#### Transcript Energy Curves

```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.
A
C
B

At C the kinetic energy is
being converted back into
potential energy.
Clearing the Hill
x1
x2

A cart that starts at x1 can
climb no further than x2
before it stops.

The potential energy is the
same at both points.

At both points there is no
energy left for kinetic energy.
Potential Energy Curve

The potential energy can be displayed as a graph.
• For height, U = mgh.
U
x
Turning Points

The total energy of a system is constant.
• A constant horizontal line of energy E

The point where the energy is all potential are the
turning points.
U
E
x1
x2
x
Well and Barrier

An object with energy E
cannot go outside the range
from x1 to x2.

The object is trapped in a
potential well.

The hill at C is a potential
barrier.
U
C
E
x1
x2
x
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
C
E
x0
x
Spring Constant Curve

The spring force has a potential energy U = ½ kx2 .
U
U
x
Near the minimum all curves are approximately a spring force.
x
Universal Gravitational Curve

Universal gravitational
potential energy also can be
plotted as a curve.
GmM
U 
r
This object will escape
the gravitational potential.
U
E1
r
E2
This object is trapped by the
gravitational potential.
```