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.