A light, flexible rope is wrapped several times around a hollow cylinder, with a

Question

A light, flexible rope is wrapped several times around a hollow cylinder, with a weight of 41.0 N and a radius of 0.29 m, that rotates without friction about a fixed horizontal axis. The cylinder is attached to the axle by spokes of a negligible moment of inertia. The cylinder is initially at rest. The free end of the rope is pulled with a constant force P for a distance of 4.60 m, at which point the end of the rope is moving at 5.70 m/s. If the rope does not slip on the cylinder, what is the value of P?

Explanation / Answer

0 + 0 + P L = ( 1/2 ) I w2 + 0
The moment of Inertia of a hollow cyclinder I =MR2
Thus, the force P =(1/2 ) MR2w2 / L
But,the mass M = W/g and v = Rw
Thus, P = ( 1/2) Wv2 /gL
substituting the given values we get

= 41*5.7^2/(2*9.8*4.6)

=14.7747338065661

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