# If work is zero, when is force nonzero?

##### 2 Answers

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. *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

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

#### Answer:

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.

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.