Conservation of Energy

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The law of conservation of energy is the fundamental principle of physics that describes how the total energy of an isolated system is always constant.

The Main Idea

For any given isolated system, the total energy will remain constant regardless of any processes or interactions that occur in the domain. Therefore, energy cannot be created or destroyed.

See Reference 1

A Mathematical Model

The most general mathematical formula to model the conservation of energy is E_initial = E_final where E is the total energy of the system.
More specifically, the total energy of the system can be described as the sum of the kinetic and potential energies. E = K + U where K is the total kinetic energy and U is the total potential energy.
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.

The above model is only applicable in an ideal, frictionless world without heat transfers. However, the adjustments needed to account for friction and heat are easy to include. For an isolated system with friction, E_initial - W + Q = E_final where W is the work done by friction and Q is the heat added to the system. In this case, W and Q are provided by the surroundings of the system.

See Reference 2

A Computational Model

The following demonstration provides a computer model that shows the changes in the different types of energy of the skater. In the initial simulation, there is no friction, so the energy changes between kinetic and potential, while the total energy remains constant. In the second simulation, friction is introduced, which results in thermal energy being created. This energy is then dissipated into the surroundings so the system of the skater loses total energy, but the total energy of the skater AND the surroundings still remains constant.

Skater

Examples

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?

See Reference 3

E_initial = E_final
K_initial + U_initial = K_final + U_final
0 J + 50 J = 30 J + U_final
U_final = 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? 

See Reference 4

E_initial = E_final
K_initial + U_initial = K_final + U_final
0 J + 50 J = 30 J + U_final
U_final = 20 J

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.

See Reference 5

Connectedness

1. How is this topic connected to something that you are interested in?
2. How is it connected to your major?
3. Is there an interesting industrial application?

History

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

See also

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

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/>.