Potential energy part 2.?

Question

A 400-N child is in a swing that is attached to ropes 2m long. Find the gravitational potential energy of the child-Earth system relative to the child's lowest position when a) the ropes are horizontal, b) the ropes make a 30 deg angle with the vertical, c) and the child is at the bottom of the circular arc.

So part (a) would give me 800J. I use the U=mgh equation to find gravitational potential energy. So would part (b) look anything like this?

b) U = 400(cos20)*2?

and part c like this?

c) U = 400(0) ?

i'm not understanding this...please help.

Answer 1

a) your answer is of course correct.

b)the vertical height of the child from his lowest point will be (2-2cos30) or 0.26m. Thus his potential energy will be 400*0.26=104J.

c)the bottom of the circular arc is the reference point. The child is at that point. therefore his h=0, and his potential energy is 0.

I agree with the previous answerer. Pls draw a simple diagram showing the point where the child is in a),b),and c). That way it will be easier for you to visualize how to apply the basic formula for potential energy of PE=Weight*height

Answer 2

Draw a picture!
Taking zero as the point where the ropes are vertical, how much higher is the swing when the ropes are at 30°?

The answer is 2m * [cos(0) - cos(30°)] but I can't show you the picture - you have to draw that for yourself, then just work out the angles.

In general the height will be 2m * [1 - cos(angle)].