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 2.74 m/s2.

(a) How much work has been done on the spool when it reaches an angular speed of 6.55 rad/s? _______J

(b) How long does it take the spool to reach this angular speed? ________ s

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

Answer 1

a) How much work has been done on the spool when it reaches an angular velocity of

6.55 rad/s?

Since

Wnet = ∆K = 1/2Iω^2 − , and

I = 1/2 MR^2 , = 0.125

Wnet = 1/2Iω^2

Wnet = 1/2*0.125*(6.55)

Wnet = 2.681 J

b) How long does it take the spool to reach this angular speed?

Since t =ω/ α and α = atan R ,

t = ωR/atan

t = 6.55*(0.500)/2.74

t = 1.19s

c) How much cord is left on the spool?

The length of cord pulled off is

L = R∆θ = R=1/2αt^2

= 1/2*2.74*1.19^2 = 1.94m

so 2.06 m remains on the spool