A puck of mass m54.0 g is attached to a taut cord passing through a small hole i

Question

A puck of mass m54.0 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 = 1.20 m/s in a circle of radius= 0.290 m. The cord is then slowly pulled from below, decreasing the radius of the circle to r = 0.150 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 (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 0.150 m?

Explanation / Answer

here,

mass ,m = 0.054 kg

initial speed , v0 = 1.2 m/s

radius ,r0 = 0.29 m

a)

r = 0.15 m

let the final speed be v

using conervation of angular momentum

m * v0 * r0 = m * v * r

1.2 * 0.29 = 0.15 * v

v = 2.32 m/s

b)

the tension in the cord at the smaller radius , T = m * v^2 /r

T = 0.054 * 2.32^2 /0.15 N

T = 1.94 N

c)

the work done , W = change in kinetic energy of puck

W = 0.5 * m * ( v^2 - u^2)

W = 0.5 * 0.054 * ( 2.32^2 - 1.2^2) J

W = 0.11 J

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