Question

Can a centripetal force ever do work on an object? Explain.

Short answer

The centripetal force does not do any work ever on an object.

Step-by-step solution

Meaning of work done

When the application of force displaces an object, work is said to be done by force. By applying force, the object may move in the direction of the force or another direction.

The total work done is the dot product of force and displacement. The expression for the work done is given by:

\(\begin{aligned}W &= F \cdot d\\W &= Fd\cos \theta \end{aligned}\)

Here, \(F\) is the applied force and \(d\) is the displacement.

The condition that explains whether a centripetal force can ever do work on an object or not

The following diagram shows the uniform circular motion of a particle.

If a particle revolves in a uniform circular motion, the centripetal force \({\vec F_C}\)acts toward the center of the circle, and \(d\vec r\) is the infinitesimal displacement, which is in the tangential direction. However, \({\vec F_C}\) and \(d\vec r\) are perpendicular to each other.

Thus, the work done will be zero.

\(\begin{aligned}W &= F\left( {dr} \right)\cos \left( {90^\circ } \right)\\W &= 0\end{aligned}\)

The dot product yields zero. Therefore, a centripetal force does not do work on an object.