Calculating Forces and Speed of Falling Bucket into a Well

  • Thread starter armolinasf
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In summary: Also, note that the force on the bucket is NOT equal to the tension in the rope. The tension in the rope is the force that accelerates the bucket, but there is an additional force on the bucket due to its weight.b)Initially all energy is gravitational potential so the final energy must equal the kinetic of the bucket and the cylinder.mgd=.5mv^2+.5I(v/r)^2v=sqrt(2mgd/(m+I/r^2)=sqrt(2(15)(9.8)(10)/(15+(.135/.15^2))=11.8 m/sc)x-xi=.5(v-vi)tt=2(x-xi)/(v-v
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armolinasf
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Homework Statement


A 15 kg bucket of water is suspended by a rope wrapped around a windlass, that is a solid cylinder .3 m in diameter with mass 12 kg. The cylinder pivots on a frictionless axle through its center. The bucket is released from rest at the top of the well and falls 10 m to the water. You can ignore the weight of the rope.

a) what is the tension in the rope while the bucket is falling?
b)with what speed the bucket strike the water?
c) what is the time of the fall?
d) while the bucket is falling what is force exerted on the cylinder by the axle



The Attempt at a Solution



a)Tension is equal to the torque of the cylinder while is equal to its moment of inertia I times its acceleration a. The tension is also equal to the weight of bucket minus the downward force that accelerates the system:
T=aI ==>a=T/I
T=m(g-a)

I=mr^2/2=(12)(.15^2)/2=.135

Since a is unknown, substitute T/I. After simplifying:

T=(mgI)/(m+I)=(15)(9.8)(.135)/(15+.135)=1.31N

b)Initially all energy is gravitational potential so the final energy must equal the kinetic of the bucket and the cylinder.

mgd=.5mv^2+.5I(v/r)^2
v=sqrt(2mgd/(m+I/r^2)=sqrt(2(15)(9.8)(10)/(15+(.135/.15^2))=11.8 m/s

c)x-xi=.5(v-vi)t
t=2(x-xi)/(v-vi)=2(10)/(11.8)=1.69s

d)The upward force exerted by the axle would just be the force to fight gravity, so it would be equal to the weight of the cylinder but in the opposite direction. But if that's the case would that force serve to slow down the cylinder? and wouldn't that affect all of the above calculations which I'm not sure are correct so thanks for the look over.
 
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  • #2
armolinasf said:
a)Tension is equal to the torque of the cylinder while is equal to its moment of inertia I times its acceleration a. The tension is also equal to the weight of bucket minus the downward force that accelerates the system:
T=aI ==>a=T/I
T=m(g-a)

I=mr^2/2=(12)(.15^2)/2=.135

Since a is unknown, substitute T/I. After simplifying:
T/I is angular acceleration, not linear acceleration. You'll need to apply a conversion factor.
T=(mgI)/(m+I)=(15)(9.8)(.135)/(15+.135)=1.31N
As a result of not "converting" accelerations, note that the units don't agree in the denominator: you can't add mass and moment of inertia.
 

What causes a bucket to fall into a well?

A bucket may fall into a well due to various reasons such as accidental dropping, mechanical failure of the pulley system, or strong winds that dislodge the bucket from its position.

How deep can a bucket fall into a well?

The depth to which a bucket can fall into a well depends on the depth of the well itself. In most cases, wells are dug to a depth of 50-100 feet, so a bucket falling into a well can potentially reach this depth.

Can a bucket fall into a well without any outside force?

No, a bucket cannot fall into a well on its own without any outside force. The most common cause of a bucket falling into a well is human error or mechanical failure of the pulley system.

What should I do if my bucket falls into a well?

If a bucket falls into a well, the first thing to do is to safely retrieve it. This can be done using a rope or other long object to hook onto the handle of the bucket and pull it back up. If the bucket is too deep to be retrieved, it is best to seek professional help.

How can I prevent a bucket from falling into a well?

To prevent a bucket from falling into a well, it is important to regularly check and maintain the pulley system, use a sturdy and secure rope to hold the bucket, and be cautious when handling the bucket near the well. It is also a good idea to have a backup rope or pulley system in case of any failures.

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