A350-n child is in a swing that is attached to a pair of ropes 2.10 m long. 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 j.(b) when the ropes make a 34.0° angle with the vertical j.(c) when the child is at the bottom of the circular arc j.

a)  U = 735 J , b) U = 125.7 J , c)   U = 0 J

Explanation:

The gravitational power energy is

      U = mg y - mg y₀

The last value is a constant, for simplicity we can make it zero, if the lowest point is at the origin of the coordinate system, which in this case we will place in the lowest part

a) Rope is horizontal

The height in this case is the same length of the rope

     y = 2.10 m

    w = mg = 350 N

    U = 350 2.10

    U = 735 J

b) when the angle is 34º

     y = L - L cos 34

    y = L (1- cos34)

    y = 2.10 (1- cos 34)

    y = 0.359 m

    U = 350 0.359

    U = 125.7 J

c) in this case this point coincides with the reference system

     y = 0

     U = 0 J