy of the Kangaroo's body and the decrease in chemical energy that was previously chemically stored in the Kangaroo's body. This computational model of the jumping Kangaroo allows one to visualize how unlike the point particle system, the extended system changes shape due to the bending of the legs, arms, and torso of the Kangaroo during the jump.

==Example==
===Simple===
'''Example 1: A Yo-yo'''

[[File:Yo-yo_as_an_extended_system.png]][http://www.example.com link title](Chabay)

'''Solution'''
'''(a)'''

System: Point Particle

Surroundings: Hand and Earth

Initial State: Point particle with initial translational kinetic energy

Final State: Point particle with final translational kinetic energy

Energy Principle (keep in mind that point particle systems only have translational kinetic energy!)
[[File:Yo-yo_part_a_solution.png]]

'''Solution'''
'''(b)'''

[[File:Yo-yo_part_b_solution.png]]

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

This topic interests me because it involves calculating work in real systems present in the real world, unlike the point particle system which focuses more on calculating work on single atoms or idealized versions of objects modeled as a point particle. Being able to apply physics to real world situations is always so exciting for me.

2. How is it connected to your major?

I am a biology major. By learning how to calculate the work done on an extended system, for example a Kangaroo jumping, I am able to incorporate and consider chemical energy changes and thermal energy changes in the Kangaroo. Knowledge in how much energy a Kangaroo uses while jumping is just one example of how I am able to use physics to forward my knowledge in the biology field as well.

3. Is there an interesting industrial application?

This is a very interesting industrial application because knowing how to calculate the work done on an extended system such as a rocket, could forward our knowledge in rocket science and what is needed to travel further into space. Once we are able to quantify how much work must be done on a system to travel a certain distance at a safe, controlled speed, we have the potential to maybe one day reach Mars and other planets!

== 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==

All images used on this page do not belong to me. All problem examples are from the Matter and Interactions Physics book referenced below.
Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9

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

Work and Energy for an Extended System

2015-12-04T06:52:28Z

Mlamarca3: /* Connectedness */

"Work and Energy for an Extended System" in progress by Morgan LaMarca

==The Main Idea==

Unlike the point particle system where the only energy possible is translational kinetic energy, an extended object can rotate, vibrate, and change shape. Though the point particle system and the extended system both have the same total mass, and are both acted on by the same net force, the point particle system, has no rotational motion, vibrational motion, or internal energy because all of the forces act at the location of the point particle. In contrast, forces act at different locations on the mass in an extended system, thus causing them to rotate, vibrate and stretch. Because of these qualities, not every part of the system always moves in the same direction as the center of mass moves.

When calculating work done on an extended system, the displacement of every point where a force is applied must be considered separately, because it matters where each force is applied.

===A Mathematical Model===

Work and Energy for an Extended System:
[[File:Work and Energy for an Extended System.png]]

This equation assumes that each force is constant during the displacement. If each force is not constant during the displacement, the work of each force as an integral of <math>\vec{F}_{i}•d\vec{r}_{i}</math> must be calculated either analytically or numerically.

===A Computational Model===

'''A Jumping Kangaroo Modeled as an Extended Object:'''

If one were to model a jumping kangaroo as a point particle system, the change in translational kinetic energy could be derived. However in the real world, Kangaroos are not a point particle, but rather an extended system where energy changes occur in the legs and arms of the kangaroo relative to the center of mass. Chemical energy and thermal energy are just two more examples of energy changes that may occur in extended systems but not in point particle systems.

