The intuitive but wrong answer is that exercise converts your mass into energy. It's easy to see why this sounds right. To exercise you need energy, and powering that is the mass you take in by eating. For many of us, we thereby hope to lose weight.
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Of course, we need food to provide energy, but the problem is that this confuses the mechanism by which we extract energy from food.
In nature, there are a few ways of storing and converting energy, and we'll start out with the ones which don't apply: it's not mechanical energy.
If it were, we'd be like grandfather's clock, using a device such as a coil spring. Every so often, somebody would have to wind us up before we stop.
We do use mechanical energy, but only for a brief moment, such as when sprinting up stairs, our calf muscles store and release tension, helping us - literally - to bound up the next step.
In any event, no mass is lost during this process, so it doesn't answer the question.
Next, we could convert mass into energy as was suggested.
The problem with this is we're invoking Einstein's famous equation, triggering the stupendous energies of nuclear reactions.
When we do this inside a nuclear reactor, we're annihilating matter, generating energy according to Einstein's famous equation, E=mc2. Since c is the speed of light, that's a very big number.
If you were to tuck into a quarter-pounder, you'd generate the energy equivalent of 2.4359 megatons of TNT. That would be a quick sprint up the stairs.
The correct answer is that the energy that powers us is derived from chemical reactions. There are no nuclear reactions, and there is no conversion of matter into energy.
In simplistic terms, we burn sugars. We harness the energy generated by converting them from higher to lower energy states. We capture the energy from this to grow tissue and twitch muscles.
Exercise requires energy, which your body preferentially acquires from fat. If you lose weight, it will be from the breakdown products, which you then excrete.
The problem is, if your only goal is to lose weight, your body responds to additional exercise by building more muscle. You'll be fitter and stronger, but you might end up weighing much the same.
There are, of course, many other benefits to exercising beyond body weight, such as building muscle and improving your metabolism.
Ultimately it's the whole package that counts, and where we put that last slice of cake.
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