A wooden block ... physics (density) problem?

Question

A wooden block is 2.5m on each side and 0.6 m thick. The density of the wood is 598 kg/m3. How high does the block float above the water? Assuming density of water is 1000 kg/m3.

Help? Thanks!

Answer 1

hi,

The volume of the block is 2.5*2.5*0.6=3.5

weight will 3.5(volume)*598(density)=2242.5

To float in a liquid the object has to replace amount of liquid of it's own weight. That liquid's volume will be the drowned part of the floating object's volume.

so the length and width are going to be same and lets consider the thickness inside the water is x.

2242.5=2.5*2.5*x*1000

x=0.3588

So block's height over the water is 0.6-0.3588=0.2412m

Answer 2

The mass of the block is as follows;

2.5mX2.5mX0.6m= 3.75 m^3

mass=598 kg/m^2X3.75m^3=2242.5 kg

Here is a quote from wikipedia;

The weight of the displaced fluid is directly proportional to the volume of the displaced fluid (specifically if the surrounding fluid is of uniform density).

Let me translate; The wood will keep sinking in to the water until the volume of water displaced has the same amount of mass as the mass of the wood that is pressing in to the water.

Mass of water that equals 2245.5 kg converts to the following volume;

2245.5 kg X 1m^3/1000kg=2.245 m^3

2.5mX2.5mXunknown height=2.245 n^3

height=0.359 meters

The height above the water line is 0.60-.359=0.241