Defining the work of a force

What is the work of a force?

In physics, the work of a force measures the energy transferred by that force when its point of application moves. Unlike everyday language, "working" is not enough to produce work in the physical sense: there must be a displacement.

The general formula

For a constant force F applied to an object that moves a distance d, with an angle alpha between the direction of the force and that of the displacement:

W = F * d * cos(alpha)

• W: work, expressed in joules (J)
• F: magnitude of the force, in newtons (N)
• d: distance traveled, in meters (m)
• alpha: angle between the force and the displacement

Concrete example

A mover pushes a box with a force of 40 N, in the same direction as the displacement (alpha = 0 degrees), over a distance of 3 m.

W = 40 * 3 * cos(0) = 40 * 3 * 1 = 120 J

Classic pitfall

Careful: if the force is perpendicular to the displacement (alpha = 90 degrees), the work is zero, even if the force is intense! This is the case of a person carrying a bag at arm's length while walking on flat ground: the weight does no work because it is vertical while the displacement is horizontal.