A 15.5-m length of hose is wound around a reel, which is initially at rest. The moment of inertia of the reel is 0.42 kg · m2, and its radius is 0.170 m. When the reel is turning, friction at the axle exerts a torque of magnitude 3.63 N · m on the reel. If the hose is pulled so that the tension in it remains a constant 23.1 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.

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  1. The applied torque minus the frictional torque is (23.1)(0.170)-3.63 = 0.28 N-m

    Torque divided by moment of inertia is the angular acceleration, alpha. Its units are radians/s^2. Calculate it

    To unreel all of the hose, you need to turn the reel through 15.5/0.17 = 91.1 radians.

    Solve this equation for the required time, t:

    91.1 radians = (1/2)*(alpha)*t^2

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