Physics Book - User contributions [en]

Conservation of Energy

2018-04-19T03:10:31Z

A2xreyna: /* Connectedness */

Alex Reyna claimed 4/18/2018

This page was originally created by ksubramanian33, as can be seen by the edit history.
 

==Main Ideas==
===Conceptual Model===
* The law of conservation of energy states that the total amount of energy of a system before and after an interaction between objects.
* This only applies to isolated systems (no outside forces acting on the system).
** Not Isolated: An object sliding across a rough floor (system = the object). There is work being done by the floor on the object because of the frictional force. Energy lost to heat due to friction is an example of mechanical energy being converted into thermal energy.
** Isolated: An object sliding across a rough floor (system = the object AND the floor). There is no work done on the system because all the forces are contained in the system.
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> [[File:IntroConservationEnergy.gif]] </div> see reference 7
[[File:energy-transformation.jpg]]
see reference 3

===Mathematical Model===
* Single Particle
** Particle Energy: Eparticle = γmc2 
** Rest Energy: Erest = mc2 
** Kinetic (particle): K = γmc2 + mc2 
* General Objects
** Kinetic: (1/2)mv2
** Gravitational Potential: (-Gm1m2)/(R2) (large distances), mgh (near the surface of the Earth)
** Spring (Elastic) Potential: (1/2)kss2 
** Thermal Energy: mCΔT 
====General Formulas====
* E = W + Q (if no heat transfer indicated, Q = 0; if no external forces acting on system, W = 0)
* E = K + U (The total energy is the sum of the kinetic and potential energies. From this, you can infer that for an isolated system, any change in kinetic energy will correspond in an equal but opposite change in the potential energy and vice versa.)
These formulas can be interchanged. For example, if you know work and heat transfer are zero, energy equals zero, so K + U will equal zero

[[File:MathConservationEnergy.png]]
 See Reference 2

 [https://www.youtube.com/watch?v=kw_4Loo1HR4 Basic Explanation of Conservation of Energy]
 [https://www.youtube.com/watch?v=EZrJNIBX2wk Skater Visualization of Transfers of Energy]

===Computational Model===
Below is a link to a segment of Vpython code that models the motion of a spring and graphs its kinetic and potential energy. It also shows how the total amount of energy of the system does not change.

"https://trinket.io/embed/glowscript/49c1365501?showInstructions=true"

==Examples==

===Particle===
An electron is accelerated to a speed of 2.95 × 108 
(a) What is the energy of the electron? 
(b) What is the rest energy of the electron? 
(c) What is the kinetic energy of the moving proton? 
(a) 
E = γmc2 
E = (5.50)(9.11 × 10-31)(3 × 108) 
E = 1.50 × 10-21 J 
(b) 
Erest = mc2 
Erest = (9.11 × 10-31)(3 × 108)2 
Erest = 2.73 × 10-22 J 
(c) 
K = E - Erest 
K = 1.50 × 10-21 - 2.73 × 10-22 
K = 1.23 × 10-21 J 

===Simple===
A ball is at rest on a table with 50 J of potential energy. It then rolls of the table, and at one point in time as it falls, the ball has 30 J of kinetic energy. 
What is the potential energy of the ball at that instant?

[[File:EasyEnergyConservation.png]]
 See Reference 3

Einitial = Efinal 
Kinitial + Uinitial = Kfinal + Ufinal 
0 J + 50 J = 30 J + Ufinal 
Ufinal = 20 J

===Middling===
A ball is at rest 50 m above the ground. You then drop the ball. What is its speed before hitting the ground? 
[[File:HardEnergyConservation.gif]]
 See Reference 4 

v = 
√2gh 
 
v = 
√2(9.8)(50) 
 
v = 31.3 m/s

===Difficult===
The driver of an SUV (m = 1700 kg) isn’t paying attention and rear ends a car (m = 950 kg) on level ground at a red light. On impact, both drivers lock their brakes. The SUV and car stick together and travel a distance of 8.2 m before they come to a stop. How fast was the SUV traveling just before the collision? The coefficient of friction between the tires and the road is 0.72.
[[File: DifficultEnergyConservation.png]]
See Reference 5 

KE2 + PE2 = KE3 + PE3 - Wnc 
(1/2)mtotalv22 + mtotalgh2 = (1/2)mtotalv32 + mtotalgh3 - Wnc 
(1/2)mtotalv22 + 0 = 0 + 0 - (μmtotalg)dcos(180°) 
(1/2)v22 = -(0.72)(9.8 m/s2)(8.2 m)(-1) 
v22 = 116 m2/s2 
v2 = 10.8 m/s 

* Notice how the mass is canceled. 

p1 = p2 
p1x = p2x 
msuvvsuv + mcarvcar = mtotalv2 
(1700 kg)vsuv + 0 = (2650 kg)(10.8 m/s) 
(1700 kg)vsuv = 28600 kgm/s 
vsuv = 17 m/s 

==Connectedness==
Industrial Engineering 
1. How is this topic connected to something that you are interested in? 
This concept is clearly connected to physics and helps explain and sometimes predict how objects transform and change as a result of different interactions. Knowing why and how things move and interact is very powerful. 
2. How is it connected to your major? 
This topic is connected to industrial engineering as the field deals heavily with optimization of production processes im manufacturing environments. Obviously, modeling and simulating industrial processes at its core uses the fundamental principles of physics. It is important to take all fundamental concepts of physics, including the conservation of energy, into account. 
3. Is there an interesting industrial application? 
The law of conservation of energy is prevalent in nearly every industrial application of physics. More specifically, it is relevant today as finding renewable and sustainable forms of energy is becoming a more prevalent social and economic issue. It will be interesting to see how this concept will be applied as we try to get more energy for less. Additionally, the law of conservation of energy can be applied at a nuclear microscopic level as radiating particles like alpha particles follow the same energy principle as objects on a macroscopic level. 

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
 Who: Many physicists contributed to the knowledge of energy, however it is most notably atributed to Julius Robert Mayer
 What: Most formally discovered the law of conservation of energy
 When: 1842
 Where: Germany
 Why: To explain what happens to energy in an isolated system
 See Reference 6

== See also ==

[[Kinetic Energy]] 
[[Potential Energy]] 
[[Work]] 
===Further reading===

Goldstein, Martin, and Inge F., (1993). The Refrigerator and the Universe. Harvard Univ. Press. A gentle introduction. 
Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0-7167-1088-9. 
Nolan, Peter J. (1996). Fundamentals of College Physics, 2nd ed. William C. Brown Publishers. 

===External links===
 [https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-conservation-of-energy Khan Academy]
 [http://www.physicsclassroom.com/class/energy/Lesson-2/Application-and-Practice-Questions Practice Questions]
 [http://physics.info/energy-conservation/problems.shtml More Practice]
 [http://gilliesphysics.weebly.com/uploads/5/7/5/2/57520801/conservation_of_energy_practice_problems.pdf Basic Examples] 
[http://www.physnet.org/modules/pdf_modules/m158.pdf The First Law of Thermodynamics]
==References==

1."Conservation of Energy." Hmolpedia. Web. 1 Dec. 2015. <http://www.eoht.info/page/Conservation+of+energy>. 
2. "University of Wisconsin Green Bay." Speed & Stopping Distance of a Roller-Coaster. Web. 1 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/2/>. 
3. "Motion." G9 to Engineering. Web. 1 Dec. 2015. <http://www.g9toengineering.com/resources/translational.htm>. 
4. "Energy of Falling Object." HyperPhysics. Web. 1 Dec. 2015. <http://hyperphysics.phy-astr.gsu.edu/hbase/flobj.html>. 
5. "Conservation of Energy & Momentum Problem: Collision of Two Cars at a Stoplight." University of Wisconsin- Green Bay Physics. Web. 2 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/6/>. 
6. "Law of Conservation of Mass Energy." Law of Conservation of Mass Energy. Web. 3 Dec. 2015. <http://www.chemteam.info/Thermochem/Law-Cons-Mass-Energy.html>.
7. "Law of Conservation of Energy" New York University. Web. 18 Apr. 2018. <http://www.nyu.edu/classes/tuckerman/adv.chem/lectures/lecture_2/node4.html>
8. "Law of Conversation of Energy" ME Mechanical. Web. 18 Apr. 2018. <https://me-mechanicalengineering.com/law-of-conservation-of-energy/>
[[Category:Energy]]

Conservation of Energy

2018-04-19T03:01:13Z

A2xreyna: /* References */

Alex Reyna claimed 4/18/2018

This page was originally created by ksubramanian33, as can be seen by the edit history.
 

==Main Ideas==
===Conceptual Model===
* The law of conservation of energy states that the total amount of energy of a system before and after an interaction between objects.
* This only applies to isolated systems (no outside forces acting on the system).
** Not Isolated: An object sliding across a rough floor (system = the object). There is work being done by the floor on the object because of the frictional force. Energy lost to heat due to friction is an example of mechanical energy being converted into thermal energy.
** Isolated: An object sliding across a rough floor (system = the object AND the floor). There is no work done on the system because all the forces are contained in the system.
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> [[File:IntroConservationEnergy.gif]] </div> see reference 7
[[File:energy-transformation.jpg]]
see reference 3

===Mathematical Model===
* Single Particle
** Particle Energy: Eparticle = γmc2 
** Rest Energy: Erest = mc2 
** Kinetic (particle): K = γmc2 + mc2 
* General Objects
** Kinetic: (1/2)mv2
** Gravitational Potential: (-Gm1m2)/(R2) (large distances), mgh (near the surface of the Earth)
** Spring (Elastic) Potential: (1/2)kss2 
** Thermal Energy: mCΔT 
====General Formulas====
* E = W + Q (if no heat transfer indicated, Q = 0; if no external forces acting on system, W = 0)
* E = K + U (The total energy is the sum of the kinetic and potential energies. From this, you can infer that for an isolated system, any change in kinetic energy will correspond in an equal but opposite change in the potential energy and vice versa.)
These formulas can be interchanged. For example, if you know work and heat transfer are zero, energy equals zero, so K + U will equal zero

[[File:MathConservationEnergy.png]]
 See Reference 2

 [https://www.youtube.com/watch?v=kw_4Loo1HR4 Basic Explanation of Conservation of Energy]
 [https://www.youtube.com/watch?v=EZrJNIBX2wk Skater Visualization of Transfers of Energy]

===Computational Model===
Below is a link to a segment of Vpython code that models the motion of a spring and graphs its kinetic and potential energy. It also shows how the total amount of energy of the system does not change.

"https://trinket.io/embed/glowscript/49c1365501?showInstructions=true"

==Examples==

===Particle===
An electron is accelerated to a speed of 2.95 × 108 
(a) What is the energy of the electron? 
(b) What is the rest energy of the electron? 
(c) What is the kinetic energy of the moving proton? 
(a) 
E = γmc2 
E = (5.50)(9.11 × 10-31)(3 × 108) 
E = 1.50 × 10-21 J 
(b) 
Erest = mc2 
Erest = (9.11 × 10-31)(3 × 108)2 
Erest = 2.73 × 10-22 J 
(c) 
K = E - Erest 
K = 1.50 × 10-21 - 2.73 × 10-22 
K = 1.23 × 10-21 J 

===Simple===
A ball is at rest on a table with 50 J of potential energy. It then rolls of the table, and at one point in time as it falls, the ball has 30 J of kinetic energy. 
What is the potential energy of the ball at that instant?

