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

# The Falling Bottle/ Mug

## Introduction

This is an eye catching demonstration which gives an insight into many concepts of physics like friction, connected motion, vertical circle etc.

## Apparatus

200 ml plastic bottle filled with water (or a coffee/tea cup), key, 1 metre sturdy thread, a pencil.

## Procedure

1. Tie the plastic bottle to one end of the thread and tie a small key to the other end of the thread.
2. Pass the thread over the body of the pencil which acts as a pencil.
3. Now hold the pencil in one hand and the key tied to the thread in other hand such that it makes an angle of around 45 degree with the horizontal.
4. Keep the length of the thread on the side of the bottle hanging over the pencil much smaller than the length of portion of the thread tied to the key over the other side of the pencil
5. Now release the key.
6. The audience hold their breath as they expect the heavier bottle to slide and crash to the ground.
7. But amazingly the bottleās downward journey is halted as the thread tied to the key curls many times around the pencil and stops any further movement.

## Discussion

When we release the key, the bottle being heavier starts accelerating down and the key tied to the thread falls down like a pendulum released from its extreme position. But as it falls down, the length of the thread goes on decreasing and its velocity goes on increasing. By the time the key reaches the bottom of the circle it acquires sufficient velocity for completing a vertical circle. So the thread loops around the pencil. The bottle still accelerates down so the thread keeps looping around the pencil till it stops the motion of the bottle.

As number of loops increase, the friction on the thread increases. The increase in the contact area of the thread with the pencil increases the normal reaction of the pencil on the thread which in turn causes the friction to increase.

## Concepts

1. The tension in the strings on the two sides are very different. This is because of the friction between the pencil surface and string.
2. As you release the keys, the bottle goes down a little. During this period the keys goes on a curved path of decreasing radius. This gives an extra speed to the key. In some time the key acquires such a speed that it can go up and wrap on the pencil.
3. As the contact between the pencil and the thread becomes larger, the friction become high and prevents the bottle to slip further. Finally both objects hang in equilibrium.