The work done on a point particle system is not the same as the work done on an extended system. Because forces are applied in many different locations on the mass in an extended system, sometimes these forces act through different distances than the displacement of the center of mass of the system, for different sections of the system move different distances. The following free-body diagram a modeled extended system illustrates how these individual forces may act at different locations:

[[File:Extended_System_Model.png]]

When considering all the possible changes in energy when a Kangaroo jumps, the energy equation for the Kangaroo modeled as an extended system (ignoring Q, or the transfer of energy due to a temperature difference between the Kangaroo and the surrounding air), should look like the following equation:
[[File:Improved_Energy_Equation_for_the_Extended_System_of_a_Kangaroo_Jumping.png]]

The change in relative kinetic energy and the change in internal energy do not appear in the energy equation for the point particle system because the point particle system only focuses on the translational motion of the center of mass point. The change in relative kinetic energy includes the rotation of the legs and the swinging of the upper body and tail of the Kangaroo. The change in internal energy includes the increase in thermal energy of the Kangaroo's body and the decrease in chemical energy that was previously chemically stored in the Kangaroo's body. This computational model of the jumping Kangaroo allows one to visualize how unlike the point particle system, the extended system changes shape due to the bending of the legs, arms, and torso of the Kangaroo during the jump.

==Example==
===Simple===
'''Example 1: A Yo-yo'''

[[File:Yo-yo_as_an_extended_system.png]][http://www.example.com link title](Chabay)

'''Solution'''
'''(a)'''

System: Point Particle

Surroundings: Hand and Earth

Initial State: Point particle with initial translational kinetic energy

Final State: Point particle with final translational kinetic energy

Energy Principle (keep in mind that point particle systems only have translational kinetic energy!)
[[File:Yo-yo_part_a_solution.png]]

'''Solution'''
'''(b)'''

[[File:Yo-yo_part_b_solution.png]]

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

This topic interests me because it involves calculating work in real systems present in the real world, unlike the point particle system which focuses more on calculating work on single atoms or idealized versions of objects modeled as a point particle. Being able to apply physics to real world situations is always so exciting for me.

2. How is it connected to your major?

I am a biology major. By learning how to calculate the work done on an extended system, for example a Kangaroo jumping, I am able to incorporate and consider chemical energy changes and thermal energy changes in the Kangaroo. Knowledge in how much energy a Kangaroo uses while jumping is just one example of how I am able to use physics to forward my knowledge in the biology field as well.

3. Is there an interesting industrial application?

This is a very interesting industrial application because knowing how to calculate the work done on an extended system such as a rocket, could forward our knowledge in rocket science and what is needed to travel further into space. Once we are able to quantify how much work must be done on a system to travel a certain distance at a safe, controlled speed, we have the potential to maybe one day reach Mars and other planets!

==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==

All images used on this page do not belong to me. All problem examples are from the Matter and Interactions Physics book referenced below.
Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9

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

Work and Energy for an Extended System

2015-12-04T06:44:26Z

Mlamarca3: /* References */

"Work and Energy for an Extended System" in progress by Morgan LaMarca

==The Main Idea==

Unlike the point particle system where the only energy possible is translational kinetic energy, an extended object can rotate, vibrate, and change shape. Though the point particle system and the extended system both have the same total mass, and are both acted on by the same net force, the point particle system, has no rotational motion, vibrational motion, or internal energy because all of the forces act at the location of the point particle. In contrast, forces act at different locations on the mass in an extended system, thus causing them to rotate, vibrate and stretch. Because of these qualities, not every part of the system always moves in the same direction as the center of mass moves.

When calculating work done on an extended system, the displacement of every point where a force is applied must be considered separately, because it matters where each force is applied.

===A Mathematical Model===

Work and Energy for an Extended System:
[[File:Work and Energy for an Extended System.png]]

This equation assumes that each force is constant during the displacement. If each force is not constant during the displacement, the work of each force as an integral of <math>\vec{F}_{i}•d\vec{r}_{i}</math> must be calculated either analytically or numerically.

===A Computational Model===

'''A Jumping Kangaroo Modeled as an Extended Object:'''

If one were to model a jumping kangaroo as a point particle system, the change in translational kinetic energy could be derived. However in the real world, Kangaroos are not a point particle, but rather an extended system where energy changes occur in the legs and arms of the kangaroo relative to the center of mass. Chemical energy and thermal energy are just two more examples of energy changes that may occur in extended systems but not in point particle systems.

