I've read about how by tilting one's body one changes one's center of mass while swinging on a playground swing, and thereby increases the energy of the swing.

But I would like to get a better sense of why one can get into a swing of ~1.5 meters above the ground on the back and front peaks of the swing (elevating an adult body weight that height each time), and do that repeatedly for, say, 10 minutes, and yet not at all feel fatigued--whereas if you were trying to jump up from the ground to that height you would be fatigued after just a few jumps.

I get the sense that the answer is related to the idea that you are "loading" the swing gradually with potential energy on each swing, and that each iteration of that requires only a little effort, but I'm still sort of surprised at how much sustained energy you can generate with so little feeling of exertion (it feels like one can keep swinging high with little effort for an hour, easily), and I thought there might be some subtleties to this that I don't understand.


Consider an idealized setting where there is essentially no friction or air resistance. Suppose someone gave you a quick push while you are on the swing. You will keep on swinging without having to expend any energy yourself. A rock sitting on the swing would behave in exactly the same way; it wouldn't have to "pump" to keep this idealized swing going up & down and back & forth once it was already moving. (As for how this phenomenon can occur, gravitational potential energy and conservation of mechanical energy would be a good starting search terms.)

Now, starting from rest at the bottom of this idealized swing, you would indeed need to do a bit of pumping to get started on your own. But you would only need to exert an amount of energy equal to your maximum change in potential energy desired (i.e., roughly $mgh$), and you would only need to exert this amount of energy once (well, a little at a time until you reach your desired height, but you wouldn't have to keep exerting this amount of energy each period).

Okay, the actual real wold. There are dissipative forces at play (air resistance, friction). Once you are already moving at your desired height/amplitude, the pumping that you do is only to counteract these dissipative forces. For, without these pesky forces, you wouldn't need to pump at all.

So, you aren't pumping/expending energy to make the swing up/down or back/forth, but rather to overcome the work done by dissipative forces.


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