Energy Transfers, Conservation And Dissipation

Push a shopping trolley along a level floor and let go. It rolls, slows and stops. Something was clearly spent to get it moving, and a moment later that something has gone. Where? Not out of existence: the wheel bearings, the axle and a thin sheet of air along the floor are all a fraction of a degree warmer than they were, and if you added up every one of those warmings you would recover, to the last joule, exactly what the trolley had. Nothing was lost. It was scattered so thinly that no machine you could build would ever gather it back.

That is the whole of this lesson in one sentence, and it is one of the few ideas in physics that never has an exception. You will learn to treat any object or group of objects as a system and to say precisely when and where its energy moved, to separate the part of a transfer that does the job you wanted from the part that merely warms the room, and to name friction and air resistance as the two forces that carry the second part away. By the end you will be able to write any change out as an account in joules: so much supplied, so much arriving where you wanted it, so much dissipated, and the three numbers balancing every single time.