[[File:EasyEnergyConservation.png]]
 See Reference 3

Einitial = Efinal 
Kinitial + Uinitial = Kfinal + Ufinal 
0 J + 50 J = 30 J + Ufinal 
Ufinal = 20 J

===Middling===
A ball is at rest 50 m above the ground. You then drop the ball. What is its speed before hitting the ground? 
[[File:HardEnergyConservation.gif]]
 See Reference 4 

v = 
√2gh 
 
v = 
√2(9.8)(50) 
 
v = 31.3 m/s

===Difficult===
The driver of an SUV (m = 1700 kg) isn’t paying attention and rear ends a car (m = 950 kg) on level ground at a red light. On impact, both drivers lock their brakes. The SUV and car stick together and travel a distance of 8.2 m before they come to a stop. How fast was the SUV traveling just before the collision? The coefficient of friction between the tires and the road is 0.72.
[[File: DifficultEnergyConservation.png]]
See Reference 5 

KE2 + PE2 = KE3 + PE3 - Wnc 
(1/2)mtotalv22 + mtotalgh2 = (1/2)mtotalv32 + mtotalgh3 - Wnc 
(1/2)mtotalv22 + 0 = 0 + 0 - (μmtotalg)dcos(180°) 
(1/2)v22 = -(0.72)(9.8 m/s2)(8.2 m)(-1) 
v22 = 116 m2/s2 
v2 = 10.8 m/s 

* Notice how the mass is canceled. 

p1 = p2 
p1x = p2x 
msuvvsuv + mcarvcar = mtotalv2 
(1700 kg)vsuv + 0 = (2650 kg)(10.8 m/s) 
(1700 kg)vsuv = 28600 kgm/s 
vsuv = 17 m/s 

==Connectedness==
Computer Science 
1. How is this topic connected to something that you are interested in? 
This concept is clearly connected to physics and helps explain and sometimes predict how our world works. Knowing why and how things move and interact is very powerful. 
2. How is it connected to your major? 
This topic is connected to computer science in the field of modeling and simulation. When you use computers to more efficiently model grand scale scenarios, it is important to take all fundamental concepts of physics, including the conservation of energy, into account. 
3. Is there an interesting industrial application? 
The law of conservation of energy is prevalent in nearly every industrial application of physics. More specifically, it is relevant today as finding renewable and sustainable forms of energy is becoming a more prevalent social and economic issue. It will be interesting to see how this concept will be applied as we try to get more energy for less. 

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
 Who: Many physicists contributed to the knowledge of energy, however it is most notably atributed to Julius Robert Mayer
 What: Most formally discovered the law of conservation of energy
 When: 1842
 Where: Germany
 Why: To explain what happens to energy in an isolated system
 See Reference 6

== See also ==

[[Kinetic Energy]] 
[[Potential Energy]] 
[[Work]] 
===Further reading===

Goldstein, Martin, and Inge F., (1993). The Refrigerator and the Universe. Harvard Univ. Press. A gentle introduction. 
Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0-7167-1088-9. 
Nolan, Peter J. (1996). Fundamentals of College Physics, 2nd ed. William C. Brown Publishers. 

===External links===
 [https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-conservation-of-energy Khan Academy]
 [http://www.physicsclassroom.com/class/energy/Lesson-2/Application-and-Practice-Questions Practice Questions]
 [http://physics.info/energy-conservation/problems.shtml More Practice]
 [http://gilliesphysics.weebly.com/uploads/5/7/5/2/57520801/conservation_of_energy_practice_problems.pdf Basic Examples] 
[http://www.physnet.org/modules/pdf_modules/m158.pdf The First Law of Thermodynamics]
==References==

1."Conservation of Energy." Hmolpedia. Web. 1 Dec. 2015. <http://www.eoht.info/page/Conservation+of+energy>. 
2. "University of Wisconsin Green Bay." Speed & Stopping Distance of a Roller-Coaster. Web. 1 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/2/>. 
3. "Motion." G9 to Engineering. Web. 1 Dec. 2015. <http://www.g9toengineering.com/resources/translational.htm>. 
4. "Energy of Falling Object." HyperPhysics. Web. 1 Dec. 2015. <http://hyperphysics.phy-astr.gsu.edu/hbase/flobj.html>. 
5. "Conservation of Energy & Momentum Problem: Collision of Two Cars at a Stoplight." University of Wisconsin- Green Bay Physics. Web. 2 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/6/>. 
6. "Law of Conservation of Mass Energy." Law of Conservation of Mass Energy. Web. 3 Dec. 2015. <http://www.chemteam.info/Thermochem/Law-Cons-Mass-Energy.html>.
7. "Law of Conservation of Energy" New York University. Web. 18 Apr. 2018. <http://www.nyu.edu/classes/tuckerman/adv.chem/lectures/lecture_2/node4.html>
8. "Law of Conversation of Energy" ME Mechanical. Web. 18 Apr. 2018. <https://me-mechanicalengineering.com/law-of-conservation-of-energy/>
[[Category:Energy]]

Conservation of Energy

2018-04-19T02:50:03Z

A2xreyna: /* References */

Alex Reyna claimed 4/18/2018

This page was originally created by ksubramanian33, as can be seen by the edit history.
 

==Main Ideas==
===Conceptual Model===
* The law of conservation of energy states that the total amount of energy of a system before and after an interaction between objects.
* This only applies to isolated systems (no outside forces acting on the system).
** Not Isolated: An object sliding across a rough floor (system = the object). There is work being done by the floor on the object because of the frictional force. Energy lost to heat due to friction is an example of mechanical energy being converted into thermal energy.
** Isolated: An object sliding across a rough floor (system = the object AND the floor). There is no work done on the system because all the forces are contained in the system.
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> [[File:IntroConservationEnergy.gif]] </div> see reference 7
[[File:energy-transformation.jpg]]
see reference 3

===Mathematical Model===
* Single Particle
** Particle Energy: Eparticle = γmc2 
** Rest Energy: Erest = mc2 
** Kinetic (particle): K = γmc2 + mc2 
* General Objects
** Kinetic: (1/2)mv2
** Gravitational Potential: (-Gm1m2)/(R2) (large distances), mgh (near the surface of the Earth)
** Spring (Elastic) Potential: (1/2)kss2 
** Thermal Energy: mCΔT 
====General Formulas====
* E = W + Q (if no heat transfer indicated, Q = 0; if no external forces acting on system, W = 0)
* E = K + U (The total energy is the sum of the kinetic and potential energies. From this, you can infer that for an isolated system, any change in kinetic energy will correspond in an equal but opposite change in the potential energy and vice versa.)
These formulas can be interchanged. For example, if you know work and heat transfer are zero, energy equals zero, so K + U will equal zero

[[File:MathConservationEnergy.png]]
 See Reference 2

 [https://www.youtube.com/watch?v=kw_4Loo1HR4 Basic Explanation of Conservation of Energy]
 [https://www.youtube.com/watch?v=EZrJNIBX2wk Skater Visualization of Transfers of Energy]

===Computational Model===
Below is a link to a segment of Vpython code that models the motion of a spring and graphs its kinetic and potential energy. It also shows how the total amount of energy of the system does not change.

"https://trinket.io/embed/glowscript/49c1365501?showInstructions=true"

==Examples==

===Particle===
An electron is accelerated to a speed of 2.95 × 108 
(a) What is the energy of the electron? 
(b) What is the rest energy of the electron? 
(c) What is the kinetic energy of the moving proton? 
(a) 
E = γmc2 
E = (5.50)(9.11 × 10-31)(3 × 108) 
E = 1.50 × 10-21 J 
(b) 
Erest = mc2 
Erest = (9.11 × 10-31)(3 × 108)2 
Erest = 2.73 × 10-22 J 
(c) 
K = E - Erest 
K = 1.50 × 10-21 - 2.73 × 10-22 
K = 1.23 × 10-21 J 

===Simple===
A ball is at rest on a table with 50 J of potential energy. It then rolls of the table, and at one point in time as it falls, the ball has 30 J of kinetic energy. 
What is the potential energy of the ball at that instant?

[[File:EasyEnergyConservation.png]]
 See Reference 3

Einitial = Efinal 
Kinitial + Uinitial = Kfinal + Ufinal 
0 J + 50 J = 30 J + Ufinal 
Ufinal = 20 J

===Middling===
A ball is at rest 50 m above the ground. You then drop the ball. What is its speed before hitting the ground? 
[[File:HardEnergyConservation.gif]]
 See Reference 4 

v = 
√2gh 
 
v = 
√2(9.8)(50) 
 
v = 31.3 m/s

===Difficult===
The driver of an SUV (m = 1700 kg) isn’t paying attention and rear ends a car (m = 950 kg) on level ground at a red light. On impact, both drivers lock their brakes. The SUV and car stick together and travel a distance of 8.2 m before they come to a stop. How fast was the SUV traveling just before the collision? The coefficient of friction between the tires and the road is 0.72.
[[File: DifficultEnergyConservation.png]]
See Reference 5 

KE2 + PE2 = KE3 + PE3 - Wnc 
(1/2)mtotalv22 + mtotalgh2 = (1/2)mtotalv32 + mtotalgh3 - Wnc 
(1/2)mtotalv22 + 0 = 0 + 0 - (μmtotalg)dcos(180°) 
(1/2)v22 = -(0.72)(9.8 m/s2)(8.2 m)(-1) 
v22 = 116 m2/s2 
v2 = 10.8 m/s 

* Notice how the mass is canceled. 

p1 = p2 
p1x = p2x 
msuvvsuv + mcarvcar = mtotalv2 
(1700 kg)vsuv + 0 = (2650 kg)(10.8 m/s) 
(1700 kg)vsuv = 28600 kgm/s 
vsuv = 17 m/s 

==Connectedness==
Computer Science 
1. How is this topic connected to something that you are interested in? 
This concept is clearly connected to physics and helps explain and sometimes predict how our world works. Knowing why and how things move and interact is very powerful. 
2. How is it connected to your major? 
This topic is connected to computer science in the field of modeling and simulation. When you use computers to more efficiently model grand scale scenarios, it is important to take all fundamental concepts of physics, including the conservation of energy, into account. 
3. Is there an interesting industrial application? 
The law of conservation of energy is prevalent in nearly every industrial application of physics. More specifically, it is relevant today as finding renewable and sustainable forms of energy is becoming a more prevalent social and economic issue. It will be interesting to see how this concept will be applied as we try to get more energy for less. 

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
 Who: Many physicists contributed to the knowledge of energy, however it is most notably atributed to Julius Robert Mayer
 What: Most formally discovered the law of conservation of energy
 When: 1842
 Where: Germany
 Why: To explain what happens to energy in an isolated system
 See Reference 6

== See also ==

[[Kinetic Energy]] 
[[Potential Energy]] 
[[Work]] 
===Further reading===

Goldstein, Martin, and Inge F., (1993). The Refrigerator and the Universe. Harvard Univ. Press. A gentle introduction. 
Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0-7167-1088-9. 
Nolan, Peter J. (1996). Fundamentals of College Physics, 2nd ed. William C. Brown Publishers. 

===External links===
 [https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-conservation-of-energy Khan Academy]
 [http://www.physicsclassroom.com/class/energy/Lesson-2/Application-and-Practice-Questions Practice Questions]
 [http://physics.info/energy-conservation/problems.shtml More Practice]
 [http://gilliesphysics.weebly.com/uploads/5/7/5/2/57520801/conservation_of_energy_practice_problems.pdf Basic Examples] 
[http://www.physnet.org/modules/pdf_modules/m158.pdf The First Law of Thermodynamics]
==References==

1."Conservation of Energy." Hmolpedia. Web. 1 Dec. 2015. <http://www.eoht.info/page/Conservation+of+energy>. 
2. "University of Wisconsin Green Bay." Speed & Stopping Distance of a Roller-Coaster. Web. 1 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/2/>. 
3. "Motion." G9 to Engineering. Web. 1 Dec. 2015. <http://www.g9toengineering.com/resources/translational.htm>. 
4. "Energy of Falling Object." HyperPhysics. Web. 1 Dec. 2015. <http://hyperphysics.phy-astr.gsu.edu/hbase/flobj.html>. 
5. "Conservation of Energy & Momentum Problem: Collision of Two Cars at a Stoplight." University of Wisconsin- Green Bay Physics. Web. 2 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/6/>. 
6. "Law of Conservation of Mass Energy." Law of Conservation of Mass Energy. Web. 3 Dec. 2015. <http://www.chemteam.info/Thermochem/Law-Cons-Mass-Energy.html>.
7. "Law of Conservation of Energy" New York University. Web. 18 Apr. 2018. <http://www.nyu.edu/classes/tuckerman/adv.chem/lectures/lecture_2/node4.html>
[[Category:Energy]]

Conservation of Energy

2018-04-19T02:36:06Z

A2xreyna: /* Conceptual Model */

Alex Reyna claimed 4/18/2018

This page was originally created by ksubramanian33, as can be seen by the edit history.
 

