Question

What should be the angle between force and the displacement for maximum and minimum work?

Answer 1

Definition of work done

When an object moves through a certain distance under the effect of a force applied to it, work is said to be done. It is given as,

$W=FS\cos \theta$

where, $F$ is force, $S$ is displacement and $\theta$ is the angle between force and displacement.

Explanation

1. Maximum work is done when force is applied in the direction of motion, that is, when $\theta =0°$.

$$\begin{gathered} W=FS\cos \theta \\ W=FS\cos 0° \\ W=FS\times 1 \\ W=FS \end{gathered}$$

2. Minimum work is done when force is applied perpendicular to the direction of motion, that is, when $\theta =90°$.

$$\begin{gathered} W=FS\cos \theta \\ W=FS\cos 90° \\ W=FS\times 0 \\ W=0 \end{gathered}$$

Therefore, the angle between force and displacement should be $0°$ for maximum work and $90°$ for minimum work.