Will Swinging Frequency of a Bucket Decrease?

  • Context: High School 
  • Thread starter Thread starter daniel_i_l
  • Start date Start date
  • Tags Tags
    decrease Frequency
Click For Summary

Discussion Overview

The discussion revolves around the effects of water leaking from a swinging bucket on its frequency of oscillation. Participants explore the implications of changing mass distribution and angular momentum in this context, focusing on theoretical considerations rather than practical applications.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that the frequency will decrease as the bucket leaks water, arguing that the center of mass moves further from the axis of rotation.
  • Another participant agrees with the initial claim, indicating support for the idea that frequency decreases.
  • A different participant cautions about the conservation of angular momentum, noting that the relationship between mass and distance to the center of mass complicates the outcome.
  • One participant introduces a mathematical expression for angular momentum, suggesting that the changes in mass and radius will influence the frequency, but the outcome is uncertain and depends on which factor changes more significantly.
  • Another participant questions the certainty of the conservation of angular momentum in this scenario, indicating that the loss of water may lead to a loss of angular momentum.
  • One participant speculates that it might still be possible for the frequency to increase if the water exits the bucket at a slow enough rate, although they express difficulty in visualizing this scenario and are working on setting up an equation to analyze it further.

Areas of Agreement / Disagreement

Participants express differing views on the effects of water loss on frequency, with some supporting the idea that frequency decreases while others raise concerns about the conservation of angular momentum and the potential for frequency to increase under certain conditions. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants acknowledge the complexity of the problem, particularly regarding the interplay between mass loss, distance to the center of mass, and angular momentum. There are indications of missing assumptions and unresolved mathematical steps that could influence the conclusions drawn.

daniel_i_l
Gold Member
Messages
864
Reaction score
0
Lets say that there's a bucket swinging on a string (the top of the bucket is connected to the string) and there's a small hole in the bottom of the bucket, will the frequency get bigger or smaller? i think that it will get smaller because as the bucket leaks the water gets closer to the bottom of the bucket so the center of the the swinging mass gets further away from the spinning axis - in effect it's as if the string got longer. am i correct?
Thanks.
-this isn't a homework problem.
 
Physics news on Phys.org
Sounds good to me.
 
Be careful, you cannot forget about conservation of angular momentum.
The bucket will swing with an angular momentum of:

L = I*w = m*r^2*w

where r is the distance to CM
As your mass decreases it is true that r will increase.
However, keep in mind that this is counterbalanced to some extent by the fact that m decreases.
Whether or not w increases or decreases depends on which factor (r^2 or m) is changing faster.
A tall skinny bucket would probably result in a smaller frequency w but a wide fat bucket would have the opposite effect.
 
LHarriger said:
Be careful, you cannot forget about conservation of angular momentum.
Are you completely certain about that? :wink:
 
cesiumfrog said:
Are you completely certain about that? :wink:

I think I see your point cesium:
As water is flung out of the bucket kinetic energy goes with it.
Consequently you experience a loss of angular momentum equal to:
[itex]\frac{dL}{dt}=\rho(t)\ r^2\omega[/itex]
where rho is your water mass flow rate out of the bucket.
Hence Angular momentum is not conserved.
oops:blushing:
All the same I think it still may be possible to to have your frequency increase if the speed and quantity of water doesn't leave too fast. However, I cannot intuitively visualize an answer and I am still digging through setting up an equation to check.
 
Last edited:
LHarriger said:
All the same I think it still may be possible to to have your frequency increase if the speed and quantity of water doesn't leave too fast. However, I cannot intuitively visualize an answer and I am still digging through setting up an equation to check.

Not visualising a http://en.wikipedia.org/wiki/Pendulum" ?
 
Last edited by a moderator:

Similar threads

Undergrad Equation of Continuity: Leaking Bucket & Minus Sign
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad Water pressure and flow restricton - does size matter?
  • · Replies 3 ·
Replies
3
Views
2K
Rate at which a bucket gets filled
  • · Replies 4 ·
Replies
4
Views
2K
What Is the Centripetal Acceleration and Tension in a Swinging Bucket?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Water molecule, bucket question
  • · Replies 1 ·
Replies
1
Views
1K
High School Extending the Lagrangian of a double pendulum to more complex systems
  • · Replies 3 ·
Replies
3
Views
1K
Basic (?) calc problem with flow out of a hole in a bucket
  • · Replies 20 ·
Replies
20
Views
4K
High School Calculate needed dimensions of table - Center of mass, levers etc
  • · Replies 11 ·
Replies
11
Views
3K
High School Does the Bernouli Effect Work On Cars?
  • · Replies 8 ·
Replies
8
Views
3K
How Does Water Leakage Affect the Frequency of a Vibrating Guitar String?
  • · Replies 1 ·
Replies
1
Views
2K