Physics Lab: Calculating Tension with T=m(g-a)

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In the physics lab discussion on calculating tension using the equation T=m(g-a), there is uncertainty about whether "g" should be negative or positive. The sign of "g" is contingent on the direction defined for "a." If "a" is considered positive in the upward direction, then "g" should be negative. Clarifying the direction of acceleration is crucial for accurate calculations. Understanding these sign conventions is essential for correctly applying the tension formula.
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I'm doing a physics lab right now and to find tension we use the equation T=m(g-a) where m is the suspended mass and t is tension. I'm not sure if g should be negative or positive. I'm guessing negative but I am not to sure.
 
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The sign of "g" will depend on which direction you define "a" to be positive.
 
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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