# Lesson Worksheet: Elastic Potential Energy Mathematics

In this worksheet, we will practice finding the work done in stretching an elastic string or spring and finding the energy stored in an elastic string or spring.

**Q1: **

A ball of mass is attached to one end of a light elastic string of natural length and modulus of elasticity , where is the acceleration due to gravity. The other end of the string is fixed at a point on the line where the base of a vertical wall meets a rough horizontal plane. The ball is held on the plane a distance of from in such a way that the string lies perpendicular to the wall. Given that the coefficient of friction between the ball and the plane is , find the speed of the ball at the moment it collides with the wall. Give your answer in terms of and . If the ball rebounds from the wall with speed , at what distance from will the ball finally come to rest?

- A,
- B,
- C,
- D,
- E,

**Q2: **

A light elastic spring has a natural length 1.4 m and modulus of elasticity 22 N. How much work is done in compressing the spring from a length of 1.3 m to a length of 1.2 m?

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

**Q3: **

One end of a light elastic string of natural length 3.9 m and modulus of elasticity 17.3 N is attached to a fixed point on a rough horizontal surface. A ball of mass 2.9 kg is attached to the other end of the string, and the ball is placed on the surface so that the string is taut but not stretched. The ball is then subjected to an impulse resulting in a velocity of 1.1 m/s directly away from . Given that the coefficient of friction between the ball and the surface is 0.3, find the distance the ball travels before it is instantaneously at rest. Give your answer in meters, correct to two decimal places, taking .

**Q4: **

A particle of mass is attached to one end of a light elastic string of natural length and modulus of elasticity . The other end of the string is fixed at a point which is at a height of above a horizontal floor. The particle is projected vertically downward from at a speed of , where . Given that when the particle hits the floor it rebounds at half the speed, find the maximum speed of during its motion.

- A
- B
- C
- D
- E

**Q5: **

A particle of mass hangs at the end of a light elastic string of natural length . The string is connected to a horizontal ceiling, and has length of at equilibrium. Find the elastic potential energy stored in the string. Consider the acceleration due to gravity to be .

- A
- B
- C
- D
- E

**Q6: **

Which of the following is the unit for elastic potential energy?

- ANewton-second
- BWatt
- CJoule
- DNewton
- ENewton per meter

**Q7: **

A spring has an elastic potential energy of 0.24 J when stretched m from its equilibrium position. Given that the spring constant , find the value of .

**Q8: **

Find the potential energy stored in a spring that has a spring constant when stretched 0.2 m from its equilibrium position. Give your answer to the nearest 2 decimal places.

**Q9: **

Find the elastic potential energy of a spring when a force acts on it and stretches it a distance 1.5 m from the equilibrium position.

**Q10: **

If a spring has an elastic potential energy of 0.72 J when stretched 0.6 m from its equilibrium position, find the spring constant in newtons per meter.