swinging a swing

[miriam_e]

A child sitting on a swing, legs too short to reach the ground is, to all intents and purposes, a closed system. Every action has an equal and opposite reaction. Forces in equal forces out. But if that's so, how does that kid manage to get the swing going?

On the surface of it, it doesn't look like it should be possible. Whether you lean back or forward your mass is still simply at the end of the pendulum that is the swing.

Yet we all intuitively know how to do it. You lean back then forward at the right times. At first the movements are tiny, but gradually you add to it, using the resonant frequency of the swing, and you can end up taking the swing to the absolute peak of its travel.

So how the hell do we do it?

Comments

[(Anonymous)]

:)
No, I mean closed in terms of movement. The kid is isolated from things they can push off from (her legs are too short to reach the ground). She can wiggle on the swing seat, but that should have no net effect because if she leans out backwards then her feet stretching out ahead balance it and center of gravity stays the same.

So how do they get the swing moving?

[zey.livejournal.com]

Kid leans backward to go forward. Kid leans forward as they're going in the backward direction.

They shift their centre of gravity to maximise movement in the forward direction and shift it to the opposite side to maximise movement when going in the backwards direction. There's probably a bit of momentum to the kid's movements too.

However, the premise to the question is false as the system's not closed. There's a child in it with glucose energy in their bloodstream which is burned to add kinetic energy. (It could only really be a closed system if the child were asleep or dead.)

[zey.livejournal.com]

You'll probably also notice the smart kids also exert some forwards and backwards pushing on the rope/chains too ;-). Really though, the best way to get a feel for it is to hop on a swing and try it.

[miriam-e.livejournal.com]

Darn. That was me, commenting earlier. I'm at my parents' and forgot to log in.

When I said a closed system I meant in regard to forces. Like a rocket in space. An astronaut can't move a spaceship by pushing on it. They have nothing external to push against.

When the kid leans back, their legs go out forward. The center of gravity remains in the same place. They are like the astronaut in the rocket. Pushing on the swing gets them nowhere.

Yet as we all know we can indeed get a swing swinging by moving around on it. What I'm trying to work out is how do we do it?

Hey! It just hit me! I think what the kid on the swing does is pump the swing's motion with gravity, because they are not a closed system after all. They are coupled with the Earth through gravity and the structure of the swing-supports standing on the planet.

It is easiest to understand if you imagine the kid standing on the swing seat (like some kids do).

All the kid needs is a slight asymmetry, then they can let themself be accelerated downward toward the Earth slightly off-center. Because of the curve of the swing's path this gives it a slight kick out from the vertical. Now the kid gently stands again as the swing moves back, and when it starts moving forward again they let themself fall downwards again, using the deceleration to push the swing forward again.

Each time this is done, the movement away from the vertical is greater so it becomes easier to add more energy to the swing from gravity.

I believe I've solved it. :)

Yay!