The work done on a point particle system is not the same as the work done on an extended system. Because forces are applied in many different locations on the mass in an extended system, sometimes these forces act through different distances than the displacement of the center of mass of the system, for different sections of the system move different distances. The following free-body diagram a modeled extended system illustrates how these individual forces may act at different locations:

[[File:Extended_System_Model.png]]

When considering all the possible changes in energy when a Kangaroo jumps, the energy equation for the Kangaroo modeled as an extended system (ignoring Q, or the transfer of energy due to a temperature difference between the Kangaroo and the surrounding air), should look like the following equation:
[[File:Improved_Energy_Equation_for_the_Extended_System_of_a_Kangaroo_Jumping.png]]

The change in relative kinetic energy and the change in internal energy do not appear in the energy equation for the point particle system because the point particle system only focuses on the translational motion of the center of mass point. The change in relative kinetic energy includes the rotation of the legs and the swinging of the upper body and tail of the Kangaroo. The change in internal energy includes the increase in thermal energy of the Kangaroo's body and the decrease in chemical energy that was previously chemically stored in the Kangaroo's body. This computational model of the jumping Kangaroo allows one to visualize how unlike the point particle system, the extended system changes shape due to the bending of the legs, arms, and torso of the Kangaroo during the jump.

==Example==
===Simple===
'''Example 1: A Yo-yo'''

[[File:Yo-yo_as_an_extended_system.png]][http://www.example.com link title](Chabay)

'''Solution'''
'''(a)'''

System: Point Particle

Surroundings: Hand and Earth

Initial State: Point particle with initial translational kinetic energy

Final State: Point particle with final translational kinetic energy

Energy Principle (keep in mind that point particle systems only have translational kinetic energy!)
[[File:Yo-yo_part_a_solution.png]]

'''Solution'''
'''(b)'''

[[File:Yo-yo_part_b_solution.png]]

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==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==

All images used on this page do not belong to me. All problem examples are from the Matter and Interactions Physics book referenced below.
Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9

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

Work and Energy for an Extended System

2015-12-04T06:31:22Z

Mlamarca3: /* Examples */

"Work and Energy for an Extended System" in progress by Morgan LaMarca

==The Main Idea==

Unlike the point particle system where the only energy possible is translational kinetic energy, an extended object can rotate, vibrate, and change shape. Though the point particle system and the extended system both have the same total mass, and are both acted on by the same net force, the point particle system, has no rotational motion, vibrational motion, or internal energy because all of the forces act at the location of the point particle. In contrast, forces act at different locations on the mass in an extended system, thus causing them to rotate, vibrate and stretch. Because of these qualities, not every part of the system always moves in the same direction as the center of mass moves.

When calculating work done on an extended system, the displacement of every point where a force is applied must be considered separately, because it matters where each force is applied.

===A Mathematical Model===

Work and Energy for an Extended System:
[[File:Work and Energy for an Extended System.png]]

This equation assumes that each force is constant during the displacement. If each force is not constant during the displacement, the work of each force as an integral of <math>\vec{F}_{i}•d\vec{r}_{i}</math> must be calculated either analytically or numerically.

===A Computational Model===

'''A Jumping Kangaroo Modeled as an Extended Object:'''

If one were to model a jumping kangaroo as a point particle system, the change in translational kinetic energy could be derived. However in the real world, Kangaroos are not a point particle, but rather an extended system where energy changes occur in the legs and arms of the kangaroo relative to the center of mass. Chemical energy and thermal energy are just two more examples of energy changes that may occur in extended systems but not in point particle systems.

