Work done

Work done?

Textbooks often define energy as the "capacity to do work." Unfortunately this definition is not easy to understand or use. It seems to say that energy is something that can do work.

It is difficult to imagine, for example, how light can do work, unless we think of some sophisticated process. E.g. plant makes food using sunlight, cow eats plant, and cow ploughs the land. It also leaves open the question as to what is work. Is it writing an essay, washing the dishes, or lifting some bricks?

In fact, it is none of the above. In physics, work done W has a very specific meaning. It is a number, and is equal to force F times the distance d moved in the direction of the force. This definition can be written as a formula: W = Fd.

If the idea of energy is abstract, then so is the definition of work done.

Consider a book on a perfectly smooth table. I push the book with force F and it moves. After a distance d, it reaches a velocity v.

Then work done is Fd, and kinetic energy is mv²/2. Both formulae look like they are just made up somehow by physicists. Are they related? After years of thinking and measuring, physicists found that the are equal. If kinetic energy is the only form of energy involved (assuming no friction, no heat), then Fd = mv²/2.

This, perhaps, is the meaning of the definition that energy is the capacity to do work. The chemical energy in my hand is converted to kinetic energy of the book. This happens through the force from my hand moving the book. So work seems to be a medium through which energy is converted from one form to another: Energy does work, work produces energy.

The Physics Notes