IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

# To Find the Coefficient of Restitution

## Objective

To find the coefficient of restitution in an inelastic collision.

## Introduction

When an object hits a wall obliquely, it reflects. If friction during the collision can be neglected, the parallel component of velocity remains unchanged but perpendicular component changes. If the collision is elastic, the net speed remains the same and hence the perpendicular component also remains the same. As a result, angle of incidence is equal to angle of reflection. However, if the collision is partially inelastic the perpendicular component decreases and the angle of reflection will exceed angle of incidence. The coefficient of restitution is obtained by $$e=\frac{\tan\theta_1}{\tan\theta_2}$$, where $$\theta_1$$ and $$\theta_2$$ are the angles of incidence and reflection. In the experiment you will use this equation.

## Apparatus

a wooden block with a trench, a sunmica board, a carrom striker, powder, scale, pencil, eraser.

## Procedure

Look at the wooden block and the sunmica board. The board can be fitted to the block just by inserting it in the trench. You can keep the whole thing on a horizontal surface, the board making an inclined plane of a small angle. This inclination has no role in the experiment.

Half the wall of the block is wood and the other half is foam. By just flipping the block you get the other kind of wall on the top.

Sprinkle some powder on the board very gently, so that a thin layer is formed. Put striker on the board at some distance from the wall and flick it so as to hit the wall obliquely. The angle should be large enough to give you significant difference between the angles of incidence and reflection, if any. As the striker moves through the powder, it makes a trail which you can see. Very carefully draw pencil lines to mark the incident and reflected directions of the center of the striker. Draw perpendicular to the wall that goes through the point of intersection of these two directions.

Now you can get $$e$$ from the equation. Repeat at least 3 times with wooden surface and 3 times with foam surface.

## Note

Designed by Shiksha Sopan.