Calculating Tension & Buoyancy in Water

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To calculate the tension in the string suspending a rubber stopper half in and half out of water, one must consider the forces acting on the stopper, including its weight and the buoyant force. The buoyant force can be calculated using Archimedes' Principle, which states that the buoyant force equals the weight of the displaced fluid. Since only half of the stopper is submerged, the buoyant force will be proportional to the volume of the submerged part, not necessarily half the total weight of the stopper. The tension in the string can be expressed as T = W - F_buoyancy, where W is the weight of the stopper and F_buoyancy is the buoyant force. Understanding these principles allows for a straightforward calculation of the tension in the string.
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Hello, if I were to suspend a rubber stopper into a graduated cylinder filled with water, with the stopper half in the h2o and half out of it, how would i calculate the tension in the string? Experimentally, i would collect the displaced volume, density (1000kg/m3), and mass of stopper. I am only in AP physics B, so i cannot use an extremely intense formula. I know buoyant force is rho x volume x gravity and weight is mass x gravity obviously. Any help on this soon would be great. Thank you!
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What forces are acting on the rubber stopper? What is causing the tension in the string in the first place?
 
Have you been taught to use free body diagrams? If so, you should have no trouble answering SteamKing's question.
 
Yes I know how to use fbds, however only half of the rubber stopper is in the water. It is not submerged. For the submerged experiment, I would do T equals W minus Force buoyancy. But when only half of the stopper is in the water (and it is not floating, it's being suspended by the string), how would this equation change? Thank you
 
Archimedes Principle
 
Boxlife27 said:
Yes I know how to use fbds, however only half of the rubber stopper is in the water. It is not submerged. For the submerged experiment, I would do T equals W minus Force buoyancy. But when only half of the stopper is in the water (and it is not floating, it's being suspended by the string), how would this equation change? Thank you
If it's only half-submerged, that only affects the magnitude of the buoyant force on the stopper. It doesn't affect qualitatively the free body diagram or the identification of the forces acting on the stopper.
 
Thank you very much for answering. How would the magnitude be affected? Would the buoyant force be in half? Or something of that nature.. Thanks
 
Boxlife27 said:
Thank you very much for answering. How would the magnitude be affected? Would the buoyant force be in half? Or something of that nature.. Thanks
Can you articulate Archimedes Principle? If you can state the principle, you should have no trouble determining the buoyant force.
 
Oh yes, I was overthinking it. Thank you all for the help
 

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