==Main Ideas==
===Conceptual Model===
* The law of conservation of energy states that the total amount of energy of a system before and after an interaction between objects.
* This only applies to isolated systems (no outside forces acting on the system).
** Not Isolated: An object sliding across a rough floor (system = the object). There is work being done by the floor on the object because of the frictional force. Energy lost to heat due to friction is an example of mechanical energy being converted into thermal energy.
** Isolated: An object sliding across a rough floor (system = the object AND the floor). There is no work done on the system because all the forces are contained in the system.
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> [[File:IntroConservationEnergy.gif]] </div> see reference 7
[[File:energy-transformation.jpg]]
see reference 3

===Mathematical Model===
* Single Particle
** Particle Energy: Eparticle = γmc2 
** Rest Energy: Erest = mc2 
** Kinetic (particle): K = γmc2 + mc2 
* General Objects
** Kinetic: (1/2)mv2
** Gravitational Potential: (-Gm1m2)/(R2) (large distances), mgh (near the surface of the Earth)
** Spring (Elastic) Potential: (1/2)kss2 
** Thermal Energy: mCΔT 
====General Formulas====
* E = W + Q (if no heat transfer indicated, Q = 0; if no external forces acting on system, W = 0)
* E = K + U (The total energy is the sum of the kinetic and potential energies. From this, you can infer that for an isolated system, any change in kinetic energy will correspond in an equal but opposite change in the potential energy and vice versa.)
These formulas can be interchanged. For example, if you know work and heat transfer are zero, energy equals zero, so K + U will equal zero

[[File:MathConservationEnergy.png]]
 See Reference 2

 [https://www.youtube.com/watch?v=kw_4Loo1HR4 Basic Explanation of Conservation of Energy]
 [https://www.youtube.com/watch?v=EZrJNIBX2wk Skater Visualization of Transfers of Energy]

===Computational Model===
Below is a link to a segment of Vpython code that models the motion of a spring and graphs its kinetic and potential energy. It also shows how the total amount of energy of the system does not change.

"https://trinket.io/embed/glowscript/49c1365501?showInstructions=true"

==Examples==

===Particle===
An electron is accelerated to a speed of 2.95 × 108 
(a) What is the energy of the electron? 
(b) What is the rest energy of the electron? 
(c) What is the kinetic energy of the moving proton? 
(a) 
E = γmc2 
E = (5.50)(9.11 × 10-31)(3 × 108) 
E = 1.50 × 10-21 J 
(b) 
Erest = mc2 
Erest = (9.11 × 10-31)(3 × 108)2 
Erest = 2.73 × 10-22 J 
(c) 
K = E - Erest 
K = 1.50 × 10-21 - 2.73 × 10-22 
K = 1.23 × 10-21 J 

===Simple===
A ball is at rest on a table with 50 J of potential energy. It then rolls of the table, and at one point in time as it falls, the ball has 30 J of kinetic energy. 
What is the potential energy of the ball at that instant?

[[File:EasyEnergyConservation.png]]
 See Reference 3

Einitial = Efinal 
Kinitial + Uinitial = Kfinal + Ufinal 
0 J + 50 J = 30 J + Ufinal 
Ufinal = 20 J

===Middling===
A ball is at rest 50 m above the ground. You then drop the ball. What is its speed before hitting the ground? 
[[File:HardEnergyConservation.gif]]
 See Reference 4 

v = 
√2gh 
 
v = 
√2(9.8)(50) 
 
v = 31.3 m/s

===Difficult===
The driver of an SUV (m = 1700 kg) isn’t paying attention and rear ends a car (m = 950 kg) on level ground at a red light. On impact, both drivers lock their brakes. The SUV and car stick together and travel a distance of 8.2 m before they come to a stop. How fast was the SUV traveling just before the collision? The coefficient of friction between the tires and the road is 0.72.
[[File: DifficultEnergyConservation.png]]
See Reference 5 

KE2 + PE2 = KE3 + PE3 - Wnc 
(1/2)mtotalv22 + mtotalgh2 = (1/2)mtotalv32 + mtotalgh3 - Wnc 
(1/2)mtotalv22 + 0 = 0 + 0 - (μmtotalg)dcos(180°) 
(1/2)v22 = -(0.72)(9.8 m/s2)(8.2 m)(-1) 
v22 = 116 m2/s2 
v2 = 10.8 m/s 

* Notice how the mass is canceled. 

p1 = p2 
p1x = p2x 
msuvvsuv + mcarvcar = mtotalv2 
(1700 kg)vsuv + 0 = (2650 kg)(10.8 m/s) 
(1700 kg)vsuv = 28600 kgm/s 
vsuv = 17 m/s 

==Connectedness==
Computer Science 
1. How is this topic connected to something that you are interested in? 
This concept is clearly connected to physics and helps explain and sometimes predict how our world works. Knowing why and how things move and interact is very powerful. 
2. How is it connected to your major? 
This topic is connected to computer science in the field of modeling and simulation. When you use computers to more efficiently model grand scale scenarios, it is important to take all fundamental concepts of physics, including the conservation of energy, into account. 
3. Is there an interesting industrial application? 
The law of conservation of energy is prevalent in nearly every industrial application of physics. More specifically, it is relevant today as finding renewable and sustainable forms of energy is becoming a more prevalent social and economic issue. It will be interesting to see how this concept will be applied as we try to get more energy for less. 

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
 Who: Many physicists contributed to the knowledge of energy, however it is most notably atributed to Julius Robert Mayer
 What: Most formally discovered the law of conservation of energy
 When: 1842
 Where: Germany
 Why: To explain what happens to energy in an isolated system
 See Reference 6

== See also ==

[[Kinetic Energy]] 
[[Potential Energy]] 
[[Work]] 
===Further reading===

Goldstein, Martin, and Inge F., (1993). The Refrigerator and the Universe. Harvard Univ. Press. A gentle introduction. 
Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0-7167-1088-9. 
Nolan, Peter J. (1996). Fundamentals of College Physics, 2nd ed. William C. Brown Publishers. 

===External links===
 [https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-conservation-of-energy Khan Academy]
 [http://www.physicsclassroom.com/class/energy/Lesson-2/Application-and-Practice-Questions Practice Questions]
 [http://physics.info/energy-conservation/problems.shtml More Practice]
 [http://gilliesphysics.weebly.com/uploads/5/7/5/2/57520801/conservation_of_energy_practice_problems.pdf Basic Examples] 
[http://www.physnet.org/modules/pdf_modules/m158.pdf The First Law of Thermodynamics]
==References==

1."Conservation of Energy." Hmolpedia. Web. 1 Dec. 2015. <http://www.eoht.info/page/Conservation+of+energy>. 
2. "University of Wisconsin Green Bay." Speed & Stopping Distance of a Roller-Coaster. Web. 1 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/2/>. 
3. "Motion." G9 to Engineering. Web. 1 Dec. 2015. <http://www.g9toengineering.com/resources/translational.htm>. 
4. "Energy of Falling Object." HyperPhysics. Web. 1 Dec. 2015. <http://hyperphysics.phy-astr.gsu.edu/hbase/flobj.html>. 
5. "Conservation of Energy & Momentum Problem: Collision of Two Cars at a Stoplight." University of Wisconsin- Green Bay Physics. Web. 2 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/6/>. 
6. "Law of Conservation of Mass Energy." Law of Conservation of Mass Energy. Web. 3 Dec. 2015. <http://www.chemteam.info/Thermochem/Law-Cons-Mass-Energy.html>.
[[Category:Energy]]

Conservation of Energy

2018-04-19T02:35:43Z

A2xreyna: /* Conceptual Model */

Alex Reyna claimed 4/18/2018

This page was originally created by ksubramanian33, as can be seen by the edit history.
 

==Main Ideas==
===Conceptual Model===
* The law of conservation of energy states that the total amount of energy of a system before and after an interaction between objects.
* This only applies to isolated systems (no outside forces acting on the system).
** Not Isolated: An object sliding across a rough floor (system = the object). There is work being done by the floor on the object because of the frictional force. Energy lost to heat due to friction is an example of mechanical energy being converted into thermal energy.
** Isolated: An object sliding across a rough floor (system = the object AND the floor). There is no work done on the system because all the forces are contained in the system.
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> [[File:IntroConservationEnergy.gif]] </div> see reference
[[File:energy-transformation.jpg]]
see reference 3

===Mathematical Model===
* Single Particle
** Particle Energy: Eparticle = γmc2 
** Rest Energy: Erest = mc2 
** Kinetic (particle): K = γmc2 + mc2 
* General Objects
** Kinetic: (1/2)mv2
** Gravitational Potential: (-Gm1m2)/(R2) (large distances), mgh (near the surface of the Earth)
** Spring (Elastic) Potential: (1/2)kss2 
** Thermal Energy: mCΔT 
====General Formulas====
* E = W + Q (if no heat transfer indicated, Q = 0; if no external forces acting on system, W = 0)
* E = K + U (The total energy is the sum of the kinetic and potential energies. From this, you can infer that for an isolated system, any change in kinetic energy will correspond in an equal but opposite change in the potential energy and vice versa.)
These formulas can be interchanged. For example, if you know work and heat transfer are zero, energy equals zero, so K + U will equal zero

[[File:MathConservationEnergy.png]]
 See Reference 2

 [https://www.youtube.com/watch?v=kw_4Loo1HR4 Basic Explanation of Conservation of Energy]
 [https://www.youtube.com/watch?v=EZrJNIBX2wk Skater Visualization of Transfers of Energy]

===Computational Model===
Below is a link to a segment of Vpython code that models the motion of a spring and graphs its kinetic and potential energy. It also shows how the total amount of energy of the system does not change.

"https://trinket.io/embed/glowscript/49c1365501?showInstructions=true"

==Examples==

===Particle===
An electron is accelerated to a speed of 2.95 × 108 
(a) What is the energy of the electron? 
(b) What is the rest energy of the electron? 
(c) What is the kinetic energy of the moving proton? 
(a) 
E = γmc2 
E = (5.50)(9.11 × 10-31)(3 × 108) 
E = 1.50 × 10-21 J 
(b) 
Erest = mc2 
Erest = (9.11 × 10-31)(3 × 108)2 
Erest = 2.73 × 10-22 J 
(c) 
K = E - Erest 
K = 1.50 × 10-21 - 2.73 × 10-22 
K = 1.23 × 10-21 J 

===Simple===
A ball is at rest on a table with 50 J of potential energy. It then rolls of the table, and at one point in time as it falls, the ball has 30 J of kinetic energy. 
What is the potential energy of the ball at that instant?

[[File:EasyEnergyConservation.png]]
 See Reference 3

Einitial = Efinal 
Kinitial + Uinitial = Kfinal + Ufinal 
0 J + 50 J = 30 J + Ufinal 
Ufinal = 20 J

===Middling===
A ball is at rest 50 m above the ground. You then drop the ball. What is its speed before hitting the ground? 
[[File:HardEnergyConservation.gif]]
 See Reference 4 

v = 
√2gh 
 
v = 
√2(9.8)(50) 
 
v = 31.3 m/s

===Difficult===
The driver of an SUV (m = 1700 kg) isn’t paying attention and rear ends a car (m = 950 kg) on level ground at a red light. On impact, both drivers lock their brakes. The SUV and car stick together and travel a distance of 8.2 m before they come to a stop. How fast was the SUV traveling just before the collision? The coefficient of friction between the tires and the road is 0.72.
[[File: DifficultEnergyConservation.png]]
See Reference 5 

KE2 + PE2 = KE3 + PE3 - Wnc 
(1/2)mtotalv22 + mtotalgh2 = (1/2)mtotalv32 + mtotalgh3 - Wnc 
(1/2)mtotalv22 + 0 = 0 + 0 - (μmtotalg)dcos(180°) 
(1/2)v22 = -(0.72)(9.8 m/s2)(8.2 m)(-1) 
v22 = 116 m2/s2 
v2 = 10.8 m/s 

* Notice how the mass is canceled. 

p1 = p2 
p1x = p2x 
msuvvsuv + mcarvcar = mtotalv2 
(1700 kg)vsuv + 0 = (2650 kg)(10.8 m/s) 
(1700 kg)vsuv = 28600 kgm/s 
vsuv = 17 m/s 

==Connectedness==
Computer Science 
1. How is this topic connected to something that you are interested in? 
This concept is clearly connected to physics and helps explain and sometimes predict how our world works. Knowing why and how things move and interact is very powerful. 
2. How is it connected to your major? 
This topic is connected to computer science in the field of modeling and simulation. When you use computers to more efficiently model grand scale scenarios, it is important to take all fundamental concepts of physics, including the conservation of energy, into account. 
3. Is there an interesting industrial application? 
The law of conservation of energy is prevalent in nearly every industrial application of physics. More specifically, it is relevant today as finding renewable and sustainable forms of energy is becoming a more prevalent social and economic issue. It will be interesting to see how this concept will be applied as we try to get more energy for less. 

