# Work = mad. Physics says so. Maths proves so.

Work = mad” may not be news to you. But did you know it is a physical fact and provable using Maths? It all started with a discussion about moments, torque, force, work, energy, power etc. We need to briefly talk about Force, and then Work.

## Force

Sir Isaac Newton is probably the greatest scientist ever. I once stood in the same room as Newton, unfortunately I was 350 years late. One of the many contributions Newton made to Physics was in the ‘field of mechanics’ (disambiguation: not a pasture of grease-monkeys, rather the area of physics concerned with the study of bodies in motion).

Newton gave us 3 Laws of Motion, and Newtons 2nd Law of Motion states “When a resultant external force acts on a body, the rate of change of velocity is proportional to and takes place in the direction of that force“. In other words, when we apply a force, F, to an object/mass, m, the object/mass will accelerate, a, (rate of change of velocity) proportionately to the size of the applied force. Newtons 2nd Law of Motion is symbolized as:

$$Force = mass \times acceleration$$

$$F = ma$$ Equation (1)

## Work

We can thank Gustave-Gaspard Coriolis for the notion of ‘Work’ in mechanics. ‘Work’ refers the distance (displacement) over which a Force is applied, and can be symbolized as:

$$Work = Force \times distance$$

$$Work = Fd$$ Equation (2)

## Finally

If we now substitute Equation (1) into Equation (2), by substituting ‘ma’ for F, we can see that

$$Work = mad$$

Q.E.D.

Note: The above derivation takes a simple non-relativistic case of a Force operating on a mass in a straight line.