Lesson: Elastic Potential Energy

Mathematics

In this lesson, we will learn how to find the work done in stretching an elastic string or spring and how to find the energy stored in an elastic string or spring.

Worksheet

Q1:

A ball of mass 𝑚 is attached to one end of a light elastic string of natural length 3𝑎 and modulus of elasticity 3𝑚𝑔, where 𝑔 is the acceleration due to gravity. The other end of the string is fixed at a point 𝑂 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 15𝑎2 from 𝑂 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 34, find the speed of the ball 𝑣 at the moment it collides with the wall. Give your answer in terms of 𝑎 and 𝑔. If the ball rebounds from the wall with speed 2𝑣9, at what distance 𝑑 from 𝑂 will the ball finally come to rest?

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?

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 𝐴 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 𝐴. 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 𝑔=9.8/ms.

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