The work done on a point particle system is not the same as the work done on an extended system. Because forces are applied in many different locations on the mass in an extended system, sometimes these forces act through different distances than the displacement of the center of mass of the system, for different sections of the system move different distances. The following free-body diagram a modeled extended system illustrates how these individual forces may act at different locations:

[[File:Extended_System_Model.png]]

When considering all the possible changes in energy when a Kangaroo jumps, the energy equation for the Kangaroo modeled as an extended system (ignoring Q, or the transfer of energy due to a temperature difference between the Kangaroo and the surrounding air), should look like the following equation:
[[File:Improved_Energy_Equation_for_the_Extended_System_of_a_Kangaroo_Jumping.png]]

The change in relative kinetic energy and the change in internal energy do not appear in the energy equation for the point particle system because the point particle system only focuses on the translational motion of the center of mass point. The change in relative kinetic energy includes the rotation of the legs and the swinging of the upper body and tail of the Kangaroo. The change in internal energy includes the increase in thermal energy of the Kangaroo's body and the decrease in chemical energy that was previously chemically stored in the Kangaroo's body. This computational model of the jumping Kangaroo allows one to visualize how unlike the point particle system, the extended system changes shape due to the bending of the legs, arms, and torso of the Kangaroo during the jump.

==Example==
===Simple===
'''Example 1: A Yo-yo'''

[[File:Yo-yo_as_an_extended_system.png]][http://www.example.com link title](Chabay)

'''Solution'''
'''(a)'''

System: Point Particle

Surroundings: Hand and Earth

Initial State: Point particle with initial translational kinetic energy

Final State: Point particle with final translational kinetic energy

Energy Principle (keep in mind that point particle systems only have translational kinetic energy!)
[[File:Yo-yo_part_a_solution.png]]

'''Solution'''
'''(b)'''

[[File:Yo-yo_part_b_solution.png]]

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==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==

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

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

Work and Energy for an Extended System

2015-12-04T06:29:58Z

Mlamarca3: /* Examples */

"Work and Energy for an Extended System" in progress by Morgan LaMarca

==The Main Idea==

Unlike the point particle system where the only energy possible is translational kinetic energy, an extended object can rotate, vibrate, and change shape. Though the point particle system and the extended system both have the same total mass, and are both acted on by the same net force, the point particle system, has no rotational motion, vibrational motion, or internal energy because all of the forces act at the location of the point particle. In contrast, forces act at different locations on the mass in an extended system, thus causing them to rotate, vibrate and stretch. Because of these qualities, not every part of the system always moves in the same direction as the center of mass moves.

When calculating work done on an extended system, the displacement of every point where a force is applied must be considered separately, because it matters where each force is applied.

===A Mathematical Model===

Work and Energy for an Extended System:
[[File:Work and Energy for an Extended System.png]]

This equation assumes that each force is constant during the displacement. If each force is not constant during the displacement, the work of each force as an integral of <math>\vec{F}_{i}•d\vec{r}_{i}</math> must be calculated either analytically or numerically.

===A Computational Model===

'''A Jumping Kangaroo Modeled as an Extended Object:'''

If one were to model a jumping kangaroo as a point particle system, the change in translational kinetic energy could be derived. However in the real world, Kangaroos are not a point particle, but rather an extended system where energy changes occur in the legs and arms of the kangaroo relative to the center of mass. Chemical energy and thermal energy are just two more examples of energy changes that may occur in extended systems but not in point particle systems.

The work done on a point particle system is not the same as the work done on an extended system. Because forces are applied in many different locations on the mass in an extended system, sometimes these forces act through different distances than the displacement of the center of mass of the system, for different sections of the system move different distances. The following free-body diagram a modeled extended system illustrates how these individual forces may act at different locations:

[[File:Extended_System_Model.png]]

When considering all the possible changes in energy when a Kangaroo jumps, the energy equation for the Kangaroo modeled as an extended system (ignoring Q, or the transfer of energy due to a temperature difference between the Kangaroo and the surrounding air), should look like the following equation:
[[File:Improved_Energy_Equation_for_the_Extended_System_of_a_Kangaroo_Jumping.png]]

The change in relative kinetic energy and the change in internal energy do not appear in the energy equation for the point particle system because the point particle system only focuses on the translational motion of the center of mass point. The change in relative kinetic energy includes the rotation of the legs and the swinging of the upper body and tail of the Kangaroo. The change in internal energy includes the increase in thermal energy of the Kangaroo's body and the decrease in chemical energy that was previously chemically stored in the Kangaroo's body. This computational model of the jumping Kangaroo allows one to visualize how unlike the point particle system, the extended system changes shape due to the bending of the legs, arms, and torso of the Kangaroo during the jump.

