Question

A 60 kg woman prepares to swing out over a pond on a rope. What tension in the top is required if she is to maintain a circular arc A). When she starts her swing by stepping off the platform, B). When she is 5.0 m above the surface of the pond, and C0. at the lowest point of her swing?

Answer 1

I think you have missed to attach the diagram with this question.

So, I am assuming the variables and you please substitute the values as given in your text book.

Length of the rope = 10 m

Initial height of the swimmer from the ground = 12 m

(a) Initially the woman is at 90 degrees from horizontal,

So, there will be no tension.

(b) Vertical height dropped = (12 - 5) = 7 metres.
KE after 7 metres drop = (60 x g x 7m) = 4116 Joules.
V after 7m. drop = sqrt.(2KE/m) = sqrt.( 8232/60) = 11.7 m/sec.
Centripetal acceleration = (v^2/r) = (11.7^2/10m) = 13.69 m/sec^2.
Tension = (ma) = 60 x 13.69 = 821.4 N

(c) KE at bottom of swing = (60 x g x 10m) = 5880 Joules.
V at bottom = sqrt.(2KE/m) = 14 m/sec.
Centripetal acceleration = v^2/r = 19.6 m/sec^2.
Tension = (ma) = 60 x 19.6 = 1176 N