A puck of mass m = 53.0 g is attached to a taut cord passing through a small hol

Question

A puck of mass m = 53.0 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 )

using conservation of angular momentum

vi ri = v r

v = vi ( ri / r )

v = 1.4 ( 0.31 / 0.14 )

v = 3.1 m/s

b )

T = m g or T = m a

T = m v2 / r

T = 0.05 X 3.12 / 0.14

T = 3.43 N

c )

W = dKE

= 0.5 m ( v2 - vi2 )

= 0.5 X 0.05 X ( 3.12 - 1.42 )

W = 0.191 J

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