Question

You do 174 J of work while pulling your sister back on a swing, whose chain is 5.10 m long. You start with the swing hanging vertically and pull it until the chain makes an angle of 32.0° with the vertical with your sister is at rest. What is your sister's mass, assuming negligible friction?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of your sister = M

Length of the chain = L = 5.1 m

Angle the chain makes with the vertical when you pull the swing = = 32^o

Change in height of your sister = H

From the figure,

L = H + LCos

H = L(1 - Cos)

Work done by you = W = 174 J

Work done by you is equal to the potential energy gained by your sister,

W = MgH

W = MgL(1 - Cos)

174 = M(9.81)(5.1)(1 - Cos(32))

M = 22.89 kg

Mass of your sister = 22.89 kg