Archimedes's Principle or something

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To estimate the mass of each leg of a person partially submerged in water, it is essential to understand the relationship between apparent weight and buoyancy. The apparent weight is reduced due to the buoyant force, which equals the weight of the water displaced by the submerged part of the body. Given that the specific gravity (SG) of the body is 1.0, the weight of the legs will equal the weight of the displaced water. In this case, with an apparent mass of 54 kg and a buoyant force calculated to be 24 kg, each leg is estimated to weigh 12 kg. This approach clarifies the connection between buoyancy and the mass of submerged body parts.
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So, the original question asks for me to estimate the mass of each leg of a person whose body past the hips is covered by water. They give me the person's actual weight and the apparent weight as well as the specific gravity of the body.

I understand w' = w - Fb, Fb = F2 - F1 where F = PA or pghA
But other than that, I'm lost. Do I need to find the amount of fluid displaced by the body first and somehow relate that to the force exerted by the weight of the person?

I'm just looking for someone to point me in the right direction...
 
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It seems there is something you are not telling us. Please state the whole problem.
 
"A 78-kg person has an apparent mass of 54 kg (because of buoyancy) when standing in water that comes up to his hips. Estimate the mass of each leg. Assume the body has SG = 1.0."
 
ayudame said:
"A 78-kg person has an apparent mass of 54 kg (because of buoyancy) when standing in water that comes up to his hips. Estimate the mass of each leg. Assume the body has SG = 1.0."
The missing ingredient was not knowing that the body above the hips was not in the water. You already said you know w and w' so you can find Fb. Fb is the weight of the water displaced by the legs. If their SG is 1.0, how does their weight compare to the weight of the displaced water?
 
Oh wow...so since SG is 1.0, the weight of the 2 legs would be equal to the water displaced, right? So Fb = 24, and divided between the 2 legs would be 12 kg.

That was a lot easier than I made it...thanks so much!
 
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