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
 Who: Many physicists contributed to the knowledge of energy, however it is most notably atributed to Julius Robert Mayer
 What: Most formally discovered the law of conservation of energy
 When: 1842
 Where: Germany
 Why: To explain what happens to energy in an isolated system
 See Reference 6

== See also ==

[[Kinetic Energy]] 
[[Potential Energy]] 
[[Work]] 
===Further reading===

Goldstein, Martin, and Inge F., (1993). The Refrigerator and the Universe. Harvard Univ. Press. A gentle introduction. 
Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0-7167-1088-9. 
Nolan, Peter J. (1996). Fundamentals of College Physics, 2nd ed. William C. Brown Publishers. 

===External links===
 [https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-conservation-of-energy Khan Academy]
 [http://www.physicsclassroom.com/class/energy/Lesson-2/Application-and-Practice-Questions Practice Questions]
 [http://physics.info/energy-conservation/problems.shtml More Practice]
 [http://gilliesphysics.weebly.com/uploads/5/7/5/2/57520801/conservation_of_energy_practice_problems.pdf Basic Examples] 
[http://www.physnet.org/modules/pdf_modules/m158.pdf The First Law of Thermodynamics]
==References==

1."Conservation of Energy." Hmolpedia. Web. 1 Dec. 2015. <http://www.eoht.info/page/Conservation+of+energy>. 
2. "University of Wisconsin Green Bay." Speed & Stopping Distance of a Roller-Coaster. Web. 1 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/2/>. 
3. "Motion." G9 to Engineering. Web. 1 Dec. 2015. <http://www.g9toengineering.com/resources/translational.htm>. 
4. "Energy of Falling Object." HyperPhysics. Web. 1 Dec. 2015. <http://hyperphysics.phy-astr.gsu.edu/hbase/flobj.html>. 
5. "Conservation of Energy & Momentum Problem: Collision of Two Cars at a Stoplight." University of Wisconsin- Green Bay Physics. Web. 2 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/6/>. 
6. "Law of Conservation of Mass Energy." Law of Conservation of Mass Energy. Web. 3 Dec. 2015. <http://www.chemteam.info/Thermochem/Law-Cons-Mass-Energy.html>.
[[Category:Energy]]

Conservation of Energy

2018-04-19T02:34:16Z

A2xreyna: /* Computational Model */

Alex Reyna claimed 4/18/2018

This page was originally created by ksubramanian33, as can be seen by the edit history.
 

==Main Ideas==
===Conceptual Model===
* The law of conservation of energy states that the total amount of energy of a system before and after an interaction between objects.
* This only applies to isolated systems (no outside forces acting on the system).
** Not Isolated: An object sliding across a rough floor (system = the object). There is work being done by the floor on the object because of the frictional force. Energy lost to heat due to friction is an example of mechanical energy being converted into thermal energy.
** Isolated: An object sliding across a rough floor (system = the object AND the floor). There is no work done on the system because all the forces are contained in the system.
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> [[File:IntroConservationEnergy.gif]] </div> see reference 1
[[File:energy-transformation.jpg]]
see reference 3

===Mathematical Model===
* Single Particle
** Particle Energy: Eparticle = γmc2 
** Rest Energy: Erest = mc2 
** Kinetic (particle): K = γmc2 + mc2 
* General Objects
** Kinetic: (1/2)mv2
** Gravitational Potential: (-Gm1m2)/(R2) (large distances), mgh (near the surface of the Earth)
** Spring (Elastic) Potential: (1/2)kss2 
** Thermal Energy: mCΔT 
====General Formulas====
* E = W + Q (if no heat transfer indicated, Q = 0; if no external forces acting on system, W = 0)
* E = K + U (The total energy is the sum of the kinetic and potential energies. From this, you can infer that for an isolated system, any change in kinetic energy will correspond in an equal but opposite change in the potential energy and vice versa.)
These formulas can be interchanged. For example, if you know work and heat transfer are zero, energy equals zero, so K + U will equal zero

[[File:MathConservationEnergy.png]]
 See Reference 2

 [https://www.youtube.com/watch?v=kw_4Loo1HR4 Basic Explanation of Conservation of Energy]
 [https://www.youtube.com/watch?v=EZrJNIBX2wk Skater Visualization of Transfers of Energy]

===Computational Model===
Below is a link to a segment of Vpython code that models the motion of a spring and graphs its kinetic and potential energy. It also shows how the total amount of energy of the system does not change.

"https://trinket.io/embed/glowscript/49c1365501?showInstructions=true"

==Examples==

===Particle===
An electron is accelerated to a speed of 2.95 × 108 
(a) What is the energy of the electron? 
(b) What is the rest energy of the electron? 
(c) What is the kinetic energy of the moving proton? 
(a) 
E = γmc2 
E = (5.50)(9.11 × 10-31)(3 × 108) 
E = 1.50 × 10-21 J 
(b) 
Erest = mc2 
Erest = (9.11 × 10-31)(3 × 108)2 
Erest = 2.73 × 10-22 J 
(c) 
K = E - Erest 
K = 1.50 × 10-21 - 2.73 × 10-22 
K = 1.23 × 10-21 J 

===Simple===
A ball is at rest on a table with 50 J of potential energy. It then rolls of the table, and at one point in time as it falls, the ball has 30 J of kinetic energy. 
What is the potential energy of the ball at that instant?

[[File:EasyEnergyConservation.png]]
 See Reference 3

Einitial = Efinal 
Kinitial + Uinitial = Kfinal + Ufinal 
0 J + 50 J = 30 J + Ufinal 
Ufinal = 20 J

===Middling===
A ball is at rest 50 m above the ground. You then drop the ball. What is its speed before hitting the ground? 
[[File:HardEnergyConservation.gif]]
 See Reference 4 

v = 
√2gh 
 
v = 
√2(9.8)(50) 
 
v = 31.3 m/s

===Difficult===
The driver of an SUV (m = 1700 kg) isn’t paying attention and rear ends a car (m = 950 kg) on level ground at a red light. On impact, both drivers lock their brakes. The SUV and car stick together and travel a distance of 8.2 m before they come to a stop. How fast was the SUV traveling just before the collision? The coefficient of friction between the tires and the road is 0.72.
[[File: DifficultEnergyConservation.png]]
See Reference 5 

KE2 + PE2 = KE3 + PE3 - Wnc 
(1/2)mtotalv22 + mtotalgh2 = (1/2)mtotalv32 + mtotalgh3 - Wnc 
(1/2)mtotalv22 + 0 = 0 + 0 - (μmtotalg)dcos(180°) 
(1/2)v22 = -(0.72)(9.8 m/s2)(8.2 m)(-1) 
v22 = 116 m2/s2 
v2 = 10.8 m/s 

* Notice how the mass is canceled. 

p1 = p2 
p1x = p2x 
msuvvsuv + mcarvcar = mtotalv2 
(1700 kg)vsuv + 0 = (2650 kg)(10.8 m/s) 
(1700 kg)vsuv = 28600 kgm/s 
vsuv = 17 m/s 

==Connectedness==
Computer Science 
1. How is this topic connected to something that you are interested in? 
This concept is clearly connected to physics and helps explain and sometimes predict how our world works. Knowing why and how things move and interact is very powerful. 
2. How is it connected to your major? 
This topic is connected to computer science in the field of modeling and simulation. When you use computers to more efficiently model grand scale scenarios, it is important to take all fundamental concepts of physics, including the conservation of energy, into account. 
3. Is there an interesting industrial application? 
The law of conservation of energy is prevalent in nearly every industrial application of physics. More specifically, it is relevant today as finding renewable and sustainable forms of energy is becoming a more prevalent social and economic issue. It will be interesting to see how this concept will be applied as we try to get more energy for less. 

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
 Who: Many physicists contributed to the knowledge of energy, however it is most notably atributed to Julius Robert Mayer
 What: Most formally discovered the law of conservation of energy
 When: 1842
 Where: Germany
 Why: To explain what happens to energy in an isolated system
 See Reference 6

== See also ==

[[Kinetic Energy]] 
[[Potential Energy]] 
[[Work]] 
===Further reading===

Goldstein, Martin, and Inge F., (1993). The Refrigerator and the Universe. Harvard Univ. Press. A gentle introduction. 
Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0-7167-1088-9. 
Nolan, Peter J. (1996). Fundamentals of College Physics, 2nd ed. William C. Brown Publishers. 

===External links===
 [https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-conservation-of-energy Khan Academy]
 [http://www.physicsclassroom.com/class/energy/Lesson-2/Application-and-Practice-Questions Practice Questions]
 [http://physics.info/energy-conservation/problems.shtml More Practice]
 [http://gilliesphysics.weebly.com/uploads/5/7/5/2/57520801/conservation_of_energy_practice_problems.pdf Basic Examples] 
[http://www.physnet.org/modules/pdf_modules/m158.pdf The First Law of Thermodynamics]
==References==

1."Conservation of Energy." Hmolpedia. Web. 1 Dec. 2015. <http://www.eoht.info/page/Conservation+of+energy>. 
2. "University of Wisconsin Green Bay." Speed & Stopping Distance of a Roller-Coaster. Web. 1 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/2/>. 
3. "Motion." G9 to Engineering. Web. 1 Dec. 2015. <http://www.g9toengineering.com/resources/translational.htm>. 
4. "Energy of Falling Object." HyperPhysics. Web. 1 Dec. 2015. <http://hyperphysics.phy-astr.gsu.edu/hbase/flobj.html>. 
5. "Conservation of Energy & Momentum Problem: Collision of Two Cars at a Stoplight." University of Wisconsin- Green Bay Physics. Web. 2 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/6/>. 
6. "Law of Conservation of Mass Energy." Law of Conservation of Mass Energy. Web. 3 Dec. 2015. <http://www.chemteam.info/Thermochem/Law-Cons-Mass-Energy.html>.
[[Category:Energy]]

Conservation of Energy

2018-04-19T02:25:41Z

A2xreyna: /* Computational Model */

Alex Reyna claimed 4/18/2018

This page was originally created by ksubramanian33, as can be seen by the edit history.
 

==Main Ideas==
===Conceptual Model===
* The law of conservation of energy states that the total amount of energy of a system before and after an interaction between objects.
* This only applies to isolated systems (no outside forces acting on the system).
** Not Isolated: An object sliding across a rough floor (system = the object). There is work being done by the floor on the object because of the frictional force. Energy lost to heat due to friction is an example of mechanical energy being converted into thermal energy.
** Isolated: An object sliding across a rough floor (system = the object AND the floor). There is no work done on the system because all the forces are contained in the system.
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> [[File:IntroConservationEnergy.gif]] </div> see reference 1
[[File:energy-transformation.jpg]]
see reference 3

===Mathematical Model===
* Single Particle
** Particle Energy: Eparticle = γmc2 
** Rest Energy: Erest = mc2 
** Kinetic (particle): K = γmc2 + mc2 
* General Objects
** Kinetic: (1/2)mv2
** Gravitational Potential: (-Gm1m2)/(R2) (large distances), mgh (near the surface of the Earth)
** Spring (Elastic) Potential: (1/2)kss2 
** Thermal Energy: mCΔT 
====General Formulas====
* E = W + Q (if no heat transfer indicated, Q = 0; if no external forces acting on system, W = 0)
* E = K + U (The total energy is the sum of the kinetic and potential energies. From this, you can infer that for an isolated system, any change in kinetic energy will correspond in an equal but opposite change in the potential energy and vice versa.)
These formulas can be interchanged. For example, if you know work and heat transfer are zero, energy equals zero, so K + U will equal zero

[[File:MathConservationEnergy.png]]
 See Reference 2

 [https://www.youtube.com/watch?v=kw_4Loo1HR4 Basic Explanation of Conservation of Energy]
 [https://www.youtube.com/watch?v=EZrJNIBX2wk Skater Visualization of Transfers of Energy]

===Computational Model===
*Below is a link to a segment of Vpython code that models the motion of a spring and graphs its kinetic and potential energy. It also shows how the total amount of energy of the system does not change.

