A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 m s^-1. What is the trajectory of the bob if the string is cut when the bob is (a) at one of its extreme positions, (b) at its mean position.

Question

A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 m s^-1. What is the trajectory of the bob if the string is cut when the bob is (a) at one of its extreme positions, (b) at its mean position.

Philoid · Accepted Answer

(a) The velocity of the bob at the extreme positions becomes zero because the kinetic energy becomes zero. Thus, there is no horizontal velocity.

The net force just after it has been cut at extreme positions is just gravitational force which always acts vertically downward. Thus, the bob will fall vertically downwards to the ground if the string is cut at the extreme positions.

(b) Given,

The speed of the bob at the mean position is 1 m/s.

The kinetic energy is thus maximum here and the direction of the velocity is tangential to the arc traced by the oscillating bob. Thus, if it is cut at the mean position then it will follow a projectile path due to the presence of the horizontal velocity.

A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 m s-1. What is the trajectory of the bob if the string is cut when the bob is (a) at one of its extreme positions, (b) at its mean position.

A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 m s^-1. What is the trajectory of the bob if the string is cut when the bob is (a) at one of its extreme positions, (b) at its mean position.