Energy Conservation by Using Mechanical
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Energy Conservation by Using Mechanical

In the physical sciences, mechanical energy is the sum of potential energy and kinetic energy. It is the energy associated with the motion and position of an object. The principle of conservation of mechanical energy states that in an isolated system that is only subject to conservative forces the mechanical energy is constant. If an object is moved in the opposite direction of a conservative net force, the potential energy will increase and if the speed (not the velocity) of the object is changed, the kinetic energy of the object is changed as well. In all real systems, however, non-conservative forces, like frictional forces, will be present, but often they are of negligible values and the mechanical energy's being constant can therefore be a useful approximation. In elastic collisions, the mechanical energy is conserved but in inelastic collisions, some mechanical energy is converted into heat. The equivalence between lost mechanical energy (dissipation) and an increase in temperature was discovered by James Prescott Joule.

Many modern devices, such as the electric motor or the steam engine, are used today to convert mechanical energy into other forms of energy, e.g. electrical energy, or to convert other forms of energy, like heat, into mechanical energy.


Student Extras Teacher's Guides
The Physics Classroom » Physics Tutorial » Work, Energy, and Power » Analysis of Situations in Which Mechanical Energy is Conserved
Work, Energy, and Power - Lesson 2 - The Work-Energy Relationship
Analysis of Situations in Which Mechanical Energy is Conserved
Internal vs. External Forces
Analysis of Situations Involving External Forces
Analysis of Situations in Which Mechanical Energy is Conserved
Application and Practice Questions
Bar Chart Illustrations
It has previously been mentioned that there is a relationship between work and mechanical energy change. Whenever work is done upon an object by an external force (or nonconservative force), there will be a change in the total mechanical energy of the object. If only internal forces are doing work (no work done by external forces), then there is no change in the total amount of mechanical energy. The total mechanical energy is said to be conserved. In this part of Lesson 2, we will further explore the quantitative relationship between work and mechanical energy in situations in which there are no external forces doing work.

The quantitative relationship between work and the two forms of mechanical energy is expressed by the following equation:

KEi + PEi + Wext = KEf + PEf
The equation illustrates that the total mechanical energy (KE + PE) of the object is changed as a result of work done by external forces. There are a host of other situations in which the only forces doing work are internal or conservative forces. In such situations, the total mechanical energy of the object is not changed. The external work term cancels from the above equation and mechanical energy is conserved. The previous equation is simplified to the following form:

KEi + PEi = KEf + PEf
In these situations, the sum of the kinetic and potential energy is everywhere the same. As the potential energy is increased due to the stretch/compression of a spring or an increase in its height above the earth, the kinetic energy is decreased due to the object slowing down. As the potential energy is decreased due to the return of a spring to its rest position or a decrease in height above the earth, the kinetic energy is increased due to the object speeding up. We would say that energy is transformed or changes its form from kinetic energy to potential energy (or vice versa); yet the total amount present is conserved - i.e., always the same.
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