"https://trinket.io/embed/glowscript/49c1365501?showInstructions=true"

==Examples==

===Particle===
An electron is accelerated to a speed of 2.95 × 108 
(a) What is the energy of the electron? 
(b) What is the rest energy of the electron? 
(c) What is the kinetic energy of the moving proton? 
(a) 
E = γmc2 
E = (5.50)(9.11 × 10-31)(3 × 108) 
E = 1.50 × 10-21 J 
(b) 
Erest = mc2 
Erest = (9.11 × 10-31)(3 × 108)2 
Erest = 2.73 × 10-22 J 
(c) 
K = E - Erest 
K = 1.50 × 10-21 - 2.73 × 10-22 
K = 1.23 × 10-21 J 

===Simple===
A ball is at rest on a table with 50 J of potential energy. It then rolls of the table, and at one point in time as it falls, the ball has 30 J of kinetic energy. 
What is the potential energy of the ball at that instant?

[[File:EasyEnergyConservation.png]]
 See Reference 3

Einitial = Efinal 
Kinitial + Uinitial = Kfinal + Ufinal 
0 J + 50 J = 30 J + Ufinal 
Ufinal = 20 J

===Middling===
A ball is at rest 50 m above the ground. You then drop the ball. What is its speed before hitting the ground? 
[[File:HardEnergyConservation.gif]]
 See Reference 4 

v = 
√2gh 
 
v = 
√2(9.8)(50) 
 
v = 31.3 m/s

===Difficult===
The driver of an SUV (m = 1700 kg) isn’t paying attention and rear ends a car (m = 950 kg) on level ground at a red light. On impact, both drivers lock their brakes. The SUV and car stick together and travel a distance of 8.2 m before they come to a stop. How fast was the SUV traveling just before the collision? The coefficient of friction between the tires and the road is 0.72.
[[File: DifficultEnergyConservation.png]]
See Reference 5 

KE2 + PE2 = KE3 + PE3 - Wnc 
(1/2)mtotalv22 + mtotalgh2 = (1/2)mtotalv32 + mtotalgh3 - Wnc 
(1/2)mtotalv22 + 0 = 0 + 0 - (μmtotalg)dcos(180°) 
(1/2)v22 = -(0.72)(9.8 m/s2)(8.2 m)(-1) 
v22 = 116 m2/s2 
v2 = 10.8 m/s 

* Notice how the mass is canceled. 

p1 = p2 
p1x = p2x 
msuvvsuv + mcarvcar = mtotalv2 
(1700 kg)vsuv + 0 = (2650 kg)(10.8 m/s) 
(1700 kg)vsuv = 28600 kgm/s 
vsuv = 17 m/s 

==Connectedness==
Computer Science 
1. How is this topic connected to something that you are interested in? 
This concept is clearly connected to physics and helps explain and sometimes predict how our world works. Knowing why and how things move and interact is very powerful. 
2. How is it connected to your major? 
This topic is connected to computer science in the field of modeling and simulation. When you use computers to more efficiently model grand scale scenarios, it is important to take all fundamental concepts of physics, including the conservation of energy, into account. 
3. Is there an interesting industrial application? 
The law of conservation of energy is prevalent in nearly every industrial application of physics. More specifically, it is relevant today as finding renewable and sustainable forms of energy is becoming a more prevalent social and economic issue. It will be interesting to see how this concept will be applied as we try to get more energy for less. 

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
 Who: Many physicists contributed to the knowledge of energy, however it is most notably atributed to Julius Robert Mayer
 What: Most formally discovered the law of conservation of energy
 When: 1842
 Where: Germany
 Why: To explain what happens to energy in an isolated system
 See Reference 6

== See also ==

[[Kinetic Energy]] 
[[Potential Energy]] 
[[Work]] 
===Further reading===

Goldstein, Martin, and Inge F., (1993). The Refrigerator and the Universe. Harvard Univ. Press. A gentle introduction. 
Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0-7167-1088-9. 
Nolan, Peter J. (1996). Fundamentals of College Physics, 2nd ed. William C. Brown Publishers. 

===External links===
 [https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-conservation-of-energy Khan Academy]
 [http://www.physicsclassroom.com/class/energy/Lesson-2/Application-and-Practice-Questions Practice Questions]
 [http://physics.info/energy-conservation/problems.shtml More Practice]
 [http://gilliesphysics.weebly.com/uploads/5/7/5/2/57520801/conservation_of_energy_practice_problems.pdf Basic Examples] 
[http://www.physnet.org/modules/pdf_modules/m158.pdf The First Law of Thermodynamics]
==References==

1."Conservation of Energy." Hmolpedia. Web. 1 Dec. 2015. <http://www.eoht.info/page/Conservation+of+energy>. 
2. "University of Wisconsin Green Bay." Speed & Stopping Distance of a Roller-Coaster. Web. 1 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/2/>. 
3. "Motion." G9 to Engineering. Web. 1 Dec. 2015. <http://www.g9toengineering.com/resources/translational.htm>. 
4. "Energy of Falling Object." HyperPhysics. Web. 1 Dec. 2015. <http://hyperphysics.phy-astr.gsu.edu/hbase/flobj.html>. 
5. "Conservation of Energy & Momentum Problem: Collision of Two Cars at a Stoplight." University of Wisconsin- Green Bay Physics. Web. 2 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/6/>. 
6. "Law of Conservation of Mass Energy." Law of Conservation of Mass Energy. Web. 3 Dec. 2015. <http://www.chemteam.info/Thermochem/Law-Cons-Mass-Energy.html>.
[[Category:Energy]]

Conservation of Energy

2018-04-19T02:22:16Z

A2xreyna:

Alex Reyna claimed 4/18/2018

This page was originally created by ksubramanian33, as can be seen by the edit history.
 

==Main Ideas==
===Conceptual Model===
* The law of conservation of energy states that the total amount of energy of a system before and after an interaction between objects.
* This only applies to isolated systems (no outside forces acting on the system).
** Not Isolated: An object sliding across a rough floor (system = the object). There is work being done by the floor on the object because of the frictional force. Energy lost to heat due to friction is an example of mechanical energy being converted into thermal energy.
** Isolated: An object sliding across a rough floor (system = the object AND the floor). There is no work done on the system because all the forces are contained in the system.
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> [[File:IntroConservationEnergy.gif]] </div> see reference 1
[[File:energy-transformation.jpg]]
see reference 3

===Mathematical Model===
* Single Particle
** Particle Energy: Eparticle = γmc2 
** Rest Energy: Erest = mc2 
** Kinetic (particle): K = γmc2 + mc2 
* General Objects
** Kinetic: (1/2)mv2
** Gravitational Potential: (-Gm1m2)/(R2) (large distances), mgh (near the surface of the Earth)
** Spring (Elastic) Potential: (1/2)kss2 
** Thermal Energy: mCΔT 
====General Formulas====
* E = W + Q (if no heat transfer indicated, Q = 0; if no external forces acting on system, W = 0)
* E = K + U (The total energy is the sum of the kinetic and potential energies. From this, you can infer that for an isolated system, any change in kinetic energy will correspond in an equal but opposite change in the potential energy and vice versa.)
These formulas can be interchanged. For example, if you know work and heat transfer are zero, energy equals zero, so K + U will equal zero

[[File:MathConservationEnergy.png]]
 See Reference 2

 [https://www.youtube.com/watch?v=kw_4Loo1HR4 Basic Explanation of Conservation of Energy]
 [https://www.youtube.com/watch?v=EZrJNIBX2wk Skater Visualization of Transfers of Energy]

===Computational Model===
*Below is a segment of Vpython code that models the motion of a spring and graphs its kinetic and potential energy. It also shows how the total amount of energy of the system does not change.
<iframe src="https://trinket.io/embed/glowscript/49c1365501" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>

==Examples==

===Particle===
An electron is accelerated to a speed of 2.95 × 108 
(a) What is the energy of the electron? 
(b) What is the rest energy of the electron? 
(c) What is the kinetic energy of the moving proton? 
(a) 
E = γmc2 
E = (5.50)(9.11 × 10-31)(3 × 108) 
E = 1.50 × 10-21 J 
(b) 
Erest = mc2 
Erest = (9.11 × 10-31)(3 × 108)2 
Erest = 2.73 × 10-22 J 
(c) 
K = E - Erest 
K = 1.50 × 10-21 - 2.73 × 10-22 
K = 1.23 × 10-21 J 

===Simple===
A ball is at rest on a table with 50 J of potential energy. It then rolls of the table, and at one point in time as it falls, the ball has 30 J of kinetic energy. 
What is the potential energy of the ball at that instant?

[[File:EasyEnergyConservation.png]]
 See Reference 3

Einitial = Efinal 
Kinitial + Uinitial = Kfinal + Ufinal 
0 J + 50 J = 30 J + Ufinal 
Ufinal = 20 J

===Middling===
A ball is at rest 50 m above the ground. You then drop the ball. What is its speed before hitting the ground? 
[[File:HardEnergyConservation.gif]]
 See Reference 4 

v = 
√2gh 
 
v = 
√2(9.8)(50) 
 
v = 31.3 m/s

===Difficult===
The driver of an SUV (m = 1700 kg) isn’t paying attention and rear ends a car (m = 950 kg) on level ground at a red light. On impact, both drivers lock their brakes. The SUV and car stick together and travel a distance of 8.2 m before they come to a stop. How fast was the SUV traveling just before the collision? The coefficient of friction between the tires and the road is 0.72.
[[File: DifficultEnergyConservation.png]]
See Reference 5 

KE2 + PE2 = KE3 + PE3 - Wnc 
(1/2)mtotalv22 + mtotalgh2 = (1/2)mtotalv32 + mtotalgh3 - Wnc 
(1/2)mtotalv22 + 0 = 0 + 0 - (μmtotalg)dcos(180°) 
(1/2)v22 = -(0.72)(9.8 m/s2)(8.2 m)(-1) 
v22 = 116 m2/s2 
v2 = 10.8 m/s 

* Notice how the mass is canceled. 

p1 = p2 
p1x = p2x 
msuvvsuv + mcarvcar = mtotalv2 
(1700 kg)vsuv + 0 = (2650 kg)(10.8 m/s) 
(1700 kg)vsuv = 28600 kgm/s 
vsuv = 17 m/s 

==Connectedness==
Computer Science 
1. How is this topic connected to something that you are interested in? 
This concept is clearly connected to physics and helps explain and sometimes predict how our world works. Knowing why and how things move and interact is very powerful. 
2. How is it connected to your major? 
This topic is connected to computer science in the field of modeling and simulation. When you use computers to more efficiently model grand scale scenarios, it is important to take all fundamental concepts of physics, including the conservation of energy, into account. 
3. Is there an interesting industrial application? 
The law of conservation of energy is prevalent in nearly every industrial application of physics. More specifically, it is relevant today as finding renewable and sustainable forms of energy is becoming a more prevalent social and economic issue. It will be interesting to see how this concept will be applied as we try to get more energy for less. 

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
 Who: Many physicists contributed to the knowledge of energy, however it is most notably atributed to Julius Robert Mayer
 What: Most formally discovered the law of conservation of energy
 When: 1842
 Where: Germany
 Why: To explain what happens to energy in an isolated system
 See Reference 6

== See also ==

[[Kinetic Energy]] 
[[Potential Energy]] 
[[Work]] 
===Further reading===

Goldstein, Martin, and Inge F., (1993). The Refrigerator and the Universe. Harvard Univ. Press. A gentle introduction. 
Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0-7167-1088-9. 
Nolan, Peter J. (1996). Fundamentals of College Physics, 2nd ed. William C. Brown Publishers. 

===External links===
 [https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-conservation-of-energy Khan Academy]
 [http://www.physicsclassroom.com/class/energy/Lesson-2/Application-and-Practice-Questions Practice Questions]
 [http://physics.info/energy-conservation/problems.shtml More Practice]
 [http://gilliesphysics.weebly.com/uploads/5/7/5/2/57520801/conservation_of_energy_practice_problems.pdf Basic Examples] 
[http://www.physnet.org/modules/pdf_modules/m158.pdf The First Law of Thermodynamics]
==References==

1."Conservation of Energy." Hmolpedia. Web. 1 Dec. 2015. <http://www.eoht.info/page/Conservation+of+energy>. 
2. "University of Wisconsin Green Bay." Speed & Stopping Distance of a Roller-Coaster. Web. 1 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/2/>. 
3. "Motion." G9 to Engineering. Web. 1 Dec. 2015. <http://www.g9toengineering.com/resources/translational.htm>. 
4. "Energy of Falling Object." HyperPhysics. Web. 1 Dec. 2015. <http://hyperphysics.phy-astr.gsu.edu/hbase/flobj.html>. 
5. "Conservation of Energy & Momentum Problem: Collision of Two Cars at a Stoplight." University of Wisconsin- Green Bay Physics. Web. 2 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/6/>. 
6. "Law of Conservation of Mass Energy." Law of Conservation of Mass Energy. Web. 3 Dec. 2015. <http://www.chemteam.info/Thermochem/Law-Cons-Mass-Energy.html>.
[[Category:Energy]]

Conservation of Energy

2018-04-19T01:51:22Z

A2xreyna: /* General Formulas */

Alex Reyna claimed 4/18/2018

This page was originally created by ksubramanian33, as can be seen by the edit history.
 