==Examples==
===Simple===
'''Example 1: A Yo-yo'''

[[File:Yo-yo_as_an_extended_system.png]][http://www.example.com link title](Chabay)

'''Solution'''
'''(a)'''

System: Point Particle

Surroundings: Hand and Earth

Initial State: Point particle with initial translational kinetic energy

Final State: Point particle with final translational kinetic energy

Energy Principle (keep in mind that point particle systems only have translational kinetic energy!)
[[File:Yo-yo_part_a_solution.png]]

'''Solution'''
'''(b)'''

[[File:Yo-yo_part_b_solution.png]]

===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==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==

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

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

File:Yo-yo part b solution.png

2015-12-04T06:27:18Z

Mlamarca3:

File:Yo-yo part a solution.png

2015-12-04T06:25:11Z

Mlamarca3:

File:Yo-yo as an extended system.png

2015-12-04T06:17:20Z

Mlamarca3:

Work and Energy for an Extended System

2015-12-04T06:08:33Z

Mlamarca3: /* A Computational Model */

File:Improved Energy Equation for the Extended System of a Kangaroo Jumping.png

2015-12-04T05:59:54Z

Mlamarca3:

Work and Energy for an Extended System

2015-12-04T05:55:14Z

Mlamarca3: /* A Computational Model */

File:Extended System Model.png

2015-12-04T05:52:36Z

Mlamarca3:

Work and Energy for an Extended System

2015-12-04T05:37:24Z

Mlamarca3: /* The Main Idea */

Work and Energy for an Extended System

2015-12-04T05:22:29Z

Mlamarca3: /* A Mathematical Model */

"Work and Energy for an Extended System" in progress by Morgan LaMarca

==The Main Idea==

State, in your own words, the main idea for this topic

===A Mathematical Model===

[[File:Work and Energy for an Extended System.png]]
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==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==

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

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

File:Work and Energy for an Extended System.png

2015-12-04T05:20:58Z

Mlamarca3:

Work and Energy for an Extended System

2015-12-04T05:08:25Z

Mlamarca3:

"Work and Energy for an Extended System" in progress by Morgan LaMarca

==The Main Idea==

State, in your own words, the main idea for this topic

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==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==

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

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

Work and Energy for an Extended System

2015-12-04T05:04:45Z

Mlamarca3: Created page with "Short Description of Topic Contents [hide] 1 The Main Idea 1.1 A Mathematical Model 1.2 A Computational Model 2 Examples 2.1 Simple 2.2 Middling 2.3 Difficult 3 Connectednes..."

Short Description of Topic

Contents [hide]
1 The Main Idea
1.1 A Mathematical Model
1.2 A Computational Model
2 Examples
2.1 Simple
2.2 Middling
2.3 Difficult
3 Connectedness
4 History
5 See also
5.1 Further reading
5.2 External links
6 References
The Main Idea[edit]
State, in your own words, the main idea for this topic Electric Field of Capacitor

A Mathematical Model[edit]
What are the mathematical equations that allow us to model this topic. For example dp⃗ dtsystem=F⃗ net where p is the momentum of the system and F is the net force from the surroundings.

A Computational Model[edit]
How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples[edit]
Be sure to show all steps in your solution and include diagrams whenever possible

Simple[edit]
Middling[edit]
Difficult[edit]
Connectedness[edit]
How is this topic connected to something that you are interested in?
How is it connected to your major?
Is there an interesting industrial application?
History[edit]
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

See also[edit]
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[edit]
Books, Articles or other print media on this topic

External links[edit]
[1]

References[edit]
This section contains the the references you used while writing this page

Main Page

2015-12-04T05:02:39Z

Mlamarca3: /* Energy */

__NOTOC__
Welcome to the Georgia Tech Wiki for Intro Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it!

Looking to make a contribution?
#Pick a specific topic from intro physics
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.
#Copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.

