Potential Energy

1. Potential Energy

2. Height • Work is a process. • When a box is lifted, work is done on the box. • At the end, the box is resting – no kinetic energy. • Where did the work go? y2 F = -mg h y1

3. Energy Change • The state of the object changes • The box is higher after the work was done • Work can be stored in a new position y2 h y1

4. Work from Height • The box can move down from its height and do work. • The work done by gravity is converted to kinetic energy • The work done by gravity is opposed by some other force, and less work is done y2 F = -mg h y1

5. Elastic Energy • As a spring compresses work is done. • Work done by gravity on the ball, W = mgh • Work done by the spring on the ball, W = -(1/2)kx2 • Work done by the spring to return the ball, W = (1/2)kx2 • There is an elastic energy. Fs = -k(-y) -y Fg = -mg

6. Potentials • Energy due to position is called potential energy (U). • An object has the potential to do work • Since the work isn’t done yet, U = -Wint. • Wint is the force acting internally to the object • The potential energy of gravity: U = mgy • The potential energy of a spring: U = (1/2)kx2

7. No Absolute • The work done on an object from a force only reflects a change in the state of the object. • Work is a process • Energy is a state • Potential energy reflects the work that may be done. • The point U = 0 is arbitrary • For instance, experiment at the top of a building of height h, U = mg(y+h) = mgy + mgh = mgy + C next