==Main Ideas==
===Conceptual Model===
* The law of conservation of energy states that the total amount of energy of a system before and after an interaction between objects.
* This only applies to isolated systems (no outside forces acting on the system).
** Not Isolated: An object sliding across a rough floor (system = the object). There is work being done by the floor on the object because of the frictional force. Energy lost to heat due to friction is an example of mechanical energy being converted into thermal energy.
** Isolated: An object sliding across a rough floor (system = the object AND the floor). There is no work done on the system because all the forces are contained in the system.
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> [[File:IntroConservationEnergy.gif]] </div> see reference 1
[[File:energy-transformation.jpg]]
see reference 3

===Mathematical Model===
* Single Particle
** Particle Energy: Eparticle = γmc2 
** Rest Energy: Erest = mc2 
** Kinetic (particle): K = γmc2 + mc2 
* General Objects
** Kinetic: (1/2)mv2
** Gravitational Potential: (-Gm1m2)/(R2) (large distances), mgh (near the surface of the Earth)
** Spring (Elastic) Potential: (1/2)kss2 
** Thermal Energy: mCΔT 
====General Formulas====
* E = W + Q (if no heat transfer indicated, Q = 0; if no external forces acting on system, W = 0)
* E = K + U (The total energy is the sum of the kinetic and potential energies. From this, you can infer that for an isolated system, any change in kinetic energy will correspond in an equal but opposite change in the potential energy and vice versa.)
These formulas can be interchanged. For example, if you know work and heat transfer are zero, energy equals zero, so K + U will equal zero

[[File:MathConservationEnergy.png]]
 See Reference 2

 [https://www.youtube.com/watch?v=kw_4Loo1HR4 Basic Explanation of Conservation of Energy]
 [https://www.youtube.com/watch?v=EZrJNIBX2wk Skater Visualization of Transfers of Energy]

==Examples==

===Particle===
An electron is accelerated to a speed of 2.95 × 108 
(a) What is the energy of the electron? 
(b) What is the rest energy of the electron? 
(c) What is the kinetic energy of the moving proton? 
(a) 
E = γmc2 
E = (5.50)(9.11 × 10-31)(3 × 108) 
E = 1.50 × 10-21 J 
(b) 
Erest = mc2 
Erest = (9.11 × 10-31)(3 × 108)2 
Erest = 2.73 × 10-22 J 
(c) 
K = E - Erest 
K = 1.50 × 10-21 - 2.73 × 10-22 
K = 1.23 × 10-21 J 

===Simple===
A ball is at rest on a table with 50 J of potential energy. It then rolls of the table, and at one point in time as it falls, the ball has 30 J of kinetic energy. 
What is the potential energy of the ball at that instant?

[[File:EasyEnergyConservation.png]]
 See Reference 3

Einitial = Efinal 
Kinitial + Uinitial = Kfinal + Ufinal 
0 J + 50 J = 30 J + Ufinal 
Ufinal = 20 J

===Middling===
A ball is at rest 50 m above the ground. You then drop the ball. What is its speed before hitting the ground? 
[[File:HardEnergyConservation.gif]]
 See Reference 4 

v = 
√2gh 
 
v = 
√2(9.8)(50) 
 
v = 31.3 m/s

===Difficult===
The driver of an SUV (m = 1700 kg) isn’t paying attention and rear ends a car (m = 950 kg) on level ground at a red light. On impact, both drivers lock their brakes. The SUV and car stick together and travel a distance of 8.2 m before they come to a stop. How fast was the SUV traveling just before the collision? The coefficient of friction between the tires and the road is 0.72.
[[File: DifficultEnergyConservation.png]]
See Reference 5 

KE2 + PE2 = KE3 + PE3 - Wnc 
(1/2)mtotalv22 + mtotalgh2 = (1/2)mtotalv32 + mtotalgh3 - Wnc 
(1/2)mtotalv22 + 0 = 0 + 0 - (μmtotalg)dcos(180°) 
(1/2)v22 = -(0.72)(9.8 m/s2)(8.2 m)(-1) 
v22 = 116 m2/s2 
v2 = 10.8 m/s 

* Notice how the mass is canceled. 

p1 = p2 
p1x = p2x 
msuvvsuv + mcarvcar = mtotalv2 
(1700 kg)vsuv + 0 = (2650 kg)(10.8 m/s) 
(1700 kg)vsuv = 28600 kgm/s 
vsuv = 17 m/s 

==Connectedness==
Computer Science 
1. How is this topic connected to something that you are interested in? 
This concept is clearly connected to physics and helps explain and sometimes predict how our world works. Knowing why and how things move and interact is very powerful. 
2. How is it connected to your major? 
This topic is connected to computer science in the field of modeling and simulation. When you use computers to more efficiently model grand scale scenarios, it is important to take all fundamental concepts of physics, including the conservation of energy, into account. 
3. Is there an interesting industrial application? 
The law of conservation of energy is prevalent in nearly every industrial application of physics. More specifically, it is relevant today as finding renewable and sustainable forms of energy is becoming a more prevalent social and economic issue. It will be interesting to see how this concept will be applied as we try to get more energy for less. 

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
 Who: Many physicists contributed to the knowledge of energy, however it is most notably atributed to Julius Robert Mayer
 What: Most formally discovered the law of conservation of energy
 When: 1842
 Where: Germany
 Why: To explain what happens to energy in an isolated system
 See Reference 6

== See also ==

[[Kinetic Energy]] 
[[Potential Energy]] 
[[Work]] 
===Further reading===

Goldstein, Martin, and Inge F., (1993). The Refrigerator and the Universe. Harvard Univ. Press. A gentle introduction. 
Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0-7167-1088-9. 
Nolan, Peter J. (1996). Fundamentals of College Physics, 2nd ed. William C. Brown Publishers. 

===External links===
 [https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-conservation-of-energy Khan Academy]
 [http://www.physicsclassroom.com/class/energy/Lesson-2/Application-and-Practice-Questions Practice Questions]
 [http://physics.info/energy-conservation/problems.shtml More Practice]
 [http://gilliesphysics.weebly.com/uploads/5/7/5/2/57520801/conservation_of_energy_practice_problems.pdf Basic Examples] 
[http://www.physnet.org/modules/pdf_modules/m158.pdf The First Law of Thermodynamics]
==References==

1."Conservation of Energy." Hmolpedia. Web. 1 Dec. 2015. <http://www.eoht.info/page/Conservation+of+energy>. 
2. "University of Wisconsin Green Bay." Speed & Stopping Distance of a Roller-Coaster. Web. 1 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/2/>. 
3. "Motion." G9 to Engineering. Web. 1 Dec. 2015. <http://www.g9toengineering.com/resources/translational.htm>. 
4. "Energy of Falling Object." HyperPhysics. Web. 1 Dec. 2015. <http://hyperphysics.phy-astr.gsu.edu/hbase/flobj.html>. 
5. "Conservation of Energy & Momentum Problem: Collision of Two Cars at a Stoplight." University of Wisconsin- Green Bay Physics. Web. 2 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/6/>. 
6. "Law of Conservation of Mass Energy." Law of Conservation of Mass Energy. Web. 3 Dec. 2015. <http://www.chemteam.info/Thermochem/Law-Cons-Mass-Energy.html>.
[[Category:Energy]]

Conservation of Energy

2018-04-19T01:46:53Z

A2xreyna: /* Conceptual Model */

Alex Reyna claimed 4/18/2018

This page was originally created by ksubramanian33, as can be seen by the edit history.
 

==Main Ideas==
===Conceptual Model===
* The law of conservation of energy states that the total amount of energy of a system before and after an interaction between objects.
* This only applies to isolated systems (no outside forces acting on the system).
** Not Isolated: An object sliding across a rough floor (system = the object). There is work being done by the floor on the object because of the frictional force. Energy lost to heat due to friction is an example of mechanical energy being converted into thermal energy.
** Isolated: An object sliding across a rough floor (system = the object AND the floor). There is no work done on the system because all the forces are contained in the system.
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> [[File:IntroConservationEnergy.gif]] </div> see reference 1
[[File:energy-transformation.jpg]]
see reference 3

===Mathematical Model===
* Single Particle
** Particle Energy: Eparticle = γmc2 
** Rest Energy: Erest = mc2 
** Kinetic (particle): K = γmc2 + mc2 
* General Objects
** Kinetic: (1/2)mv2
** Gravitational Potential: (-Gm1m2)/(R2) (large distances), mgh (near the surface of the Earth)
** Spring (Elastic) Potential: (1/2)kss2 
** Thermal Energy: mCΔT 
====General Formulas====
* E = W + Q (if no heat transfer indicated, Q = 0; if no external forces acting on system, W = 0)
* E = K + U (The total energy is the sum of the kinetic and potential energies. From this, you can infer that for an isolated system, any change in kinetic energy will correspond in an equal but opposite change in the potential energy and vice versa.)
These formulas can be interchanged. For example, is you know work and heat transfer are zero, energy equals zero, so K + U will equal zero

[[File:MathConservationEnergy.png]]
 See Reference 2

 [https://www.youtube.com/watch?v=kw_4Loo1HR4 Basic Explanation of Conservation of Energy]
 [https://www.youtube.com/watch?v=EZrJNIBX2wk Skater Visualization of Transfers of Energy]

==Examples==

===Particle===
An electron is accelerated to a speed of 2.95 × 108 
(a) What is the energy of the electron? 
(b) What is the rest energy of the electron? 
(c) What is the kinetic energy of the moving proton? 
(a) 
E = γmc2 
E = (5.50)(9.11 × 10-31)(3 × 108) 
E = 1.50 × 10-21 J 
(b) 
Erest = mc2 
Erest = (9.11 × 10-31)(3 × 108)2 
Erest = 2.73 × 10-22 J 
(c) 
K = E - Erest 
K = 1.50 × 10-21 - 2.73 × 10-22 
K = 1.23 × 10-21 J 

===Simple===
A ball is at rest on a table with 50 J of potential energy. It then rolls of the table, and at one point in time as it falls, the ball has 30 J of kinetic energy. 
What is the potential energy of the ball at that instant?

[[File:EasyEnergyConservation.png]]
 See Reference 3

Einitial = Efinal 
Kinitial + Uinitial = Kfinal + Ufinal 
0 J + 50 J = 30 J + Ufinal 
Ufinal = 20 J

===Middling===
A ball is at rest 50 m above the ground. You then drop the ball. What is its speed before hitting the ground? 
[[File:HardEnergyConservation.gif]]
 See Reference 4 

v = 
√2gh 
 
v = 
√2(9.8)(50) 
 
v = 31.3 m/s

===Difficult===
The driver of an SUV (m = 1700 kg) isn’t paying attention and rear ends a car (m = 950 kg) on level ground at a red light. On impact, both drivers lock their brakes. The SUV and car stick together and travel a distance of 8.2 m before they come to a stop. How fast was the SUV traveling just before the collision? The coefficient of friction between the tires and the road is 0.72.
[[File: DifficultEnergyConservation.png]]
See Reference 5 

KE2 + PE2 = KE3 + PE3 - Wnc 
(1/2)mtotalv22 + mtotalgh2 = (1/2)mtotalv32 + mtotalgh3 - Wnc 
(1/2)mtotalv22 + 0 = 0 + 0 - (μmtotalg)dcos(180°) 
(1/2)v22 = -(0.72)(9.8 m/s2)(8.2 m)(-1) 
v22 = 116 m2/s2 
v2 = 10.8 m/s 

* Notice how the mass is canceled. 

p1 = p2 
p1x = p2x 
msuvvsuv + mcarvcar = mtotalv2 
(1700 kg)vsuv + 0 = (2650 kg)(10.8 m/s) 
(1700 kg)vsuv = 28600 kgm/s 
vsuv = 17 m/s 

==Connectedness==
Computer Science 
1. How is this topic connected to something that you are interested in? 
This concept is clearly connected to physics and helps explain and sometimes predict how our world works. Knowing why and how things move and interact is very powerful. 
2. How is it connected to your major? 
This topic is connected to computer science in the field of modeling and simulation. When you use computers to more efficiently model grand scale scenarios, it is important to take all fundamental concepts of physics, including the conservation of energy, into account. 
3. Is there an interesting industrial application? 
The law of conservation of energy is prevalent in nearly every industrial application of physics. More specifically, it is relevant today as finding renewable and sustainable forms of energy is becoming a more prevalent social and economic issue. It will be interesting to see how this concept will be applied as we try to get more energy for less. 

