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Potential Energy and Conservative Forces

Potential energy is the energy of an object due to position alone. Gravitational potential energy is the energy associated with the position of an object in a gravitational field. How does this work?

Remember the woman in Section B? She pushed a cart to a new height h, doing work W = mgh. It would make sense to define gravitational potential energy as


where m is the mass of the object in question, g is the acceleration due to gravity, and h is the height. The height is measured relative to some standard, such as sea level or street level. It does not matter what the standard is, because we are always interested in changes in height or changes in potential energy. This formula works for all situations near the surface of the Earth.
Any force with an associated potential energy is called a potential force or a conservative force. Examples include the forces due to springs and the electrostatic force (see Chapter 14). The force the woman exerts on the cart and magnetic forces are not conservative forces.
Example: We are now in a position to FOLLOW THE ENERGY for the woman and the cart. It is clear that the energy ends up as potential energy. How does the energy start? Kinetic? No, because the cart is hardly moving both before and after its trip. The energy starts in her muscles, where it was stored as chemical energy. Thus the flow of energy is chemical to gravitational potential energy.

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