Question

2) 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?

I really need explanation in how to get this one, with drawings it'd be way better, thank you!!

A) 22.9 kg
B) 19.5 kg
C) 26.3 kg
D) 28.4 kg
Answer: A


I don't know how to get to the answer

Answer 1

The work done is the change in energy. So, when the person on the swing is raised, there is an increase in potential energy equal to the amount of work done.
Then Ep = mgh. All you need to know now, is h, the height the vertical height the person on the swing was raised from the rest position. (The equation editor isn't working properly today, so bear with me here.)
You know the angle made from the vertical and the length of the chain. So x = 5.10 cos(32). That gives you a value of 4.33. Subtract that from the length of the chain to get the height, h.

Now you know Ep, h and g, so use Ep = mgh to find mass.

Answer 2

I didn't quite get why we use 5.10 cos(32) and substract it, let me see if the drawing tool works.

Answer 3

I do get how to use the equations, but I can't picture it on the drawing, could you help me with it?