Question

A 12.2 m length of hose is wound around a reel, which is initially at rest. the moment of inertia of the reel is 0.5 kg m2, and its radius is 0.19 m. when the reel is turning, friction at the axle exerts a torque of magnitude 3.36 n m on the reel. if the hose is pulled so that the tension in it remains a constant 27.9 n, how long does it take to completely unwind the hose from the reel? neglect the mass and thickness of the hose on the reel, and assume that the hose unwinds without slipping.

Answer 1

To find the time it takes to completely unwind the hose from the reel, you need to calculate the angular acceleration of the reel using the torque exerted on it. The time can then be determined using the equation for angular acceleration. However, without knowing the final angular velocity, the exact time cannot be determined.

Step-by-step explanation:

To find the time it takes to completely unwind the hose from the reel, we need to first calculate the angular acceleration of the reel using the torque exerted on it. The torque can be calculated using the equation:

Torque = Moment of inertia * Angular acceleration

Plugging in the given values, we have:

3.36 N m = 0.5 kg m^2 * Angular acceleration

Solving for the angular acceleration, we find:

Angular acceleration = 3.36 N m / 0.5 kg m^2 = 6.72 rad/s^2

Next, we can use the equation for angular acceleration to find the time it takes to completely unwind the hose:

Angular acceleration = (Final angular velocity - Initial angular velocity) / Time

Since the reel is initially at rest, the initial angular velocity is 0. Plugging in the given values, we have:

6.72 rad/s^2 = (0 - Final angular velocity) / Time

Solving for the time, we find:

Time = (0 - Final angular velocity) / 6.72 rad/s^2

The tension in the hose remains constant throughout, so we can set the tension equal to the moment of inertia times the angular acceleration:

Tension = Moment of inertia * Angular acceleration

27.9 N = 0.5 kg m^2 * Angular acceleration

27.9 N = 0.5 kg m^2 * 6.72 rad/s^2

Solving for the angular acceleration, we find:

Angular acceleration = 27.9 N / (0.5 kg m^2) = 55.8 rad/s^2

Now we can use the equation for angular acceleration to find the time it takes to completely unwind the hose:

55.8 rad/s^2 = (0 - Final angular velocity) / Time

Since the reel is initially at rest, the initial angular velocity is 0. Plugging in the given values, we have:

55.8 rad/s^2 = (0 - Final angular velocity) / Time

Solving for the time, we find:

Time = (0 - Final angular velocity) / 55.8 rad/s^2

So, the time it takes to completely unwind the hose from the reel depends on the final angular velocity. Without knowing the final angular velocity, we cannot determine the exact time.