Download Elastic Potential Energy Practice

Elastic Potential Energy Problems
1. A spring-loaded toy gun is used to shoot a
ball of mass m = 2 kg straight up in the air,
as shown in the figure. The spring has spring
constant k = 500 N/m. If the spring is
compressed a distance of 25.0 centimeters
from its equilibrium position y = 0 and then
released, the ball reaches a maximum height
hmax (measured from the equilibrium position
of the spring). There is no air resistance, and
the ball never touches the inside of the gun.
Assume that all movement occurs in a
straight line up and down along the y axis.
a) Which of the following statements are
true? Briefly explain your reasoning.
i. Mechanical energy is conserved because Remind yourself of what mechanical energy is.
no outside forces are doing work on the ball.
ii. The forces of gravity and the spring have potential energies associated with them.
iii. No forces are acting on the ball once it is released from the spring gun.
b) Find the (instantaneous) velocity of the ball once the spring in the gun is released.
In this case, the elastic potential energy in the spring is being converted to kinetic energy.
c) What will be the maximum height hmax of the ball?
You can either determine this by considering elastic potential -> gravitational potential or kinetic -> gravitational potential
d) Which of the following actions, if done independently, would increase the maximum
height reached by the ball? Briefly explain your reasoning for any and all choices.
- reducing the spring constant
- increasing the spring constant
-decreasing the mass of the ball
- increasing the mass of the ball
- decreasing the distance the spring is compressed
- increasing the distance the spring is compressed
- tilting the gun so that it is at an angle.
2) A force of 50 N is required to stretch a spring 5 cm beyond its natural length. How
much work (energy put into the spring) is done in stretching the spring 7 cm beyond the
natural length?
Determine the spring constant (k) using the first set of values and then answer the question about energy
for the 7 cm extension.
3. A spring-operated dart gun fires 0.010 kg darts. Arming the gun requires 185 N of
force and results in the compression of the spring by 10 cm.
You don’t need the mass of 0.010 kg for parts (a) and (b).
a) Find the spring constant.
b) Find the energy stored in the spring.
c) Find the instantaneous velocity of the dart when released from the gun.
d) If the dart is launched vertically, how high will it rise (maximum height)?
Refer to parts (b) and (c) of question 1.
4. A 80 kg (800 N) acrobat stands on a spring-loaded platform as a part of a stunt. If the
spring under the platform has a spring constant of 1.6 * 103 N/m, how much should the
spring be compressed to launch the acrobat to a height of 5 m?
Assume that all the energy
transforms from elastic potential to
gravitational potential.
5. A spring has a natural length of 2 meters. An object of 30 N hangs from the spring
and stretches it to a total length of 2.5 meters.
a) Find the spring constant
b) How far beyond its natural length would an object of 80 N stretch the spring?
c) How much work is required to stretch the spring to a total length of 3 m?
In other words, how much energy is associated with a 3 m extension of the spring?
6. You have two springs that are identical except spring 1 is stiffer than spring 2. In the
following cases, determine which spring requires more work (no calculations needed):
There is no need for calculations but feel free to make up your own values of k if that helps you think about this question.
a) They are stretched using the same force.
b) They are stretched the same distance.
7. An object hangs motionless from a spring. When the object is lifted up, the sum of
the elastic potential energy of the spring and the gravitational potential energy will..
a) increase! !
b) stay the same! !
c) decrease