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
 Who: Many physicists contributed to the knowledge of energy, however it is most notably atributed to Julius Robert Mayer
 What: Most formally discovered the law of conservation of energy
 When: 1842
 Where: Germany
 Why: To explain what happens to energy in an isolated system
 See Reference 6

== See also ==

[[Kinetic Energy]] 
[[Potential Energy]] 
[[Work]] 
===Further reading===

Goldstein, Martin, and Inge F., (1993). The Refrigerator and the Universe. Harvard Univ. Press. A gentle introduction. 
Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0-7167-1088-9. 
Nolan, Peter J. (1996). Fundamentals of College Physics, 2nd ed. William C. Brown Publishers. 

===External links===
 [https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-conservation-of-energy Khan Academy]
 [http://www.physicsclassroom.com/class/energy/Lesson-2/Application-and-Practice-Questions Practice Questions]
 [http://physics.info/energy-conservation/problems.shtml More Practice]
 [http://gilliesphysics.weebly.com/uploads/5/7/5/2/57520801/conservation_of_energy_practice_problems.pdf Basic Examples] 
[http://www.physnet.org/modules/pdf_modules/m158.pdf The First Law of Thermodynamics]
==References==

1."Conservation of Energy." Hmolpedia. Web. 1 Dec. 2015. <http://www.eoht.info/page/Conservation+of+energy>. 
2. "University of Wisconsin Green Bay." Speed & Stopping Distance of a Roller-Coaster. Web. 1 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/2/>. 
3. "Motion." G9 to Engineering. Web. 1 Dec. 2015. <http://www.g9toengineering.com/resources/translational.htm>. 
4. "Energy of Falling Object." HyperPhysics. Web. 1 Dec. 2015. <http://hyperphysics.phy-astr.gsu.edu/hbase/flobj.html>. 
5. "Conservation of Energy & Momentum Problem: Collision of Two Cars at a Stoplight." University of Wisconsin- Green Bay Physics. Web. 2 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/6/>. 
6. "Law of Conservation of Mass Energy." Law of Conservation of Mass Energy. Web. 3 Dec. 2015. <http://www.chemteam.info/Thermochem/Law-Cons-Mass-Energy.html>.
[[Category:Energy]]

File:Energy-transformation.jpg

2018-04-19T01:42:25Z

A2xreyna: Link for image: https://me-mechanicalengineering.com/law-of-conservation-of-energy/

Link for image:
https://me-mechanicalengineering.com/law-of-conservation-of-energy/

Conservation of Energy

2018-04-19T00:55:56Z

A2xreyna:

Alex Reyna claimed 4/18/2018

This page was originally created by ksubramanian33, as can be seen by the edit history.
 

==Main Ideas==
===Conceptual Model===
* The law of conservation of energy states that the total amount of energy of a system before and after an interaction between objects.
* This only applies to isolated systems (no outside forces acting on the system).
** Not Isolated: An object sliding across a rough floor (system = the object). There is work being done by the floor on the object because of the frictional force. Energy lost to heat due to friction is an example of mechanical energy being converted into thermal energy.
** Isolated: An object sliding across a rough floor (system = the object AND the floor). There is no work done on the system because all the forces are contained in the system.
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> [[File:IntroConservationEnergy.gif]] </div> see reference 1

===Mathematical Model===
* Single Particle
** Particle Energy: Eparticle = γmc2 
** Rest Energy: Erest = mc2 
** Kinetic (particle): K = γmc2 + mc2 
* General Objects
** Kinetic: (1/2)mv2
** Gravitational Potential: (-Gm1m2)/(R2) (large distances), mgh (near the surface of the Earth)
** Spring (Elastic) Potential: (1/2)kss2 
** Thermal Energy: mCΔT 
====General Formulas====
* E = W + Q (if no heat transfer indicated, Q = 0; if no external forces acting on system, W = 0)
* E = K + U (The total energy is the sum of the kinetic and potential energies. From this, you can infer that for an isolated system, any change in kinetic energy will correspond in an equal but opposite change in the potential energy and vice versa.)
These formulas can be interchanged. For example, is you know work and heat transfer are zero, energy equals zero, so K + U will equal zero

[[File:MathConservationEnergy.png]]
 See Reference 2

 [https://www.youtube.com/watch?v=kw_4Loo1HR4 Basic Explanation of Conservation of Energy]
 [https://www.youtube.com/watch?v=EZrJNIBX2wk Skater Visualization of Transfers of Energy]

==Examples==

===Particle===
An electron is accelerated to a speed of 2.95 × 108 
(a) What is the energy of the electron? 
(b) What is the rest energy of the electron? 
(c) What is the kinetic energy of the moving proton? 
(a) 
E = γmc2 
E = (5.50)(9.11 × 10-31)(3 × 108) 
E = 1.50 × 10-21 J 
(b) 
Erest = mc2 
Erest = (9.11 × 10-31)(3 × 108)2 
Erest = 2.73 × 10-22 J 
(c) 
K = E - Erest 
K = 1.50 × 10-21 - 2.73 × 10-22 
K = 1.23 × 10-21 J 

===Simple===
A ball is at rest on a table with 50 J of potential energy. It then rolls of the table, and at one point in time as it falls, the ball has 30 J of kinetic energy. 
What is the potential energy of the ball at that instant?

[[File:EasyEnergyConservation.png]]
 See Reference 3

Einitial = Efinal 
Kinitial + Uinitial = Kfinal + Ufinal 
0 J + 50 J = 30 J + Ufinal 
Ufinal = 20 J

===Middling===
A ball is at rest 50 m above the ground. You then drop the ball. What is its speed before hitting the ground? 
[[File:HardEnergyConservation.gif]]
 See Reference 4 

v = 
√2gh 
 
v = 
√2(9.8)(50) 
 
v = 31.3 m/s

===Difficult===
The driver of an SUV (m = 1700 kg) isn’t paying attention and rear ends a car (m = 950 kg) on level ground at a red light. On impact, both drivers lock their brakes. The SUV and car stick together and travel a distance of 8.2 m before they come to a stop. How fast was the SUV traveling just before the collision? The coefficient of friction between the tires and the road is 0.72.
[[File: DifficultEnergyConservation.png]]
See Reference 5 

KE2 + PE2 = KE3 + PE3 - Wnc 
(1/2)mtotalv22 + mtotalgh2 = (1/2)mtotalv32 + mtotalgh3 - Wnc 
(1/2)mtotalv22 + 0 = 0 + 0 - (μmtotalg)dcos(180°) 
(1/2)v22 = -(0.72)(9.8 m/s2)(8.2 m)(-1) 
v22 = 116 m2/s2 
v2 = 10.8 m/s 

* Notice how the mass is canceled. 

p1 = p2 
p1x = p2x 
msuvvsuv + mcarvcar = mtotalv2 
(1700 kg)vsuv + 0 = (2650 kg)(10.8 m/s) 
(1700 kg)vsuv = 28600 kgm/s 
vsuv = 17 m/s 

==Connectedness==
Computer Science 
1. How is this topic connected to something that you are interested in? 
This concept is clearly connected to physics and helps explain and sometimes predict how our world works. Knowing why and how things move and interact is very powerful. 
2. How is it connected to your major? 
This topic is connected to computer science in the field of modeling and simulation. When you use computers to more efficiently model grand scale scenarios, it is important to take all fundamental concepts of physics, including the conservation of energy, into account. 
3. Is there an interesting industrial application? 
The law of conservation of energy is prevalent in nearly every industrial application of physics. More specifically, it is relevant today as finding renewable and sustainable forms of energy is becoming a more prevalent social and economic issue. It will be interesting to see how this concept will be applied as we try to get more energy for less. 

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
 Who: Many physicists contributed to the knowledge of energy, however it is most notably atributed to Julius Robert Mayer
 What: Most formally discovered the law of conservation of energy
 When: 1842
 Where: Germany
 Why: To explain what happens to energy in an isolated system
 See Reference 6

== See also ==

[[Kinetic Energy]] 
[[Potential Energy]] 
[[Work]] 
===Further reading===

Goldstein, Martin, and Inge F., (1993). The Refrigerator and the Universe. Harvard Univ. Press. A gentle introduction. 
Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0-7167-1088-9. 
Nolan, Peter J. (1996). Fundamentals of College Physics, 2nd ed. William C. Brown Publishers. 

===External links===
 [https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-conservation-of-energy Khan Academy]
 [http://www.physicsclassroom.com/class/energy/Lesson-2/Application-and-Practice-Questions Practice Questions]
 [http://physics.info/energy-conservation/problems.shtml More Practice]
 [http://gilliesphysics.weebly.com/uploads/5/7/5/2/57520801/conservation_of_energy_practice_problems.pdf Basic Examples] 
[http://www.physnet.org/modules/pdf_modules/m158.pdf The First Law of Thermodynamics]
==References==

1."Conservation of Energy." Hmolpedia. Web. 1 Dec. 2015. <http://www.eoht.info/page/Conservation+of+energy>. 
2. "University of Wisconsin Green Bay." Speed & Stopping Distance of a Roller-Coaster. Web. 1 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/2/>. 
3. "Motion." G9 to Engineering. Web. 1 Dec. 2015. <http://www.g9toengineering.com/resources/translational.htm>. 
4. "Energy of Falling Object." HyperPhysics. Web. 1 Dec. 2015. <http://hyperphysics.phy-astr.gsu.edu/hbase/flobj.html>. 
5. "Conservation of Energy & Momentum Problem: Collision of Two Cars at a Stoplight." University of Wisconsin- Green Bay Physics. Web. 2 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/6/>. 
6. "Law of Conservation of Mass Energy." Law of Conservation of Mass Energy. Web. 3 Dec. 2015. <http://www.chemteam.info/Thermochem/Law-Cons-Mass-Energy.html>.
[[Category:Energy]]

Conservation of Energy

2018-04-19T00:22:57Z

A2xreyna:

Alex Reyna claimed 4/18/2018

This page was originally created by ksubramanian33, as can be seen by the edit history.
 

==Main Ideas==
===Conceptual Model===
* The law of conservation of energy states that the total amount of energy of a system before and after an interaction between objects.
* This only applies to isolated systems (no outside forces acting on the system).
** Not Isolated: An object sliding across a rough floor (system = the object). There is work being done by the floor on the object because of the frictional force.
** Isolated: An object sliding across a rough floor (system = the object AND the floor). There is no work done on the system because all the forces are contained in the system.
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> [[File:IntroConservationEnergy.gif]] </div> see reference 1

===Mathematical Model===
* Single Particle
** Particle Energy: Eparticle = γmc2 
** Rest Energy: Erest = mc2 
** Kinetic (particle): K = γmc2 + mc2 
* General Objects
** Kinetic: (1/2)mv2
** Gravitational Potential: (-Gm1m2)/(R2) (large distances), mgh (near the surface of the Earth)
** Spring (Elastic) Potential: (1/2)kss2 
** Thermal Energy: mCΔT 
====General Formulas====
* E = W + Q (if no heat transfer indicated, Q = 0; if no external forces acting on system, W = 0)
* E = K + U (The total energy is the sum of the kinetic and potential energies. From this, you can infer that for an isolated system, any change in kinetic energy will correspond in an equal but opposite change in the potential energy and vice versa.)
These formulas can be interchanged. For example, is you know work and heat transfer are zero, energy equals zero, so K + U will equal zero

[[File:MathConservationEnergy.png]]
 See Reference 2

 [https://www.youtube.com/watch?v=kw_4Loo1HR4 Basic Explanation of Conservation of Energy]
 [https://www.youtube.com/watch?v=EZrJNIBX2wk Skater Visualization of Transfers of Energy]

==Examples==

===Particle===
An electron is accelerated to a speed of 2.95 × 108 
(a) What is the energy of the electron? 
(b) What is the rest energy of the electron? 
(c) What is the kinetic energy of the moving proton? 
(a) 
E = γmc2 
E = (5.50)(9.11 × 10-31)(3 × 108) 
E = 1.50 × 10-21 J 
(b) 
Erest = mc2 
Erest = (9.11 × 10-31)(3 × 108)2 
Erest = 2.73 × 10-22 J 
(c) 
K = E - Erest 
K = 1.50 × 10-21 - 2.73 × 10-22 
K = 1.23 × 10-21 J 

===Simple===
A ball is at rest on a table with 50 J of potential energy. It then rolls of the table, and at one point in time as it falls, the ball has 30 J of kinetic energy. 
What is the potential energy of the ball at that instant?

