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A puck of mass 71 g is attached to a cord passing through a small hole in a fric

ID: 1700207 • Letter: A

Question

A puck of mass 71 g is attached to a cord passing through a small hole in a frictionless, horizontal surface. The puck is initially orbiting with speed 1.6 m/s in a circle of radius 0.7 m. The cord is then slowly pulled from below, decreasing the radius of the circle to 0.2 m.
What is the speed of the puck when the radius is .2 m?
Find the tension in the cord at the smaller radius.
How much work is done by the hand in pulling the cord so that the radius of the puck's motion changes from 0.7 to 0.2?

Explanation / Answer

The mass of the puck is m = 71 g
The initial radius Ri = 0.7 m
Initial speed vi = 1.6 m/s
The final radius Rf = 0.2 m

According to conservation of angular momentum

Iiwi = Ifwf

Ii is the initial moment of inrertia = mRi^2
If is the final moment of inrertia = mRf^2
wi is the initial angular speed = vi/Ri
wf is the final angular speed = vf/Rf

mRi^2 * vi/Ri = mRf^2 *vf/Rf
viRi = vfRf
vf = viRi/Rf
vf = 1.6*0.7/0.2
vf = 5.6 m/s

The tension in the string will be equal to the centripetal force acting inwards when the puck is rotating in a smaller circle

T = Fc = mvf^2/Rf

T = 0.071*5.6^2 / 0.2

T = 11.1328 N

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