__POTENTIAL ENERGY VS POSITION GRAPH__

- Value <-> potential energy
- total energy - value <-> kinetic energy (since K+U = E)
- Where U=E, kinetic energy is zero. Object is at a momentary stop.
- Where U<E, kinetic energy is positive. Object is moving.
- Where U>E, forbidden region. Object cannot be there without being given more energy.
- Slope <-> opposite of force (F = -dU/dx)
- Sloping up (such as / ) <-> force is to left or toward smaller values of position.
- example: gravitational potential energy is sloping up everywhere, and the force is always toward smaller values of height, i. e. down.
- Sloping Down ( such as \ ) <-> force is to right or toward larger values of position.
- example: for a compressed spring, potential energy is sloping down, and the force is toward larger (less negative) values of x.
- Horizontal <-> no force (maybe just for an instant)
- If U=E at a point where the U curve is horizontal, then there is no kinetic energy and there is no force. This corresponds to an object at rest remaining at rest.