A 350-N child is in a swing that is attached to a pair of ropes 1.90 m long.

Question

Find the gravitational potential energy of the child–Earth system relative to the child's lowest position at the following times.

(a) when the ropes are horizontal

(b) when the ropes make a 33.0° angle with the vertical

(c) when the child is at the bottom of the circular arc



Answer 1

W = mg = 350 N

R = 1.9 m

a) mgR = 350 * 1.9 = 665 J

b) mg*(R-Rcosθ) = mg(1-cosθ) = 350*(1-cos33) = 56.46 J

c) 0, reference point is measured from the bottom of the circular arc.