# Buoyancy (Archimede's Principle) Problem

• Von Neumann
In summary, the conversation discusses how a person's body would be affected when floating in salt water compared to ordinary water. The difference in specific gravities and the volume of water displaced are important factors in determining the impact of the salt water's density.
Von Neumann
Question:

Suppose a person weighing 530 Newtons is floating in a salt lake (concentration of 20% NaCl) with a specific gravity of 1.148. How much less of the person's body would be in the salt water as compared to if he were floating in ordinary water (w/ density 1.00g/cm^3)?

Comment:

One answer people keep giving me is that the weight "lost" is equal to the difference in specific gravities multiplied by the original weight. It doesn't seem obvious to me why someone would draw such a conclusion. I understand from Archimede's Principle that, as a result of the saltwater being more dense than ordinary water, less water must be displaced in order to balance the constant downward force mg of the person. However, I am having trouble expressing this mathematically.

Well, what volume of water is displaced to support 530N? Now the same question for salt water? The difference is what you are looking for.

I really appreciate your help, but I'm really not sure how to go about finding the displaced water. The buoyant force must equal the weight of the displaced water, as well as the weight of the person because the system is in equilibrium, right?

Von Neumann said:
I really appreciate your help, but I'm really not sure how to go about finding the displaced water. The buoyant force must equal the weight of the displaced water, as well as the weight of the person because the system is in equilibrium, right?

The person will sink until he/she displaces a volume of water that weighs 530N. Does that help?

I think I understand!

F=mg
F=ρVg
=>V=F/(ρg)

So in freshwater:

V=530N/(1000kg/m^3*9.8m/s^2)=0.054m^3

And in salt water:

V=530N/(1148kg/m^3*9.8m/s^2)=0.047m^3

Is this correct?

Von Neumann said:
I think I understand!

F=mg
F=ρVg
=>V=F/(ρg)

So in freshwater:

V=530N/(1000kg/m^3*9.8m/s^2)=0.054m^3

And in salt water:

V=530N/(1148kg/m^3*9.8m/s^2)=0.047m^3

Is this correct?

Yes. The difference in the volumes are what they are looking for. Or possibly the ratio. You can see how that would be connected with the ratio of specific gravities, right?

Last edited:
Thank you very much!

It seems that the specific gravities are intimately related to the density, making them useful in this problem.

## What is buoyancy?

Buoyancy is the upward force exerted by a fluid (such as water) on an object immersed in it. It is a result of the difference in pressure between the top and bottom of the object.

## What is Archimedes' Principle?

Archimedes' Principle states that the buoyant force on an object is equal to the weight of the fluid that the object displaces. In other words, the weight of the fluid that is pushed out of the way by the object is equal to the buoyant force acting on the object.

## How do you calculate buoyancy?

Buoyancy can be calculated by multiplying the density of the fluid by the volume of the displaced fluid and the acceleration due to gravity. This is represented by the formula: Buoyant force = density x volume x acceleration due to gravity.

## What factors affect buoyancy?

The buoyancy of an object is affected by its volume, weight, and the density of the fluid it is immersed in. The shape and density of the object also play a role in determining its buoyancy.

## How does buoyancy help objects float?

When the buoyant force acting on an object is greater than its weight, the object will float. This is because the upward force of the fluid is stronger than the downward force of gravity, allowing the object to remain suspended in the fluid.

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