Question

If work is zero, when is force nonzero?

Answer 1

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.

Answer 2

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

Explanation:

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.