Mathematics of Movement

Work

In physics, Work is not a place we go to get a paycheck. It is something we do all the time, whether we are at our employment, making a meal, sleeping, etc. Mathematically, Work is defined as

Work = Force × Displacement

W=FD

Work is measured in joules (J), which is the amount of work performed when 1 Newton (N) of Force changes an object’s position by one meter.

Force

Force is additionally defined as

Force = mass × acceleration

F = ma

, where mass is measured in kilograms and acceleration is measured in meters / second.

Displacement

Displacement requires that any object that is displaced be moved from its original location to another location. Think of picking up a stone, walking across a field, and putting it down. The calculated Work is the mass of the stone multiplied by the length of the field – mass (m) multiplied by Displacement (D).

This means that in theory, weight training involves no Work, because we pick up the weight and put it down again, theoretically in the same spot. While it’s the subject of a funny Planet Fitness ad, Displacement needs to be thought of in weight training as the number of cycles of movement, or the number of repetitions, per set of a given exercise.

More Information on the Mathematics of Movement

Force as a Component of Work