A puck of mass m = 47.0 g is attached to a taut cord passing through a small hol

Question

A puck of mass m = 47.0 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 = 1.30 m/s in a circle of radius ri = 0.320 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 0.320 m to 0.130 m?

_____J

Explanation / Answer

a)

Angular momentum is conserved:
V1*r1 = V2*r2

From here we get V2

= V1[r1/r2]

= 1.30[0.320/0.130]

= 3.2 m/s

b) T = m*a

= m*V2^2/r2

= 0.047 * 3.2^2/.130 = 3.702 N

c) W = dKE = 0.5m*(V2^2 - V1^2) = 0.2009 J

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