Circular motion of a bucket filled with water

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Discussion Overview

The discussion revolves around the dynamics of a bucket filled with water undergoing vertical circular motion. Participants explore the forces acting on the water and the bucket, particularly focusing on the contact force at the top of the circular path and the implications of removing the bottom of the bucket. The conversation includes theoretical considerations, force balances, and the effects of different velocities on the system.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question why a contact force exists between the water and the bucket at the top of the circular motion.
  • Others suggest that the bucket must accelerate downwards at more than 1g to maintain this contact force.
  • A participant proposes that if the bottom of the bucket is removed, the water will exit tangentially, similar to a mass on a string in vertical motion, provided the bucket's speed is sufficient.
  • There is a discussion about the conditions under which the reaction force exists, with some stating that if the centripetal acceleration is equal to g, the reaction force would be zero.
  • Participants explore the implications of varying velocities on the reaction force and fluid pressure at the bottom of the bucket.
  • Some participants discuss the effects of tangential velocity and whether it remains constant during the motion.
  • There is a consideration of angular acceleration in scenarios involving extensible strings and varying tension in the system.

Areas of Agreement / Disagreement

Participants express differing views on the conditions necessary for the contact force and the behavior of the water when the bucket's bottom is removed. The discussion remains unresolved regarding the specific dynamics at play, particularly concerning the assumptions about acceleration and the implications of different forces.

Contextual Notes

Participants reference force balances and equations related to centripetal motion, but there are unresolved assumptions regarding the nature of the forces involved and the conditions under which they apply.

  • #31
Does anyone else besides me feel like this thread is going down the rabbit hole?
 
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  • #32
Faiq said:
When there is a vertical motion with an object connected to the centre by an extensible string, there are varying magnitudes of tension at each point because of the change in centripetal force. What I am asking is whether this situation could give rise to an angular acceleration?
What do you mean by an "extensible string"? Do you still envision a circular path? Do you still envision a circular path centered on the attachment point of the string? Where along the path do you expect angular acceleration to occur?
 
  • #33
jbriggs444 said:
What do you mean by an "extensible string"? Do you still envision a circular path? Do you still envision a circular path centered on the attachment point of the string? Where along the path do you expect angular acceleration to occur?
What I mean by an extensible string is the amount of tension in the string is significant enough to cause an extension which will result in varying values of radius. As a result, an elliptical motion will be generated.
I want to know whether at any point will angular acceleration occur in such a case.
 
  • #34
Faiq said:
What I mean by an extensible string is the amount of tension in the string is significant enough to cause an extension which will result in varying values of radius. As a result, an elliptical motion will be generated.
I want to know whether at any point will angular acceleration occur in such a case.
You have not specified how the central force varies with string extension. That affects string length which, in turn, affects angular velocity and angular acceleration. Chet seems to have the right idea. There is little point in pursuing this line of inquiry.
 
  • #35
This problem has gotten way too complicated way too fast. It violates the three most important rules about modeling:

1. Keep it simple
2. Keep it simple
3. Keep it simple

Because of inexperience, @Faiq has greatly underestimated the complexity of a problem with a (deformable) fluid in the bucket (which would involve complicated fluid mechanics inside the bucket) and an elastic rope. So we need to take some steps back. Let's start out by analyzing the following two simpler problems:

1. A rigid mass attached to an inextensible string moving in a circle. The bucket is replaced by the rigid mass. The center of the circle remains fixed and dissipative effects are negligible. So the motion will go on forever. What is the tangential velocity of the mass as a function of angle above the horizontal if the velocity of the mass at the top of the arc is V? What is the tangential acceleration of the mass as a function of the angle?

2. Same as problem 1, except with a string that obeys Hooke's law.

Go to it @Faiq.

Chet
 
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  • #36
Yes Thank you for modelling my query as a formal physics question.
 

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