Simple pendulum in different situations

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Discussion Overview

The discussion revolves around the behavior of a simple pendulum with a hollow spherical bob under two conditions: when the bob is filled with water and when the water inside freezes. Participants explore whether these conditions affect the time period of the pendulum and the underlying reasons for any differences.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that the time period will differ between the two cases due to the behavior of the water, suggesting that liquid water may introduce chaotic motion similar to a double-pendulum.
  • Others argue that if the water is stationary and the bob expands when frozen, the time period should remain unchanged based on the formula T=2π√(L/g), assuming no friction and neglecting volume changes.
  • One participant emphasizes that if the bob is completely filled with water, it can be treated as a solid mass, which would not affect the time period.
  • There is a claim that the pendulum's behavior is mass independent under the given constraints, although this point is contested by some participants who seek clarification on the mass dependency of the pendulum's period.

Areas of Agreement / Disagreement

Participants express differing views on whether the time period changes based on the state of the water (liquid vs. frozen) and the implications of mass independence. The discussion remains unresolved regarding the effects of these conditions on the pendulum's time period.

Contextual Notes

Participants have made assumptions regarding the neglect of friction, volume changes, and the treatment of the pendulum as mass independent, which may not hold in real-world scenarios.

Adikshith Ojha
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Say there is a pendulum which is suspended by a massless thread or rod or whatever, the bob is spherical and hollow. Now consider 2 cases 1) the pendulum is completely filled with water 2) the water inside freezes. will there be a difference in the time periods? If so, why?
 
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My first instinct is that not only will the period be different, but the behavior may even become chaotic when the water is liquid, like a double-pendulum.
The water sloshing inside the bob would add an extra degree of freedom, like a second pendulum.

Unless the bob is completely filled with water. I wouldn't expect a difference in that case.
 
If you disregard the friction of the water, isn't the water stationary? Also, if the water freezes, the bob has to expand right? since the period of a pendulum is 2pisqrt(l/g), there would be no difference. However, if the bob expands, that would slightly change l.
 
Well, I guess I should've stated some more conditions (being a student, I take them for granted) there is no friction due to water and neglect any changes in volume. Anyway, both of you say that there is Jo change, that must be it then.
 
Equation needed: T=2π√(L/G). If the water is uniformly distributed and also fills up the entire sphere (to avoid sloshing which changes this whole problem), and we're ignorning friction, expansion, etc... Then no there should be no difference. The bob's center of mass remains in the center of the water (liquid/ice) as you can treat a sphere filled completely with water as a "solid" mass (ignoring the complicated stuff as this appears to).
 
Exactly what the previous poster mentioned. Because of your given constraints, and not a real world scenario, the Pendulum is mass independent. Therefore, I could fill it up with hot sauce, and the answer would be the same.
 
MidgetDwarf said:
Exactly what the previous poster mentioned. Because of your given constraints, and not a real world scenario, the Pendulum is mass independent. Therefore, I could fill it up with hot sauce, and the answer would be the same.
I think you need to clarify this. Pendulum is not mass independent.
 
just dani ok said:
I think you need to clarify this. Pendulum is not mass independent.
the period of the pendulum is mass independent.
 
MidgetDwarf said:
the period of the pendulum is mass independent.
sorry, my mistake.
 

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