When is work done by a zero force?

Answer 1

Work, in physics, is defined as the dot product of a Force times displacement. The dot product just means that Work is not a vector quantity.

Vectors have magnitude and direction. Work has only magnitude, like energy, and no defined direction. In physics, quantities with no direction are called scalar quantities.

Here is the equation for Work:

w = F * d

or, work equals Force dot (times) Displacement.

If I push hard on a large building with all the Force I can muster, let us say 100 pounds of force, and if the building refuses to move (the building has not been displaced), then the work done is zero.

We can see from the equation above, and the example, that if the object we apply a force to does not move, then it is just some quantity times zero.

So despite how hard one has tried to move an object with all the force that can be mustered, if the object does not move as a result, no work has been done. It does not matter how tired I am from pushing hard.

Physically speaking, no work got done.

Answer 2

Work is define by : W = ⌠F∙dS

where F is the force that does the work.

dS is the displacement differential of a border by force F.

F and S are vectors and F∙dS is a scalar product of both vectors.

With zero force you get zero work.

Answer 3

Work is done by a force only when there is a displacement along the direction of the force. If the force is zero, then no work is done, regardless of the displacement.