If work is zero, when is force nonzero?

Question

Emily Abbate · Accepted Answer

Force and displacement are perpendicular each other when work done is zero.

If displacement and force are perpendicular to each other, work done is zero. #=>theta=90^o# so # W=0# Work done is zero i.e., force and displacement are perpendicular to each other is verified in the following cases: a) When a body is in circular motion no work is done by centripetal force. b) In pulling a body on a horizontal surface, no work is done against gravitational force. c) If a man with a load on his head walks horizontally no work is done against gravitational force.

Emily Abbate · Answer

Normally, when we talk about force and displacement, we refer to the definition of work in a one-dimensional representation:

#w = -vecFDeltavecx#

where work is negative with respect to the worker who is say, pushing a box.

One can specify that this force is parallel to the displacement, i.e. #vecF = vecF_"||" = vecFcostheta#. When #theta = 0^@#, the work is pointing exactly in the direction of the displacement.

On the other hand, if we imagine a force entirely perpendicular to the desired displacement, there is no component of the force that causes the displacement.

#vecF_(_|_) = vecFsin(0^@) = vecFcos(90^@)#

(since #sin(x + pi/2) = cos(x)#.)

When #theta = 90^@#, one pushes perpendicular to the desired displacement, but #sin0^@ = cos90^@ = 0#.

So, I don't think such a force is nonzero.

Charlotte Aaron · Answer

undefined Force is nonzero when there is a displacement occurring against a resisting force, but the angle between the force and displacement vectors is such that the component of force in the direction of displacement is zero.