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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Ali

Physics

25 September, 21:42

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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Karlee Rangel · 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