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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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princessesther2011

Answer:

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

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