Mastering physics problem regarding speed and tension

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The discussion focuses on determining the speed at which the tension is equal in both wires attached to a 2.0 kg sphere revolving in a horizontal circle. Participants suggest analyzing the vertical forces acting on the sphere in relation to the tension components and applying equations for horizontal forces based on angular velocity and radius. The conversation emphasizes finding the lengths of the wires to calculate the radius needed for the equations. Ultimately, the solution involves substituting values to derive the angular velocity. The user successfully finds the answer with the help of hints provided.
hieule
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Two wires are tied to the 2.0 kg sphere shown in the figure View Figure . The sphere revolves in a horizontal circle at constant speed.

For what speed is the tension the same in both wires?

What is the tension?



I reallllly need some hints to figure the first part, and the second part...thank you
 

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hieule said:
Two wires are tied to the 2.0 kg sphere shown in the figure View Figure . The sphere revolves in a horizontal circle at constant speed.

For what speed is the tension the same in both wires?

What is the tension?
Find the vertical force on the sphere in terms of the vertical components of the tension (1).

Then write the equation (2) for the horizontal force on the sphere (in terms of \omega and r

Then find the lengths of the wires in order to find r.

Substitute r into (2) (both tensions = T) and use T from (1) to find \omega

AM
 
yeah, got the answer, thanks
 
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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