A 22kg child on a 1.75m long swing is released from rest when the swing supports make an angle of 35 degrees with the vertical.

Question

1.What is the child's maximum potential energy?
2.Disregarding friction, find the child's theoretical speed at the lowest point.
3.If the actual speed of the child at the lowest point is 2.2m/s, how much mechanical energy is lost to friction?

I do not understand what to do.

Answer 1

height above bottom of swing = 1.75 *(1-cos 35)
= .316 meters up

so potential energy relative to bottom of swing
= m g h
= 22 (9.81)(.316) = 68.3 Joules

(1/2) m v^2 = 68.3
so
v^2 = 2 * 68.3 /22
v = 2.49 m/s

loss = 68.3 - (1/2)(22)(2.2)^2