You do 120 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 32.0â° with the vertical with your sister is at rest. what is your sister's mass, assuming negligible friction?

The work done to pull the sister back on the swing is equal to the increase in potential energy of the sister:
(1)

where m is the sister's mass, g is the gravitational acceleration and  is the increase in altitude of the sister with respect to its initial position.

By calling  the angle of the chain with respect to the vertical, the increase in altitude is given by
(2)
where L is the length of the chain.

Putting (2) inside (1), we find

from which we can find the mass of the sister: