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Work - Mechanical Energy Relationships:
If non-conservative forces do net work upon an object, then the total mechanical energy of that object is changed. The sum of the kinetic and potential energies will change as work is done upon the object. If non-conservative forces do NOT do net work, then the total mechanical energy will be conserved.
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Definition of Total Mechanical Energy:
The total mechanical energy possessed by an object is the sum of its kinetic energy and potential energy.
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The coaster car is coasting and resistance forces are negligible - gravity is the only force doing work upon it. So the mechanical energy of the coaster car is conserved. It is the same initially as finally. See Know the Law section.
Mechanical energy takes two forms - kinetic and potential. The total amount of mechanical energy is simply the sum of these two amounts (see Dictionary section). At any given location along the path of the coaster car, the total mechanical energy can be determined by adding the kinetic energy and the potential energy. If mechanical energy is said to be conserved, then the sum of the two forms - KE and PE - will be the same at any given location along the path of the car. If the total amount is known and the PE is known, the KE can be quite easily calculated.
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