A light, flexible, non-stretching cable is wrapped several time around a winch drum, a solid cylinder of mass 50 kg and diameter 0.120 m, which rotates about a stationary horizontal axis held by frictionless bearing. The free end of the cable is pulled with a constant 9.0-N force for a distance 2.0 m. It unwinds without slipping and turns the cylinder. If the cylinder is initially at rest, find its angular speed and the final speed of the cable.

Question

Daniella Larson

Physics

9 December, 04:44

A light, flexible, non-stretching cable is wrapped several time around a winch drum, a solid cylinder of mass 50 kg and diameter 0.120 m, which rotates about a stationary horizontal axis held by frictionless bearing. The free end of the cable is pulled with a constant 9.0-N force for a distance 2.0 m. It unwinds without slipping and turns the cylinder. If the cylinder is initially at rest, find its angular speed and the final speed of the cable.

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Answers (1)

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Braydon Coffey · Answer 1

Final speed = 0.85m/s

Angular speed = 14.17rad/s

Explanation:

Force (F) = 9N, mass (m) = 50kg, diameter (d) = 0.120m, radius (r) = d/2 = 0.120/2 = 0.06m, distance (s) = 2m

F = ma

acceleration (a) = F/m = 9/50 = 0.18m/s^2

From the equations of motion,

v^2 = u^2 + 2as (u is initial velocity = 0m/s)

v^2 = 0 + 2*0.18*2 = 0.72

v = √0.72 = 0.85m/s

Final speed (v) = 0.85m/s

Angular speed (w) = v/r = 0.85/0.06 = 14.17rad/s