A 14.0-m length of hose is wound around a reel, which is initially at rest. The

Question

A 14.0-m length of hose is wound around a reel, which is initially at rest. The moment of inertia of the reel is 0.590 kg

A 14.0-m length of hose is wound around a reel, which is initially at rest. The moment of inertia of the reel is 0.590 kgA?m2, and its radius is 0.170 m. When turning, friction at the axle exerts a torque of magnitude 3.00 NA?m on the reel. If the hose is pulled so that the tension in it remains a constant 24.0 N, how long does it take to completely unwind the hose from the reel? Neglect the mass of the hose, and assume that the hose unwinds without slipping.

Explanation / Answer

Radius = 0.170, for rotation of one turn, 2 pi radians cable length will be 2 pi r = 1.068 m
for 14 m , it must rotate by ( 14 / 1.1068 ) x 2 pi = 82.353 radians. (Total angle of rotation)

Torque = moment of inertia x angular acceleration
3.0 = 0.590 x angular acceleration
angular acceleration = 5.0847 rad/ sec^2

Total angle of rotation= initial angular velocity x time + 0.5 x angular acceleration x time^2
82.353 = 0 + 0.5 x 5.0847 x t^2
t^2 = 32.39
t = 5.6914 seconds

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