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 37.0 N and a radius of 0.20 m, that rotates without function 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 4.90 m, at which point the end of the rope is moving at 6.25 m/s. If the rope does not slip on the cylinder, what is the value of P?

Explanation / Answer

m = mass of cylinder

weight of cylinder = W = mg = 37

m = 37/g = 37/9.8 = 3.8 kg

R = radius of cylinder = 0.20 m

I = moment of inertia of cylinder = MR2 = (3.8) (0.2)2 = 0.152 kgm2

P = force appied

d = distance moved = 4.90 m

v = speed of rope = 6.25 m/s

w = angular speed = v/R = 6.25/0.2 = 31.25 rad/s

using conservation of energy

work done by the force applied = rotational KE of the cylinder

P d = (0.5) I w2

P (4.90) = (0.5) (0.152) (31.25)2

P = 15.16 N

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