# Gravitational Potential Energy of a swing

1. Sep 28, 2006

### bearhug

A 395 N child is in a swing that is attached to ropes 1.8 m long. Find the gravitational potential energy of the child+Earth system relative to the child's lowest position when the ropes make a 30° angle with the vertical.

What I did with this problem is I drew a diagram and then figured that y would be 1.8cos30

U=mgy
U=395(1.8cos30)= 6.16e2 J

Is there anything that I did wrong with this problem it's confusing me with the angle. I feel like there's more to do than this but I'm not sure what.

Thanks for any help

2. Sep 28, 2006

### Noein

The 'y' in the formula is the vertical displacement measured from the lowest point on the swing.

3. Sep 28, 2006

### bearhug

That doesn't really help.

4. Sep 28, 2006

### Noein

Draw the swing with the child just sitting there. Then draw the swing when it's pulled back 30o. The 'y' is how high the child has moved vertically.

5. Sep 28, 2006

### Rozenwyn

The gravitational potential you calculated just now is at a height of $$1.8\cos{30}$$m from the ground. However the guy is hanging down from a swing that's 1.8m long.

6. Sep 28, 2006

### bearhug

So it's the difference. Thanks for clarifying.