Archimedes's Principle or something

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In summary, the conversation discusses a problem where a person's body is partially submerged in water and the task is to estimate the mass of each leg. The person's actual weight and apparent weight in water are given, along with the specific gravity of the body. The missing piece of information is that the body above the hips is not in the water. By using the formula Fb = F2 - F1, where F = PA or pghA, the weight of the water displaced by the legs can be found. Since the specific gravity is 1.0, the weight of the legs would be equal to the weight of the displaced water. Therefore, the mass of each leg can be estimated by dividing the weight of the water displaced
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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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  • #2
It seems there is something you are not telling us. Please state the whole problem.
 
  • #3
"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."
 
  • #4
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?
 
  • #5
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!
 

1. What is Archimedes's Principle?

Archimedes's Principle states that the buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by the object. This principle is used to explain why certain objects float or sink in a fluid.

2. Who was Archimedes and why is this principle named after him?

Archimedes was a Greek mathematician, physicist, engineer, and inventor who lived in the 3rd century BC. He first discovered and described the principle in his work, "On Floating Bodies". The principle was named after him as he was the first to explain and prove it mathematically.

3. How is Archimedes's Principle used in everyday life?

This principle is used in many everyday applications such as ships, submarines, hot air balloons, and even swimming. It is also used in designing and building structures such as dams and bridges to ensure they can withstand the buoyant forces of water.

4. Can Archimedes's Principle be applied to gases as well?

Yes, this principle can be applied to both liquids and gases. It states that the buoyant force on an object is equal to the weight of the fluid (or gas) displaced by the object. However, the density of gases is much lower than liquids, so the effects of buoyancy may not be as noticeable.

5. How does the shape and size of an object affect its buoyancy according to Archimedes's Principle?

The shape and size of an object can greatly affect its buoyancy. An object with a larger volume will displace more fluid, resulting in a greater buoyant force. Additionally, the shape of the object can also impact its buoyancy as objects with a larger surface area will experience greater upward force due to the pressure differences between the top and bottom of the object.

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