# Simple gravitational potential energy

1. Mar 30, 2016

### sireh

1. The problem statement, all variables and given/known data
A 400-N child is in a swing that is attached to a pair of ropes 2.00 m long. Find the gravitational potential energy of the child-Earth system relative to the child’s lowest position when

(b) the ropes make a 30.0° angle with the vertical

2. Relevant equations
Ug=mgy

3. The attempt at a solution
b.) Ug = 400N ⋅ 2m(1-cos30)
Ug = 107J

I understand everything about the problem (and was able to do the other parts of it without issue) except where the 1-cos30 comes from. Even drawing it out I just can't visualize where that is coming from. I originally thought that it would just be 2m(cos30) but the answer key says that is wrong.

2. Mar 30, 2016

### drvrm

i think the potential energy change is initial state when it was at the lowest point and then it was raised to an angle 30 degree- so the the child was raised to certain height and that height matters for P.E. calculation -i.e. your y... so making some triangle with original position and raised position calculate y -the amount of vertical distance raised to be multiplied to the load raised....

3. Mar 30, 2016

### jbriggs444

How much higher is the 30 degree point than the bottom point?

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