<div class="toccolours mw-collapsible mw-collapsed">
===Interactions===
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
**[[Ball and Spring Model of Matter]]
*[[Detecting Interactions]]
*[[Fundamental Interactions]]
*[[Determinism]]
*[[System & Surroundings]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Gravitational Force]]
*[[Electric Force]]
*[[Conservation of Energy]]
*[[Conservation of Charge]]
*[[Terminal Speed]]
*[[Simple Harmonic Motion]]
*[[Speed and Velocity]]
*[[Electric Polarization]]
*[[Perpetual Freefall (Orbit)]]
*[[2-Dimensional Motion]]
*[[Center of Mass]]
*[[Reaction Time]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Special Relativity]]
*[[Quantum Theory]]
*[[Maxwell's Electromagnetic Theory]]
*[[Atomic Theory]]
*[[String Theory]]
*[[Elementary Particles and Particle Physics Theory]]
*[[Law of Gravitation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Notable Scientists===
<div class="mw-collapsible-content">
*[[Christian Doppler]]
*[[Albert Einstein]]
*[[Ernest Rutherford]]
*[[Joseph Henry]]
*[[Michael Faraday]]
*[[J.J. Thomson]]
*[[James Maxwell]]
*[[Robert Hooke]]
*[[Carl Friedrich Gauss]]
*[[Nikola Tesla]]
*[[Andre Marie Ampere]]
*[[Sir Isaac Newton]]
*[[J. Robert Oppenheimer]]
*[[Oliver Heaviside]]
*[[Rosalind Franklin]]
*[[Erwin Schrödinger]]
*[[Enrico Fermi]]
*[[Robert J. Van de Graaff]]
*[[Charles de Coulomb]]
*[[Hans Christian Ørsted]]
*[[Philo Farnsworth]]
*[[Niels Bohr]]
*[[Georg Ohm]]
*[[Galileo Galilei]]
*[[Gustav Kirchhoff]]
*[[Max Planck]]
*[[Heinrich Hertz]]
*[[Edwin Hall]]
*[[James Watt]]
*[[Count Alessandro Volta]]
*[[Josiah Willard Gibbs]]
*[[Richard Phillips Feynman]]
*[[Sir David Brewster]]
*[[Daniel Bernoulli]]
*[[William Thomson]]
*[[Leonhard Euler]]
*[[Robert Fox Bacher]]
*[[Stephen Hawking]]
*[[Amedeo Avogadro]]
*[[Wilhelm Conrad Roentgen]]
*[[Pierre Laplace]]
*[[Thomas Edison]]
*[[Hendrik Lorentz]]
*[[Jean-Baptiste Biot]]
*[[Lise Meitner]]
*[[Lisa Randall]]
*[[Felix Savart]]
*[[Heinrich Lenz]]
*[[Max Born]]
*[[Archimedes]]
*[[Jean Baptiste Biot]]
*[[Carl Sagan]]
*[[Eugene Wigner]]
*[[Marie Curie]]
*[[Pierre Curie]]
*[[Werner Heisenberg]]
*[[Johannes Diderik van der Waals]]
*[[Louis de Broglie]]
*[[Aristotle]]
*[[Émilie du Châtelet]]
*[[Blaise Pascal]]
*[[Benjamin Franklin]]
*[[James Chadwick]]
*[[Henry Cavendish]]
*[[Thomas Young]]
*[[James Prescott Joule]]
*[[John Bardeen]]
*[[Leo Baekeland]]
*[[Alhazen]]
*[[Willebrod Snell]]
*[[Fritz Walther Meissner]]
*[[Johannes Kepler]]
*[[Johann Wilhelm Ritter]]
*[[Philipp Lenard]]
*[[Xuesen Qian]]
