Potential Energy

Potential energy, U, is the energy of position. For a spring, the work done in compressing the spring is stored, so the potential energy of a spring is given by

Uspring = k x2

where x is the displacement of the spring and k is the spring constant.

For gravity, the potential energy is

Ugravity = m g h

where h is the height.

For both the spring and gravity, the absolute value of the potential energy is arbitrary. One can define zero potential energy anywhere one likes because what matters is the change in potential energy, as this is the only quantity that enters the work-energy theorem. This is genrally true for all potential energies: They are only defined up to an additive constant (that has to be kept the same for the entire motion, though).

Choosing the potential energy to be zero at the beginning of the motion is usually a good choice.

Question:

To store exactly 1 Joule of potential energy in a spring with k = 45 N/m, how much would the spring have to be stretched beyond its equilibrium length?

Answer:

© MultiMedia Physics, 1999