Archimedes's Principle or something

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Homework Help Overview

The discussion revolves around estimating the mass of a person's legs when submerged in water, using Archimedes's principle and concepts of buoyancy. The original poster presents a scenario involving a person's actual weight, apparent weight, and specific gravity.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to relate the buoyant force to the weight of the displaced fluid and questions how to proceed with the calculations. Some participants seek clarification on the complete problem context, while others suggest focusing on the relationship between the weight of the legs and the buoyant force.

Discussion Status

The discussion is active, with participants exploring the implications of specific gravity and buoyancy. Some guidance has been provided regarding the relationship between the weight of the legs and the buoyant force, but no consensus has been reached on the final calculations.

Contextual Notes

There is a noted assumption that the body above the hips is not submerged, which is crucial for understanding the problem. The specific gravity of the body is given as 1.0, which influences the calculations regarding buoyancy and weight comparison.

ayudame
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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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