# Archimedes Principle: An object, part aluminum, part wood, floats in water.

See attached file.

Two blocks are cemented together top to bottom and the whole object is placed in water. Known values are the density of the wood Dw= .650 kg/m^3, of aluminum Da = 2700 kg/m^3, and of water Dliq= 1000 kg/m^3.

See attachment #1 for diagram, (not to scale).

PART a. If the object barely floats, with the top surface ot the wood level with the surface of the water, find the ratio of the volumes, Vw/Va.

PART b. With the object barely floating, if the mass of the aluminum part is Ma= 8 kg, find the mass of the wood part.

PART c. If the object floats with the wood only 75 percent submerged, find the ratio of the volumes, Vw/Va.

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#### Solution Preview

See attached file.

Complete your own drawing showing all vertical forces then see attachment #2 to check your work.

PART a.

With forces shown in attachment #2, expressing that total upward force = total downward force on the barely floating object, we can write:

(1) Ma g + Mw g = Dliq g (Vw + Va).

In order to ...

#### Solution Summary

The solution explains exactly how to work through the problem, and provides calculations for answers.