A 40.0 kg child is in a swing that is attached to ropes 2.00 m long. Find the gravitational potential energy associated with the child relative to the child’s lowest position under the following conditions:

a. when the ropes are horizontal
b. when the ropes make a 30.0° angle with the vertical
c. at the bottom of the circular arc

A. As the ropes are horizontal the child has travelled 2m of vertical displacement from his lowest position.

Gpe @ A=mgh=40*9.81*2=784.8J

B. At 30degree vertical angle the vertical displacement from lowest position is given by

2-2cos(30)=2-1.73=0.27m

Gpe @B= 40*9.81*0.27=106 J

C: at the bottom of circular arc it's Gpe is zero relative to lowest position as bottom of arc itself is lowest position.