# Falling bucket of water physics

A bucket of water of mass m1 is suspended by a rope wrapped around a windlass, that is a solid cylinder with diameter d with mass m2. 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.

I know the tension in the rope (T), the speed with which the bucket hits the water (v), and the time of the fall (t).

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

I am not really sure how to go about this problem. I have never solved any of its type before.

At first, I tried to do a free-body diagram of the windlass. The forces pointing down would be the weight of the windless and the tension force T. The normal force would be pointing up, and since the windlass itself is not moving linearly, I set N(normal force)=weight of windlass + tension. That didn't turn out to be correct, tho...

I just need a little clue to start me off...

Thanks so much!

Ryan

Last edited:

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Astronuc
Staff Emeritus
The problem is similar to Atwood's machine - http://hyperphysics.phy-astr.gsu.edu/hbase/atwd.html, but rather than having a second mass rising on the other side of the pulley, the change in rotation of the pulley and its moment of inertia provide resistance to the acceleration of the bucket m1.

http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#mi

The bucket would fall at g (acceleration of gravity) if it was not connected by the rope to the pulley. Since the pulley provides a resisting force, the bucket accelerates at less than g.

See if you can determine the relationship of the acceleration of the bucket, tension T in rope, and the resisting force (torque) of the pulley.

That should get you started.

Hmmm...I see what you're trying to get at, but I am still not sure how it helps. Mainly, I am not even too sure what the target variable is (as in how to get it into an equation).

One thing I forgot to mention is that we also know the acceleration (a). These are the known values:

mass of bucket = m1
mass of pulley = m2
acceleration = a
diameter = d
height that the bucket falls from = h
tension in string = T
speed of bucket when it hits the water = v
time it takes bucket to hit water = t

The reason why I have all these numbers is because this is a multi-step problem, and I correctly solved for everything else. This is the last question of the problem, so I believe they want me to do something with the numbers I solved for (v, T, a, t) to find the target variable.

Going with what you did, I would have...

net force in y direction = m1g - T = m1a

net torque of pulley = I(omega) = T(d/2)

There are no unknowns in these 2 equations since I already used them to find the a, T, t, and v.

I guess the main area I am having trouble with is I don't even know what equation to use to figure out my target variable (don't even know what my target variable should be)...

Ryan