Question

If force is applied at an angle $\theta$ to the direction of displacement of a body, how will you derive the amount of work done?

Answer 1

1. When force is applied at an angle $\theta$ to the direction of displacement, work done is given as —

$$\begin{gathered} W=F\times s\times \cos \theta \\ where, \\ W\to Workdone \\ F\to Force \\ s\to Displacementofthepointofapplicationinthedirectionofforce \\ \theta \to Anglebetweenforceanddisplacement \end{gathered}$$

2. Based on the value of the angle between force and displacement work done can be positive, negative or zero.

Value of $\theta$	Value of $\cos \theta$	Nature of work done
$0\le \theta <90°$	$0<\cos \theta \le 1$	Positive
$\theta =90°$	$\cos \theta =0$	Zero
$90°<\theta \le 180°$	$-1\le \cos \theta <0$	Negative