Question

(a) What happens to the work done when the dispacement of body is at right angles to the direction of force acting on it? Explain your answer.
(b) A force of 50 N acts on a body and moves it a distance of 4 m on horizontal surface. Calculate the work done if the direction of force is at an angle of 60° to the horizontal surface.

Answer 1

(a) When the force is perpendicular to the direction of motion, the work done in such cases is zero. We have a relation as,
W = FS cos θ

Where,
(W) - Work done
(F) - Force
(S) - Displacement
(θ) - Angle between force and distance
When the force is perpendicular to the direction of motion, cos 90° = 0, and hence the work done is also zero.
Example - The work done by the earth on a satellite moving in a circular orbit around it is zero because gravitational force of attraction and displacement of sattelite at any instant are perpendicular to each other.

(b) We have a situation in which, work is done by force acting obliquely.
Force, (F) = 50 N
Distance travelled by the body, (S) = 4 m
Angle between force and direction of distance, (θ) = 60°
We have a relation as,
W = (F)(S) cos θ
So,
$$\begin{gathered} W=\left(50\right)\left(4\right)\cos 60° \\ =200\left(\frac{1}{2}\right)\mathrm{J} \\ =\boxed{100\mathrm{J}} \end{gathered}$$
So, the work done is 100 J.