The Mathematics of Work
1 A weight lifter goes into a training room where there are two barbells. One is a 150 N barbell and the other is 200 N. The SI unit for force is the newton, N. This means that it should take 150 N of vertical force to lift one of the barbells and 200 N to lift the other. The weight lifter lifts up one, places it down, and then lifts the other. Which lift caused the lifter to do more work?
2 It might seem logical to say the heavier weight caused more work to be done because more force would be needed to lift it. But from a scientific point of view, you do not have enough information to answer the question. Until you know how far each barbell was lifted, you really don’t know how much work has been done. To figure this out mathematically, you multiply the force used (F) by the distance (d) the force caused the object to travel. It is important to remember that the distance traveled must be in the same direction as the force applied.
3 Force is expressed in newtons, and distance in the metric system is expressed in meters, so it makes sense that one way to describe units of work would be in newton-meters. Another name for these units is the joule (J). If the weight lifter in our last example lifted both barbells, a distance of 2 m, these would be the calculations that expressed the amount of work being done:
4 As expected, more work took place lifting the 200 N barbell, when both barbells were lifted the same distance. So increasing the amount of force applied increases the amount of work done. Don’t forget about distance, though. Increasing the distance the object moves should also increase the work done.