Density of Submerged Objects in Water: Wood & Person

[jerick232002]

1.) What is the density of a piece of wood that floats in water with 70% of its volume submerged?

2.) calculate the density of a person who floats in water with 5% of her volume above the surface?

 

[JaredJames]

I assume this is a school work question and so you're going to have to show some working before we can help.

 

[jerick232002]

i don't know how. i think first to do is to look for the value of mass? and then?please help me..

 

[JaredJames]

Well the questions aren't about finding an exact solution, you need to rearrange the equations, inserting any known values and then you will come out with a ratio.

 

[jerick232002]

the exact solution is d=m/v?right? but the only given is the percent, volume?what I am going to do?first step?

 

[JaredJames]

Density = Mass / Volume

For an object to float, it has to displace an amount of water equal to it's weight. In this case, when 70% of the wood is submerged, that amount of water equals the weight of the wood.

So how can you put all of this together with equations and come up with a way of expressing the volume?

 

[jerick232002]

Mass = 1000 g /Volume??

 

[JaredJames]

When weight of object = weight of water displaced the object floats.

Weight of object = mg = weight of water displaced = mg

Density = Mass / Volume

Mass = Density x Volume

Weight of object = D_woodV_woodg

Weight of water displaced = D_water0.7V_woodg

So you get:

D_woodV_woodg = D_water0.7V_woodg

You can take out gravity:

D_woodV_wood = D_water0.7V_wood

You can also cancel out V_wood:

D_wood = 0.7D_water

D = Density, V = Volume, g = gravity

Can you follow this?