Work done when the force is not along the direction of motion
Back to Top
In many cases when we pull or push an object, we find that force and displacement are not in the same direction.
Let a constant force F acting on a body produce a displacement S as shown in the figure. Let q be the angle between the directions of the force and displacement.
Displacement in the direction of the force = Component of s along AX
= AC
Work done = Force x displacement in the direction of force
W = F s cos q
If the displacement s is in the direction of the force F,
q = 0, cos
q =1
Then, W = Fs x 1
W = Fs
If q = 90o, cos 90 = 0
Therefore, W = Fs x 0 = 0 i.e, no work is done by the force on the body.
Some illustrations are given below
Back to Top
01. When a body moves along a frictionless horizontal surface, its weight and the normal reaction of the surface are both perpendicular to the direction of motion. Hence, these forces, namely the weight of the body and the normal reaction do no work.
02. If a stone tied at the end of a string is whirled around in a circle with uniform speed, the centripetal force comes into action. This force is normal to the direction of motion of the stone at each instant. So this force does no work though it is responsible for keeping the stone in circular motion.
A boy whirling the stone tied to a string
