) A 1.62 kg wooden board floats in water with 22.0% of its volume above the surface.
a) Calculate the density of the wood. (ans: 0.780 g/cm3)
b) How much mass must be placed on the wood to sink it? (ans: 457 g)

Question

) A 1.62 kg wooden board floats in water with 22.0% of its volume above the surface. 
a) Calculate the density of the wood. (ans: 0.780 g/cm3) 
b) How much mass must be placed on the wood to sink it? (ans: 457 g)

anonymous · Answer

Maybe you need to know the density of water first? I don't know but I think it would help...

anonymous · Answer

density of water 1g/cm3

anonymous · Answer

Due to the buoyancy (the fact the board is floating), you know that the weight of the wooden board is equal to the weight of  the water that the board displaces.  So
$$W_{water} = W_{board}$$
$$ \rho_{water} V_{displaced} = m_{board}g$$
And you know that
$$V_{displaced} = .22 V_{board}$$

anonymous · Answer

also
$$ \rho_{water} = 1000kg/m^3$$

anonymous · Answer

Then 
$$\rho_{board}=\frac{V_{board}}{m_{board}}$$


For the last part, you can find out how much (volumeless) mass is required to sink it again by looking at the first equation, knowing that to sink

$$\rho_{water}V_{board} < (m_{board}+M)g$$
where M is the mass added

anonymous · Answer

Make sense? ^_^

anonymous · Answer

This makes perfect sense. Thank you so much! I was having trouble relating percent to volume.

anonymous · Answer

Oh, I'm sorry, I made a mistake.  The percent volume of the board that's actually displacing water is 1-.22 = .78 .

Welcome ^_^  Buoyancy problems are always tricky methinks, especially when things are just given in terms of other values in the problem :P

anonymous · Answer

oh fortunately that is what i wrote anyway. 

Hey thanks again man i didn't actually expect to find help on here lol.

anonymous · Answer

Very welcome - there are lots of helpful folks on this site! ^_^