*[[Robert A. Millikan]]
*[[Joseph Louis Gay-Lussac]]
*[[Guglielmo Marconi]]
*[[Luis Walter Alvarez]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[Velocity]]
*[[Relative Velocity]]
*[[Density]]
*[[Charge]]
*[[Spin]]
*[[SI Units]]
*[[Heat Capacity]]
*[[Specific Heat]]
*[[Wavelength]]
*[[Conductivity]]
*[[Malleability]]
*[[Weight]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Inertia]]
*[[Non-Newtonian Fluids]]
*[[Color]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Tension]]
* [[Hooke's Law]]
*[[Centripetal Force and Curving Motion]]
*[[Compression or Normal Force]]
* [[Length and Stiffness of an Interatomic Bond]]
* [[Speed of Sound in a Solid]]
* [[Iterative Prediction of Spring-Mass System]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Momentum===
<div class="mw-collapsible-content">
* [[Vectors]]
* [[Kinematics]]
* [[Conservation of Momentum]]
* [[Predicting Change in multiple dimensions]]
* [[Derivation of the Momentum Principle]]
* [[Momentum Principle]]
* [[Impulse Momentum]]
* [[Curving Motion]]
* [[Projectile Motion]]
* [[Multi-particle Analysis of Momentum]]
* [[Iterative Prediction]]
* [[Analytical Prediction]]
* [[Newton's Laws and Linear Momentum]]
* [[Net Force]]
* [[Center of Mass]]
* [[Momentum at High Speeds]]
* [[Change in Momentum in Time for Curving Motion]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
* [[Moment of Inertia for a ring]]
* [[Rotation]]
* [[Torque]]
* [[Systems with Zero Torque]]
* [[Systems with Nonzero Torque]]
* [[Right Hand Rule]]
* [[Angular Velocity]]
* [[Predicting the Position of a Rotating System]]
* [[Translational Angular Momentum]]
* [[The Angular Momentum Principle]]
* [[Angular Momentum of Multiparticle Systems]]
* [[Rotational Angular Momentum]]
* [[Total Angular Momentum]]
* [[Gyroscopes]]
* [[Angular Momentum Compared to Linear Momentum]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Energy===
<div class="mw-collapsible-content">
*[[The Photoelectric Effect]]
*[[Photons]]
*[[The Energy Principle]]
*[[Predicting Change]]
*[[Rest Mass Energy]]
*[[Kinetic Energy]]
*[[Potential Energy]]
**[[Potential Energy for a Magnetic Dipole]]
**[[Potential Energy of a Multiparticle System]]
*[[Work]]
*[[Work and Energy for an Extended System]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
*[[Point Particle Systems]]
*[[Real Systems]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
*[[Translational, Rotational and Vibrational Energy]]
*[[Franck-Hertz Experiment]]
*[[Power (Mechanical)]]
*[[Transformation of Energy]]

