A puck of mass m = 51.0 g is attached to a taut cord passing through a small hol

Question

A puck of mass m = 51.0 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 = 0.290 m. The cord is then slowly pulled from below, decreasing the radius of the circle to r = 0.120 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 0.290 m to 0.120 m?

_______ J

Explanation / Answer

a)

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

V2 = V1[r1 / r2]

V2 = 1.6 * ( 0.29 / 0.12)

V2= 3.867 m/s

b)

T = m * a = m * V2^2 / r2

T = 0.051 * 3.867² / 0.12 = 6.35 N

c)

W = dKE = 0.5 * m * (V2² - V1²)

W = 0.5 * 0.051 * ( 3.867^2 - 1.6^2)

W = 0.316 J

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