Part A A child of mass plays on a swing having support ropes

Part A A child of mass plays on a swing having support ropes of length L. A friend pulls her back until the ropes are from the vertical and releases her from rest. What is the expression for the potential energy for the child just as she is released, compared with the potential energy at the bottom of the swing? Submit My Answers Give Up Part B What is the expression for how fast will she be moving at the bottom of the swing? u= Submit My Answers Give Up Part C How much work does the tension in the ropes do as the child swings from the initial position to the bottom? Submit My Answers Give Up

Solution

A)The height that the child goes up while swinging is:

h = L[1 - cos(theta)]

So the potential energy is:

U = m g h

U = m g L[1 - cos(theta)]

b)from the conserbation of energy

KE = PE

1/2 m v^2 = m g L[1 - cos(theta)]

v = sqrt [2 g L (1 - cos(theta))]

c)No work is done by the tension in the rope.

W = 0 J