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:
where m is the sister's mass, g is the gravitational acceleration and
By calling
where L is the length of the chain.
Putting (2) inside (1), we find
from which we can find the mass of the sister: