The work formula
The table on the previous page can now be replaced by a single line. Work done is the product of the force and the displacement it produces.
Work done by a force
work = force × displacement in the direction of the force
The displacement is measured along the line of the force, not along whatever path the object happened to take.
Why the direction matters
The formula does not say "distance moved" — it says displacement in the direction of the force. Those are the same number only when the object moves along the line the force acts in, which is the case in every problem in this chapter.
Only the displacement along the force counts
If an object is pushed horizontally while it also drifts sideways, only the part of the movement that lies along the push goes into the formula. Movement at right angles to a force takes no work from it at all.
The unit falls out of the formula
Force is measured in newtons and displacement in metres, so the product of the two is a newton metre. That is exactly what the previous page called a joule.
N m = J
One newton metre is one joule — the same unit under two names.
Work is force times displacement
Write it as work = force × displacement, and take the displacement along the direction of the force. The answer is in joules whenever the force is in newtons and the displacement in metres.