Name
Period
Date
Energy: Worksheet 7
Potential Energy & Equilibrium
1. The figure below shows the graph of a potential
energy function U vs. x .
U
B
F
a. At each point indicated, state whether the force
Fx is positive, negative, or zero.
C
E
A
x
D
b. At which point does the force have the greatest magnitude? How do you know?
c. Identify any equilibrium points, and state whether the equilibrium is stable,
unstable, or neutral.
2. A particle’s potential energy function is given by U ( x ) 
constant.
a. Sketch the U (x) curve.
C
where C is a positive
x
b. Find the force as a function of x .

U x 

x
c. Is this force directed toward the origin or away from it? How do you know?
d. Does the potential energy increase or decrease as x increases?
e. Answer parts (a) through (d) if C is a negative constant.

x

U x 
Energy: Worksheet 7
page 2

3. A particle of mass 2.0 kg moves along the x axis through a region in which its
potential energy U (x) varies as shown below.
a. Sketch the
U (J )
corresponding Force vs.
Position graph.
2

x (m)
0
-2
-4
-6
b. When the particle is

at x  4.0 m , its velocity
is  2.0 m . What is the
s
particle’s total
mechanical energy?
-8
-10

F (N )
2
4
6
8
10
12
14
3
2
1

x (m)
0
-1
-2
-3
2
4
6
8
10
12
14

c. Between what limits of x can the particle move? How do you know?

d. What is the particle’s speed at x  7.0 m ?