A puck of mass m = 54.0 g is attached to a taut cord passing through a small hol

Question

A puck of mass m = 54.0 g is attached to a taut cord passing through a small hole in a frictionless, horizontal surface (see figure below). The puck is initially orbiting with speed vi = 1.60 m/s in a circle of radius ri = 0.310 m. The cord is then slowly pulled from below, decreasing the radius of the circle to r = 0.130 m.

(a) What is the puck's speed at the smaller radius?
m/s

(b) Find the tension in the cord at the smaller radius.
N

(c) How much work is done by the hand in pulling the cord so that the radius of the puck's motion changes from 0.310 m to 0.130 m?
J

Explanation / Answer

a) Angular momentum of the puck is conserved since no external torque is present.

mv1r1 = mv2r2

=> 1.60 * 0.310 = 0.130v2

=> v2 = 3.82 m/s

b) T2 = mv22/r2 = 0.054 * 3.822 / 0.130 = 6.06 N

c) Work done, W = KE = m(v22 - v12)/2 = 0.054 * (3.822 - 1.602) / 2 = 0.325 J

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