Fluid mechanics - ice melting into water

[JRPK8@mizzou.]

Homework Statement

A pure ice cube sits in water, floating. Prove that the water level will not change after the ice cube melts (meaning, the volume displaced by the cube will equal the volume of water added once the cube is melted).

density of water = 1000 kg / m^3
density of ice = 920 kg / m^3

Homework Equations

D = m/V F(net) = mg - pVg

The Attempt at a Solution

F(net on the cube) = mg - pVg D = m / V
mg = pVg D * V = m(water afterwards)
m = p (V) (920/1000) * V = m(water after melting)
m = (920/1000) V .92 * V = mass (water after melting)
m (submerged cube) = .92 V


Thus, m(submerged cube) = m(water after melting)

 

[LowlyPion]

Maybe just cite the conservation of matter?

Since it was all water in the first place and nothing was added or removed ...