Energy Transfers, Conservation And Dissipation Of Energy

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 say precisely when and where its energy moved, to follow a pendulum bob trading height for speed and back again, to separate the part of a transfer that does the job you wanted from the part that merely warms the room, and to turn that split into a number using efficiency. By the end you will be able to draw the accounting out as a Sankey diagram, where the width of every arrow is the size of a transfer and the widths coming out must always add up to the width going in.