# Worksheet: Elastic Potential Energy

In this worksheet, we will practice using F = kx (Hooke's law) and E = ½kx² to find the force and the potential energy of a compressed spring.

**Q1: **

A box that has 50 J of kinetic energy slides on a frictionless surface. The box hits a spring and compresses the spring a distance of 25 cm from its equilibrium length. If the same box with the same initial energy slides on a rough surface, it only compresses the spring a distance of 15 cm. How much energy must have been lost by the box when sliding on the rough surface?

**Q2: **

In the movie Monty Python and the Holy Grail, a cow of mass 110 kg is catapulted from the top of a castle wall 9.1 m high, onto the people down below. The cow is launched from a spring of with a constant of N/m that was initially compressed by 0.50 m from equilibrium. The gravitational potential energy is set to zero at the base of the castle wall.

What is the gravitational potential energy of the cow as it just clears the castle wall, treating the cow as a point particle?

- A J
- B J
- C J
- D J
- E J

What is the elastic spring energy of the cow before the catapult is released?

- A J
- B J
- C J
- D J
- E J

What is the speed of the cow at the instant that it hits the ground?

**Q3: **

A child of mass 32 kg jumps up and down on a trampoline. The trampoline exerts a spring restoring force on the child with a spring constant of N/m. At the highest point of the bounce, the child is 1.0 m vertically above the unstretched surface level of the trampoline. What distance is the trampoline compressed by when the child jumps on it? Neglect the bending of the child’s legs or any transfer of energy of the child into the trampoline while jumping.

**Q4: **

A pogo stick has a spring constant of N/m. A child stands on the pogo stick, pointing the stick vertically upward and compressing it by 12.0 cm. The child and pogo stick have a combined mass of 40.0 kg. The child jumps, which exerts negligible force but causes the pogo stick to return to its equilibrium length. What is the maximum upward vertical displacement of the child?

**Q5: **

In a Coyote/Road Runner cartoon clip, a spring expands quickly and sends the coyote into a rock. The spring extends by 5.0 m and accelerates the coyote of mass 20 kg to a speed of 15 m/s.

What is the spring constant of this spring?

If the coyote were sent vertically upward with the energy given to him by the spring, what maximum height would it reach, assuming air resistance was negligible?

**Q8: **

A block of mass 230 g is attached to one end of a spring that has a spring constant of 120 N/m. The other end of the spring is attached to a support while the block rests on a smooth horizontal table and can slide freely without any friction. The block is pushed horizontally to compress the spring by 12 cm. The block is then released from rest.

How much potential energy is stored in the spring when the spring is fully compressed?

Determine the speed of the block when the spring has recoiled to its equilibrium length.

**Q12: **

A spring has a force constant of 53.0 N/m. An object, initially at rest, with a mass of 0.960 kg is suspended from it. The object descends, stretching the string, oscillates, and then comes to rest.

How much is the spring stretched when the object has come to rest after oscillating?

Calculate the decrease in the gravitational potential energy of the object between its position at the point at which it is attached to the unextended spring and its position at the point at which it comes to rest after oscillating.

Calculate the energy stored in the spring by its extension.

**Q13: **

Old-fashioned pocket watches needed to be wound daily so they would not run down and lose time due to the friction in the internal components. This required a large number of turns of the winding key, but not much force per turn, and it was possible to overwind and break the watch. In which of the following ways was the energy stored?

- AA weak spring deformed a long way.
- BA weak spring deformed a short way.
- CA large mass raised a short distance.
- DA strong spring deformed a short way.
- EA small mass raised a long distance.

**Q14: **

You are loading a toy dart gun, which has two settings. The spring in the toy gun is compressed twice as far in the more powerful setting as it is in the less powerful setting. If it takes 5.0 J of work to compress the dart gun to the lower setting, how much work does it take for the higher setting?

**Q15: **

A perfectly elastic spring has an equilibrium length of 0.20 m and a spring constant of 0.400 kN/m. The spring is extended so that its length becomes 0.23 m.

How much elastic potential energy is contained in the spring when it is extended?

The spring is further extended so that its length becomes 0.26 m. What is the increase in the elastic potential energy due to the additional extension?

**Q18: **

0.54 J of work is done on a perfectly elastic spring to extend it a distance cm beyond its equilibrium length. The spring is then compressed by the same distance , as shown in the diagram.

What is the spring constant of the spring?

How much work must be done on the spring to increase to 12.0 cm?

Calculate the work done on the spring to compress it by 6.0 cm from its equilibrium length.