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

# A Magical Coin

## Introduction

In most of the popular science books studied by the students we come across a concept of inertia of rest in relation to the Newton's first law of motion. A body at rest maintains its state of rest if the net force on it is zero. This unwillingness to change its state of rest is described as the inertia of rest.

To demonstrate the inertia of rest there are many experiments. But do these experiments really achieve the condition in which a body can exhibit inertia of rest? We attempt to analyze it by this demonstration.

## Apparatus

a match box and a coin

## Procedure

1. Insert the coin between the match box case and its drawer till it is not visible.
2. Tap the match box with your finger sharply.
3. See the coin emerging out of the box.

## Discussion

It seems as if the sharp taps given to the match box are making it go down. The coin on the other hand seems to be at rest, as instead of going down with the match box, it emerges up.

So is the coin really at rest? Is the force experienced by the coin zero?

When the coin is inserted vertically in the match box drawer, its weight acts downward. This is balanced by the force of friction on it acting upward. The force of friction on the coin is due to its contact with the inner surface of the match box drawer. So the coin is in equilibrium.

On tapping, the match box gets a large impulse which accelerates it downwards. The coin in contact with the drawer now experiences a force of friction downwards. The acceleration of the match box is large, so the force of friction on the coin tries to attain this acceleration and shoots up to its maximum possible value. But the maximum force of friction only manages to move the coin down with acceleration much smaller than the match box. So relative to the match box, the coin moves a much smaller distance downwards and hence it emerges out of the match box.

If the force applied on the match box is small, the coin will not emerge from the match box. In this case the force of friction on the coin will be sufficient to produce acceleration equal to the match box. So both of them will now move the same distance down together.