Question

A bucket of water of mass 16.0 kg is suspended by a rope wrapped around a windlass, that is a solid cylinder with diameter 0.320 m with mass 13.0 kg . The cylinder pivots on a frictionless axle through its center. The bucket is released from rest at the top of a well and falls a distance 10.6 m to the water. You can ignore the weight of the rope.

What is the tension in the rope while the bucket is falling?

Take the free fall acceleration to be g = 9.80 m/s2 .

With what speed does the bucket strike the water?

Take the free fall acceleration to be g = 9.80 m/s2 .

What is the time of fall?

Take the free fall acceleration to be g = 9.80 m/s2 .

While the bucket is falling, what is the force exerted on the cylinder by the axle?

Take the free fall acceleration to be g = 9.80 m/s2 .

Answer 1

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SOLUTION:

Free body diagram (FBD):

Given data:

Mass of bucket,

Mass of windlass,

Radius of windlass,

Acceleration due to gravity,

Let T be the tension on the rope and a be the acceleration of the bucket.

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PART (a):

From FBD, we have:

Also, Torque on the windlass (cylinder) is given by:

From (2), we have, Tension on the rope:

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PART (b):

We have, Acceleration of the bucket,

Distance traveled,

Initial speed,

Therefore, Final speed is given by:

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PART (c):

Time required is given by:

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PART (d):

From FBD, force on the axle is given by:

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