Question

A rock is being twirled in a circle on the end of a string. The string provides the centripetal force needed to keep the ball moving in a circle. Does the force of tension exerted by the string on the rock do work on the ball in this situation? Explain.

Answer 1

Answer:

No

Explanation:

The force of tension exerted by the string on the rock acts as centripetal force, so its direction is always towards the centre of the circle.

However, the direction of motion of the rock is always tangential to the circle: this means that the force is always perpendicular to the direction of motion of the rock.

As we know, the work done by a force on an object is

$W=Fd cos \theta$

where

F is the magnitude of the force

d is the displacement of the object

$\theta$ is the angle between the force and the displacement

In this situation, F and d are perpendicular, so $\theta=90^{\circ}$, therefore $cos \theta = 0$ and the work done is zero:

$W=0$