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 = 1.40 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 = 0.140 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 0.140 m?
____ J

Explanation / Answer

a) Angular momentum is conserved:
vi*ri = v*r v = vi[ri/r] =1.40[.310/.140] = 3.1 m/s

b) T = m*a = m*v²/r = .047*3.1²/.140 = 3.226 N

c) W = dKE = ½m*(v² - vi²) = 0.179 J

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