[[File:EasyEnergyConservation.png]]
 See Reference 3

Einitial = Efinal 
Kinitial + Uinitial = Kfinal + Ufinal 
0 J + 50 J = 30 J + Ufinal 
Ufinal = 20 J

===Middling===
A ball is at rest 50 m above the ground. You then drop the ball. What is its speed before hitting the ground? 
[[File:HardEnergyConservation.gif]]
 See Reference 4 

v = 
√2gh 
 
v = 
√2(9.8)(50) 
 
v = 31.3 m/s

===Difficult===
The driver of an SUV (m = 1700 kg) isn’t paying attention and rear ends a car (m = 950 kg) on level ground at a red light. On impact, both drivers lock their brakes. The SUV and car stick together and travel a distance of 8.2 m before they come to a stop. How fast was the SUV traveling just before the collision? The coefficient of friction between the tires and the road is 0.72.
[[File: DifficultEnergyConservation.png]]
See Reference 5 

KE2 + PE2 = KE3 + PE3 - Wnc 
(1/2)mtotalv22 + mtotalgh2 = (1/2)mtotalv32 + mtotalgh3 - Wnc 
(1/2)mtotalv22 + 0 = 0 + 0 - (μmtotalg)dcos(180°) 
(1/2)v22 = -(0.72)(9.8 m/s2)(8.2 m)(-1) 
v22 = 116 m2/s2 
v2 = 10.8 m/s 

* Notice how the mass is canceled. 

p1 = p2 
p1x = p2x 
msuvvsuv + mcarvcar = mtotalv2 
(1700 kg)vsuv + 0 = (2650 kg)(10.8 m/s) 
(1700 kg)vsuv = 28600 kgm/s 
vsuv = 17 m/s 

==Connectedness==
Computer Science 
1. How is this topic connected to something that you are interested in? 
This concept is clearly connected to physics and helps explain and sometimes predict how our world works. Knowing why and how things move and interact is very powerful. 
2. How is it connected to your major? 
This topic is connected to computer science in the field of modeling and simulation. When you use computers to more efficiently model grand scale scenarios, it is important to take all fundamental concepts of physics, including the conservation of energy, into account. 
3. Is there an interesting industrial application? 
The law of conservation of energy is prevalent in nearly every industrial application of physics. More specifically, it is relevant today as finding renewable and sustainable forms of energy is becoming a more prevalent social and economic issue. It will be interesting to see how this concept will be applied as we try to get more energy for less. 

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
 Who: Many physicists contributed to the knowledge of energy, however it is most notably atributed to Julius Robert Mayer
 What: Most formally discovered the law of conservation of energy
 When: 1842
 Where: Germany
 Why: To explain what happens to energy in an isolated system
 See Reference 6

== See also ==

[[Kinetic Energy]] 
[[Potential Energy]] 
[[Work]] 
===Further reading===

Goldstein, Martin, and Inge F., (1993). The Refrigerator and the Universe. Harvard Univ. Press. A gentle introduction. 
Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0-7167-1088-9. 
Nolan, Peter J. (1996). Fundamentals of College Physics, 2nd ed. William C. Brown Publishers. 

===External links===
 [https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-conservation-of-energy Khan Academy]
 [http://www.physicsclassroom.com/class/energy/Lesson-2/Application-and-Practice-Questions Practice Questions]
 [http://physics.info/energy-conservation/problems.shtml More Practice]
 [http://gilliesphysics.weebly.com/uploads/5/7/5/2/57520801/conservation_of_energy_practice_problems.pdf Basic Examples] 
[http://www.physnet.org/modules/pdf_modules/m158.pdf The First Law of Thermodynamics]
==References==

1."Conservation of Energy." Hmolpedia. Web. 1 Dec. 2015. <http://www.eoht.info/page/Conservation+of+energy>. 
2. "University of Wisconsin Green Bay." Speed & Stopping Distance of a Roller-Coaster. Web. 1 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/2/>. 
3. "Motion." G9 to Engineering. Web. 1 Dec. 2015. <http://www.g9toengineering.com/resources/translational.htm>. 
4. "Energy of Falling Object." HyperPhysics. Web. 1 Dec. 2015. <http://hyperphysics.phy-astr.gsu.edu/hbase/flobj.html>. 
5. "Conservation of Energy & Momentum Problem: Collision of Two Cars at a Stoplight." University of Wisconsin- Green Bay Physics. Web. 2 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/6/>. 
6. "Law of Conservation of Mass Energy." Law of Conservation of Mass Energy. Web. 3 Dec. 2015. <http://www.chemteam.info/Thermochem/Law-Cons-Mass-Energy.html>.
[[Category:Energy]]

Conservation of Energy

2018-04-18T23:12:28Z

A2xreyna:

Alex Reyna claimed 4/18/2018

This page was originally created by ksubramanian33, as can be seen by the edit history.
 

==Main Ideas==
===Conceptual Model===
* Conservation of energy means that the total energy of a system will be the same before and after an event.
* This only applies to isolated systems (no outside forces acting on the system).
** Not Isolated: An object sliding across a rough floor (system = the object). There is work being done by the floor on the object because of the frictional force.
** Isolated: An object sliding across a rough floor (system = the object AND the floor). There is no work done on the system because all the forces are contained in the system.
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> [[File:IntroConservationEnergy.gif]] </div> see reference 1

===Mathematical Model===
* Single Particle
** Particle Energy: Eparticle = γmc2 
** Rest Energy: Erest = mc2 
** Kinetic (particle): K = γmc2 + mc2 
* General Objects
** Kinetic: (1/2)mv2
** Gravitational Potential: (-Gm1m2)/(R2) (large distances), mgh (near the surface of the Earth)
** Spring (Elastic) Potential: (1/2)kss2 
** Thermal Energy: mCΔT 
====General Formulas====
* E = W + Q (if no heat transfer indicated, Q = 0; if no external forces acting on system, W = 0)
* E = K + U (The total energy is the sum of the kinetic and potential energies. From this, you can infer that for an isolated system, any change in kinetic energy will correspond in an equal but opposite change in the potential energy and vice versa.)
These formulas can be interchanged. For example, is you know work and heat transfer are zero, energy equals zero, so K + U will equal zero

[[File:MathConservationEnergy.png]]
 See Reference 2

 [https://www.youtube.com/watch?v=kw_4Loo1HR4 Basic Explanation of Conservation of Energy]
 [https://www.youtube.com/watch?v=EZrJNIBX2wk Skater Visualization of Transfers of Energy]

==Examples==

===Particle===
An electron is accelerated to a speed of 2.95 × 108 
(a) What is the energy of the electron? 
(b) What is the rest energy of the electron? 
(c) What is the kinetic energy of the moving proton? 
(a) 
E = γmc2 
E = (5.50)(9.11 × 10-31)(3 × 108) 
E = 1.50 × 10-21 J 
(b) 
Erest = mc2 
Erest = (9.11 × 10-31)(3 × 108)2 
Erest = 2.73 × 10-22 J 
(c) 
K = E - Erest 
K = 1.50 × 10-21 - 2.73 × 10-22 
K = 1.23 × 10-21 J 

===Simple===
A ball is at rest on a table with 50 J of potential energy. It then rolls of the table, and at one point in time as it falls, the ball has 30 J of kinetic energy. 
What is the potential energy of the ball at that instant?

[[File:EasyEnergyConservation.png]]
 See Reference 3

Einitial = Efinal 
Kinitial + Uinitial = Kfinal + Ufinal 
0 J + 50 J = 30 J + Ufinal 
Ufinal = 20 J

===Middling===
A ball is at rest 50 m above the ground. You then drop the ball. What is its speed before hitting the ground? 
[[File:HardEnergyConservation.gif]]
 See Reference 4 

v = 
√2gh 
 
v = 
√2(9.8)(50) 
 
v = 31.3 m/s

===Difficult===
The driver of an SUV (m = 1700 kg) isn’t paying attention and rear ends a car (m = 950 kg) on level ground at a red light. On impact, both drivers lock their brakes. The SUV and car stick together and travel a distance of 8.2 m before they come to a stop. How fast was the SUV traveling just before the collision? The coefficient of friction between the tires and the road is 0.72.
[[File: DifficultEnergyConservation.png]]
See Reference 5 

KE2 + PE2 = KE3 + PE3 - Wnc 
(1/2)mtotalv22 + mtotalgh2 = (1/2)mtotalv32 + mtotalgh3 - Wnc 
(1/2)mtotalv22 + 0 = 0 + 0 - (μmtotalg)dcos(180°) 
(1/2)v22 = -(0.72)(9.8 m/s2)(8.2 m)(-1) 
v22 = 116 m2/s2 
v2 = 10.8 m/s 

* Notice how the mass is canceled. 

p1 = p2 
p1x = p2x 
msuvvsuv + mcarvcar = mtotalv2 
(1700 kg)vsuv + 0 = (2650 kg)(10.8 m/s) 
(1700 kg)vsuv = 28600 kgm/s 
vsuv = 17 m/s 

==Connectedness==
Computer Science 
1. How is this topic connected to something that you are interested in? 
This concept is clearly connected to physics and helps explain and sometimes predict how our world works. Knowing why and how things move and interact is very powerful. 
2. How is it connected to your major? 
This topic is connected to computer science in the field of modeling and simulation. When you use computers to more efficiently model grand scale scenarios, it is important to take all fundamental concepts of physics, including the conservation of energy, into account. 
3. Is there an interesting industrial application? 
The law of conservation of energy is prevalent in nearly every industrial application of physics. More specifically, it is relevant today as finding renewable and sustainable forms of energy is becoming a more prevalent social and economic issue. It will be interesting to see how this concept will be applied as we try to get more energy for less. 

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
 Who: Many physicists contributed to the knowledge of energy, however it is most notably atributed to Julius Robert Mayer
 What: Most formally discovered the law of conservation of energy
 When: 1842
 Where: Germany
 Why: To explain what happens to energy in an isolated system
 See Reference 6

== See also ==

[[Kinetic Energy]] 
[[Potential Energy]] 
[[Work]] 
===Further reading===

Goldstein, Martin, and Inge F., (1993). The Refrigerator and the Universe. Harvard Univ. Press. A gentle introduction. 
Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0-7167-1088-9. 
Nolan, Peter J. (1996). Fundamentals of College Physics, 2nd ed. William C. Brown Publishers. 

===External links===
 [https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-conservation-of-energy Khan Academy]
 [http://www.physicsclassroom.com/class/energy/Lesson-2/Application-and-Practice-Questions Practice Questions]
 [http://physics.info/energy-conservation/problems.shtml More Practice]
 [http://gilliesphysics.weebly.com/uploads/5/7/5/2/57520801/conservation_of_energy_practice_problems.pdf Basic Examples] 
[http://www.physnet.org/modules/pdf_modules/m158.pdf The First Law of Thermodynamics]
==References==

1."Conservation of Energy." Hmolpedia. Web. 1 Dec. 2015. <http://www.eoht.info/page/Conservation+of+energy>. 
2. "University of Wisconsin Green Bay." Speed & Stopping Distance of a Roller-Coaster. Web. 1 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/2/>. 
3. "Motion." G9 to Engineering. Web. 1 Dec. 2015. <http://www.g9toengineering.com/resources/translational.htm>. 
4. "Energy of Falling Object." HyperPhysics. Web. 1 Dec. 2015. <http://hyperphysics.phy-astr.gsu.edu/hbase/flobj.html>. 
5. "Conservation of Energy & Momentum Problem: Collision of Two Cars at a Stoplight." University of Wisconsin- Green Bay Physics. Web. 2 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/6/>. 
6. "Law of Conservation of Mass Energy." Law of Conservation of Mass Energy. Web. 3 Dec. 2015. <http://www.chemteam.info/Thermochem/Law-Cons-Mass-Energy.html>.
[[Category:Energy]]