# Pressure and density in flluids

1. May 20, 2005

### sghaussi

hi! I was wondering if someone can help me with this physics probelm:

A single ice cube with mass X g floats in a glass completely full of Y cm^3 of water. You can ignore the water's surface tension and its variation in density with temperature (as long as it remains a liquid).

What volume of water does the ice cube displace?

I know these densities -
Water: 1.00 x 10^3 kg/m^3
Ice: 0.92 x 10^3 kg/m^3

density = m / V (m is mass and V is volume)

if I rearrange this equation I get:

V = m / density

I just plugged in my known mass and density for hte ice and i found the volume of the ice. That volume would be the same volume that the ice takes up in the cup of full water, right? I don't think it is because I keep getting hte wrong asnwer. Am even using the write equation? I'm stuck and confused, hope someone can help me! =)

2. May 20, 2005

### Pyrrhus

water in its liquid form is more dense than water in its solid form (ice), so the ice will be partially submerged. This means the water displaced will be equal or less to the volume of the ice. Use Archimedes' Principle.

Last edited: May 20, 2005
3. May 20, 2005

### Dr.Brain

Probably you havent read our text well before attempting the problems.This problem is a direct application of Archimedes Principle which states that:

"A body whooly or partially immersed inside a liquid is buoyed up by a force which is equal to the weight of the body inside the liquid"

Therefore,as per your problem,in equilibrium,The buoyant force balances the weight of the body:

Weight of the cube= Desnity(cube)(total volume of cube)

Therefore:

$d_iVg= d_wV_og$

$where V_o=Fraction of volume og cube inside water.$

Now calculate V_o ...that will give you the vlume of cube inside water...and that will be the volume occupied by the cube in water...simple isnt it?