Fluids: Buoyancy Homework - Prove Archimedes' Principle

[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?

Your help is appreciated!

 

[Shooting Star]

You have written:

Buoyant force = rho x V x g

rho = m/V

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

 

[mgb_phys]

Start with a cube, side L and submerged depth D
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.

 

[chantalprince]

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.

 

[Shooting Star]

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