Energy Curves

Roller Coaster Track  A cart at point A has potential energy.  A cart at point B has converted potential energy into kinetic energy.  At C the kinetic energy is being converted back into potential energy. A B C

Clearing the Hill  A cart that starts at x 1 can climb no further than x 2 before it stops.  The potential energy is the same at both points.  At both points there is no energy left for kinetic energy. x1x1 x2x2

Potential Energy Curve  The potential energy can be displayed as a graph. For height, U = mgh.For height, U = mgh. U x

Turning Points  The total energy of a system is constant. A constant horizontal line of energy EA constant horizontal line of energy E  The point where the energy is all potential are the turning points. U x x1x1 x2x2 E

Well and Barrier  An object with energy E cannot go outside the range from x 1 to x 2.  The object is trapped in a potential well.  The hill at C is a potential barrier. U x x1x1 x2x2 E C

Equilibrium  At the minimum point in the curve, an object cannot gain kinetic energy.  There is no velocity, and the object is at rest.  The object is at equilibrium. U x x0x0 E C

Spring Constant Curve  The spring force has a potential energy U = ½ kx 2. U x U x Near the minimum all curves are approximately a spring force.

Universal Gravitational Curve  Universal gravitational potential energy also can be plotted as a curve. U r E2E2 E1E1 This object will escape the gravitational potential. This object is trapped by the gravitational potential.