A 15.0-m length of hose is wound around a reel, which is initially at rest. the moment of inertia of the reel is 0.570 kg·m2, and its radius is 0.170 m. when turning, friction at the axle exerts a torque of magnitude 3.50 n·m on the reel. if the hose is pulled so that the tension in it remains a constant 29.0 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.

Question

Physics

Kailyn Bolton

6 February, 00:45

A 15.0-m length of hose is wound around a reel, which is initially at rest. the moment of inertia of the reel is 0.570 kg·m2, and its radius is 0.170 m. when turning, friction at the axle exerts a torque of magnitude 3.50 n·m on the reel. if the hose is pulled so that the tension in it remains a constant 29.0 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.

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Doodles · Answer 1

Net torque τ = 25N*0.15m - 3.2N·m = 0.55 N·m

τ = Iα

0.55 N·m = 0.4kg·m² * α

α = 1.375 rad/s²

a = αr = 1.375rad/s² * 0.15m = 0.21 m/s²

s = ½at²

15 m = ½ * 0.21m/s² * t²

t = 12.1 s