Elastic potential energy
Elastic potential energy is energy that is stored in the deformation of matter, such as the stretching of a
rubber band or the compression of a spring. The amount of energy depends on both the amount of
deformation x and also the “stiffness” of the object—described by its spring constant k.
Typical elastic potential energies at 5 cm (0.05 m) deformation
x
F
k
Ep
(m)
(N)
(N/m)
(J)
#16 rubber band
0.05
1.25
25
0.03
31
0.04
40 cm spring
0.05
1.56
#33 rubber band
0.05
2.00
40
0.05
#84 rubber band
0.05
25.0
500
0.62
Bike front suspension
0.05
125
2,500
3.12
Car suspension
0.05
2500
50,000
62.5
Applying new knowledge
1. Write out a sentence that has the same meaning as the equation below.
Ep =
1 2
kx
2
2. The elastic potential energy of a #16 rubber band stretched by 10 cm is closest to which value?
A. 0.12 J
3.
B. 2.5 J
C. 12 J
D. 250 J
A #84 rubber band is 0.5 inch wide and 3.5 inches long. How many centimeters must this rubber
band be stretched to have an elastic potential energy of 5.0 joules? Enter your answer in the
response grid below.
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4. Are these statements about the spring constant true or false?
a. ___ The spring constant is a measure of the stiffness of the spring.
b. ___ The spring constant tells you how many newtons of force it takes to stretch the spring
one meter.
c. ___ If a spring stretches easily, it has a high spring constant.
d. ___ The spring constant of a spring varies with x, the amount of stretch or compression of
the spring.
5. What is the required spring constant for a spring to have an elastic potential energy of 100 J when
compressed 0.10 meters?
6. A spring stores 100 joules of elastic potential energy when it is stretched a distance d.
How much energy does it store when it is stretched three times as far?
A. 33 J
B. 300 J
C. 600 J
D. 900 J
2