# Fluids: Buoyancy Homework - Prove Archimedes' Principle

• chantalprince
In summary, the conversation discussed using Archimedes' Principle to prove two facts: 1) the fraction of an object's total volume that is immersed when floating in a liquid is equal to the ratio of its density to the liquid's density, and 2) when ice melts in a glass of water, the water level does not change. The equations used were the buoyant force equation and the density equation. The conversation also discussed starting with a cube and writing equations for volume and mass in terms of length, depth, and density. However, it was noted that the object in the problem is irregularly shaped, so using a cube may not work.
chantalprince

## Homework Statement

Using Archimedes' Principle and the diagram shown: (diagram is a "mass" of something in a liquid with an immersed portion (Vb) and an Un-immersed portion (Va)).

A. prove that if an object is floating in a liquid, the fraction of the object's total volume that is immersed (below the surface) is the ratio of its density (rho of the object) to the liquids density (rho of the liq.)

B. prove that when ice melts in a glass of water, the water level does not change.

## Homework Equations

Buoyant force = rho x V x g

rho = m/V

## The Attempt at a Solution

I really don't know where to begin. I feel like I understand these concepts, but I don't know how to go about proving these things. I realize that the buoyant force is equal to the weight of the displaced fluid, but I don't know where to take it.

Will anybody help me to get started and walk me through this?

You have written:

Buoyant force = rho x V x g

rho = m/V

What do the terms represent? V of what? rho of what?

Write an equation for the volume above an dbelow the water, in terms of L and D.
Write the mass of the box and the mass of displaced water, in terms of L D and density.

If I start with a cube, aren't all of the sides the same? In this problem, its not a cube I am working with. I sort of see where you are going with it, but might it work if I used the volume for a rectangle instead? The object in the problem is irregularly shaped. It is smaller on top than bottom. It is wider and taller in the immersed portion than in the above the water portion.

Start with any shape, but try to understand what the eqns say.

## 1. What is buoyancy and how does it relate to Archimedes' Principle?

Buoyancy is the upward force exerted by a fluid on an object immersed in it. According to Archimedes' Principle, this force is equal to the weight of the fluid displaced by the object. In other words, the more volume of fluid an object displaces, the greater the buoyant force will be.

## 2. How can Archimedes' Principle be proven through homework exercises?

To prove Archimedes' Principle through homework exercises, students are typically given problems involving objects of different shapes and densities that are partially or completely submerged in a fluid. By applying the principle, students can calculate the buoyant force and compare it to the weight of the displaced fluid to demonstrate its validity.

## 3. What are some real-world applications of Archimedes' Principle?

Archimedes' Principle is used in many real-world applications, such as determining the buoyancy of boats and ships, designing submarines and other underwater vessels, and calculating the weight and volume of objects. It is also used in industries such as oil and gas exploration, where it helps in determining the volume of oil reserves and the buoyancy of drilling equipment.

## 4. Can Archimedes' Principle be applied to all fluids?

Yes, Archimedes' Principle can be applied to all fluids, including liquids and gases. It is a fundamental law of fluid mechanics and holds true for all types of fluids, as long as the fluid is incompressible and the object is completely or partially submerged in it.

## 5. What factors can affect the accuracy of calculations based on Archimedes' Principle?

The accuracy of calculations based on Archimedes' Principle can be affected by factors such as the density and temperature of the fluid, the shape and density of the object, and the presence of other forces acting on the object (such as gravity or air resistance). It is important to consider these factors and make appropriate adjustments when applying the principle in real-world situations.

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