# Shifting Centre of Mass Puzzle?

1. Jul 26, 2009

### PeterPumpkin

1. The problem statement, all variables and given/known data

A child crouches on a swing. She is held AT REST, at 30 degrees to the vertical. The distance from her centre of mass (CM) while crouching to the suspension point is 3 m. The swing is released. When she reaches the lowest point, she SUDDENLY stands up. Her CM is now 2.6m from the suspension point.

What happens? (Assume the child is a single point mass.)

2. Relevant equations
Equations PE= KE ie mgh = 1/2 m v (squared) = 1/2 I omega (squared)

3. The attempt at a solution

Effectively the CM travels from A to B to C.

Considering the crouching part (A to B). mgh = 1/2 m v (squared).

Now she SUDDENLY stands up: Since, 3*cos 30 = 2.6 the CM when she is standing is the same height as the CM when she started at A. Therefore ALL the KE when is crouching at B is converted totally to PE.

CONCLUSION: She should stop when she stands up.

According to the answer she should swing a further 37.4 degrees. Where is the fallacy in my argument?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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2. Jul 26, 2009

### RoyalCat

You were wrong to assume that the kinetic energy from her swinging was what went into lifting her center of mass.
When she stood up, in what direction did she stand up? Did she counter-act the velocity at all?
Assume none of the kinetic energy got converted when she stood up, and you should see what happens.

What happened to the child's moment of inertia once she stood up? If we assume kinetic energy is preserved, what other quantity can we deduce is preserved that will help us solve the problem?

This is a pretty cool question. I may not be much of a child anymore, but that doesn't mean I don't like playing on the swings every now and then. It's pretty awesome to see how real-world experience ties in with the stuff you learn on paper.

3. Jul 26, 2009

### Staff: Mentor

No, she does work when she pushes herself up, adding energy to the system. (Non-conservative forces are at work.)

4. Jul 26, 2009

### PeterPumpkin

I'd assumed they were internal forces.