A force does not work, when
- the displacement is zero: When the displacement in the direction of the force is zero by the definition of work, w=F×d = F×0 = 0 joules. The examples are, standing the whole day on the ground, pushing the walls of a house.
- the displacement is perpendicular to the direction of the force: When displacement is perpendicular to force applied. This means only one thing. The displacement on the body is not caused by the force we are taking into consideration. Actually, the work done is calculated using the formula, W = F×s×cos(θ), where θ is the angle between force and displacement as shown in the figure
Now if the displacement is perpendicular to the force i.e., θ = 90°, we get
W = F×s×cos(θ) = F×s×cos(90°) = F×s×0 = 0