Calculating the Physics of a Windlass System

[Dep87]

I don't know how to do this.

A bucket of water of mass m_1 is suspended by a rope wrapped around a windlass, that is a solid cylinder with diameter d with mass m_2. 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 h to the water. You can ignore the weight of the rope.

1. What is the tension in the rope while the bucket is falling?
Take the free fall acceleration to be g.

2. With what speed does the bucket strike the water?
Take the free fall acceleration to be g.

3. What is the time of fall?
Take the free fall acceleration to be g.

4. While the bucket is falling, what is the force exerted on the cylinder by the axle?
Take the free fall acceleration to be g.

 

[OlderDan]

The cylinder has a moment of inertia of __________
The center of mass of the cylinder does not move, so the total force acting on the cylinder is __________
The cylinder does rotate with angular acceleration so there must be a _______________ that comes fom the ___________
The bucket accelerates downward in response to the net force that is the combination of ____________ and ________

 

[kyle8921]

I would approach this problem by using the principles of Newton's laws of motion and conservation of energy.

1. To calculate the tension in the rope, we can use the equation T = m_1g, where T is the tension, m_1 is the mass of the bucket, and g is the acceleration due to gravity. This equation assumes that the rope is inextensible and that there is no friction in the system.

2. To calculate the speed at which the bucket strikes the water, we can use the equation v = √(2gh), where v is the final velocity, g is the acceleration due to gravity, and h is the height from which the bucket falls. This equation assumes that there is no air resistance and that all of the potential energy is converted to kinetic energy.

3. The time of fall can be calculated using the equation t = √(2h/g), where t is the time of fall, h is the height from which the bucket falls, and g is the acceleration due to gravity.

4. The force exerted on the cylinder by the axle can be calculated using Newton's second law, F = ma, where F is the force, m is the mass of the cylinder, and a is the acceleration. In this case, the acceleration is equal to the acceleration due to gravity, g. Therefore, the force exerted on the cylinder is F = mg.

It is important to note that these calculations assume ideal conditions and do not take into account factors such as air resistance and friction, which may affect the results. However, they provide a good starting point for understanding the physics of a windlass system. Further analysis and experimentation may be necessary to get more precise and accurate results.