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A 4.00-m length of light nylon cord is wound around a uniform cylindrical spool

ID: 1444594 • Letter: A

Question

A 4.00-m length of light nylon cord is wound around a uniform cylindrical spool of radius 0.500 m and mass 1.00 kg. The spool is mounted on a frictionless axle and is initially at rest. The cord is pulled from the spool with a constant acceleration of magnitude 2.66 m/s2.

(a) How much work has been done on the spool when it reaches an angular speed of 7.30 rad/s?
  
(b) How long does it take the spool to reach this angular speed?

(c) How much cord is left on the spool when it reaches this angular speed?

Explanation / Answer

a) Work Done on the spool = I ^2


where I is moment of inertia = = MR^2/2

I = 0.5 * 1 * 0.5 * 0.5

I = 0.125 kgm^2

Work done W = I * angular velocity

Work = 0.5 * 0.125* 7.3* 7.3

W = 3.33 Joules

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b) angular accleration = a/R

Alpha = 2.66/0.5

Alpha = 5.32 rad/s^2

time t= / = 7.3/5.32

t = 1.372 sec

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c) angular displacemnt = 0.5 *A * t^2

theta = 0.5 * 5.32 * 1.372 * 1.372

theta = 5 radians

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