*[[Energy Graphs]]
**[[Energy graphs and the Bohr model]]
*[[Air Resistance]]
*[[Electronic Energy Levels]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Specific Heat Capacity]]
*[[Electronic Energy Levels and Photons]]
*[[Energy Density]]
*[[Bohr Model]]
*[[Quantized energy levels]]
**[[Spontaneous Photon Emission]]
*[[Path Independence of Electric Potential]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Collisions===
<div class="mw-collapsible-content">
*[[Collisions]]
*[[Maximally Inelastic Collision]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Frame of Reference]]
*[[Rutherford Experiment and Atomic Collisions]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Ring]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
** [[Charged Cylinder]]
** [[Charge Density]]
**[[A Solid Sphere Charged Throughout Its Volume]]
*[[Electric Potential]]
**[[Potential Difference Path Independence]]
**[[Potential Difference in a Uniform Field]]
**[[Potential Difference of point charge in a non-Uniform Field]]
**[[Sign of Potential Difference]]
**[[Potential Difference in an Insulator]]
**[[Energy Density and Electric Field]]
** [[Systems of Charged Objects]]
*[[Electric Force]]
*[[Polarization]]
**[[Polarization of an Atom]]
*[[Charge Motion in Metals]]
*[[Charge Transfer]]
*[[Magnetic Field]]
**[[Right-Hand Rule]]
**[[Direction of Magnetic Field]]
**[[Magnetic Field of a Long Straight Wire]]
**[[Magnetic Field of a Loop]]
**[[Magnetic Field of a Solenoid]]
**[[Bar Magnet]]
**[[Magnetic Dipole Moment]]
***[[Stern-Gerlach Experiment]]
**[[Magnetic Force]]
**[[Earth's Magnetic Field]]
**[[Atomic Structure of Magnets]]
*[[Combining Electric and Magnetic Forces]]
**[[Magnetic Torque]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Biot-Savart Law for Currents]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
**[[Moving Point Charge]]
**[[Non-Coulomb Electric Field]]
**[[Motors and Generators]]
**[[Solenoid Applications]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Charging and Discharging a Capacitor]]
*[[Thin and Thick Wires]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Resistivity]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
**[[AC]]
*[[Ohm's Law]]
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[RC]]
*[[AC vs DC]]
*[[Charge in a RC Circuit]]
*[[Current in a RC circuit]]
*[[Circular Loop of Wire]]
*[[Current in a RL Circuit]]
*[[RL Circuit]]
*[[LC Circuit]]
*[[Surface Charge Distributions]]
*[[Feedback]]
*[[Transformers (Circuits)]]
*[[Resistors and Conductivity]]
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
**[[Magnetic Fields]]
*[[Ampere's Law]]
**[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
**[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
**[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Faraday's Law]]
**[[Curly Electric Fields]]
**[[Inductance]]
***[[Transformers from a physics standpoint]]
***[[Energy Density]]
**[[Lenz's Law]]
***[[Lenz Effect and the Jumping Ring]]
**[[Motional Emf using Faraday's Law]]
*[[Ampere-Maxwell Law]]
*[[Superconductors]]
**[[Meissner effect]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Radiation===
<div class="mw-collapsible-content">
*[[Producing a Radiative Electric Field]]
*[[Sinusoidal Electromagnetic Radiaton]]
*[[Lenses]]
*[[Energy and Momentum Analysis in Radiation]]
**[[Poynting Vector]]
*[[Electromagnetic Propagation]]
**[[Wavelength and Frequency]]
*[[Snell's Law]]
*[[Effects of Radiation on Matter]]
*[[Light Propagation Through a Medium]]
*[[Light Scaterring: Why is the Sky Blue]]
*[[Light Refraction: Bending of light]]
*[[Cherenkov Radiation]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Sound===
<div class="mw-collapsible-content">
*[[Doppler Effect]]
*[[Nature, Behavior, and Properties of Sound]]
*[[Resonance]]
*[[Sound Barrier]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Waves===
<div class="mw-collapsible-content">
*[[Multisource Interference: Diffraction]]
*[[Standing waves]]
*[[Gravitational waves]]
*[[Plasma waves]]
*[[Wave-Particle Duality]]
*[[Electromagnetic Waves]]
*[[Electromagnetic Spectrum]]
*[[Color Light Wave]]
*[[Mechanical Waves]]
*[[Pendulum Motion]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Real Life Applications of Electromagnetic Principles===
<div class="mw-collapsible-content">
*[[Electromagnetic Junkyard Cranes]]
*[[Maglev Trains]]
*[[Spark Plugs]]
*[[Metal Detectors]]
*[[Speakers]]
*[[Radios]]
*[[Ampullae of Lorenzini]]
*[[Generator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Optics===
<div class="mw-collapsible-content">
*[[Mirrors]]
*[[Refraction]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Computing===
<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
</div>
</div>

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A page for review of [[Vectors]] and vector operations

Newton's Laws and Linear Momentum

2015-11-30T15:04:22Z

Mlamarca3: Created page with " == Linear Momentum == Linear momentum, denoted by the letter '''p''', is a vector quantity which represents the product of an object's velocity, '''v''', and mass, '''m''',..."

== Linear Momentum ==

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

[[File:Momentum_pic.jpg]]

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

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

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

Main Page

2015-11-30T15:03:59Z

Mlamarca3: /* Momentum */

Linear Momentum

2015-11-30T15:00:31Z

File:Momentum pic.jpg

2015-11-30T14:54:30Z

Mlamarca3: