Circular Motion Problem: Downy Ball in Rotating Washing Machine

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The discussion revolves around a physics problem involving a Downy ball modeled as a spherical shell in a rotating washing machine. The main question is about the movement of an air bubble within the ball after the machine starts spinning, specifically whether the bubble moves closer to or further from the center of the washing machine. Participants express confusion about the Downy ball's behavior and the definitions of terms like "center of the dryer" and the nature of its motion. Clarification is sought on how the rotation affects the bubble's position and the overall dynamics of the system. Understanding these concepts is crucial for solving the problem effectively.
irvine752
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Homework Statement


A Downy ball which can be modeled as a sealed, spherical shell of diameter d is rotating with constant angular velocity in a clothes washing machine. Assume that the Downy ball is confined circular path that undergoes no rotations in a plane perpendicular to the angular momentum vector. The sphere is nearly filled with a fluid having uniform densityρ, and also contains one small bubble of air at atmospheric pressure. Your answer should be a function of variables and constants. Assume that the diameter of the sphere is d and the radius of motion is R.
a)The bubble has an initial position directly above the center of the sphere. Where is the bubble, relative to its original position, after the washing machine starts to spin? (Is it closer to the center of the washing machine or further away)

Homework Equations


P = Po + DVh


The Attempt at a Solution



Honestly, I'm not quite sure how to set up this problem. I need help.
 
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What the heck is a Downey Ball, and how does it move in the dryer and in this question specifically? Is it a ball that is pulled part-way up the cylinder of the dryer by the rotation of the cylinder? And what is meant by the "center of the dryer"? Does that mean the axis of rotation of the dryer drum, or the left-right position of the horizontal center of the dryer?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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