Floating Wood: Finding the Ratio Above Water

[gaily4]

A block of wood with a density that is 750 kg/m3 is floating in a tank of water. How much of the wood is above the surface of the water



D=M/V



I've been trying for hours to try to figure this one out. The only info I'm given the the density of a block of wood in the water at 750kg/m^3. I'm thinking that it has something to so with the approx. density of water at 1000kg/m^3, so the ratio is 4:3 so that approx 25% would be above the water, but not at all sure I'm on the right track.

 

[gneill]

You're on the right track. Now all you need to do is derive it :-)

Why not try a strictly symbolic approach. Let the density of the wood be r1 and that of the water r2. Now suppose the volume of the block is v. What's the weight of the block? How much water needs to be displaced for it to float? ...

 

[tiny-tim]

welcome to pf!

hi gaily4! welcome to pf!

hint: find all the forces on the wood (and remember that force = https://www.physicsforums.com/library.php?do=view_item&itemid=80" times area)

 

[gaily4]

thank you ...I think I get it!

 

[rwisz]

I could really use some help.

I can understand your confusion and frustration in trying to solve this problem. However, I can assure you that you are on the right track. Let me explain further.

First, let's define the variables in the given problem. D represents density, M represents mass, and V represents volume. In this case, we are given the density of the wood (750 kg/m3) and we need to find the ratio of the wood above the surface of the water. To do this, we need to use the density equation, D=M/V, in combination with the concept of buoyancy.

Buoyancy is the upward force exerted by a fluid on an object that is partially or fully submerged in it. This force is equal to the weight of the fluid displaced by the object. In this case, the fluid is water and the object is the block of wood.

To find the ratio of the wood above the surface of the water, we need to compare the weight of the wood to the weight of the water it has displaced. Since the density of water is 1000 kg/m3, we can assume that the volume of water displaced by the wood is equal to the volume of the wood itself. Therefore, the weight of the water displaced by the wood is equal to the weight of the wood.

Now, let's apply this information to the density equation. Since we know the density of the wood (750 kg/m3), we can set it equal to the density of the water displaced by the wood (1000 kg/m3). This gives us the following equation:

750 kg/m3 = M/V

We know that the mass of the wood is equal to its density (750 kg/m3) multiplied by its volume (V). Therefore, we can substitute this into the equation:

750 kg/m3 = (750 kg/m3) x V

Solving for V, we get:

V = 1 m3

This means that the volume of the wood is 1 m3. Since the wood is floating, we can assume that the entire volume is above the surface of the water. Therefore, the ratio of the wood above the surface of the water is 1:1 or 100%.

In conclusion, the block of wood is fully submerged in the water, with all of its volume above the surface. I hope this explanation helps you understand the problem better. If you have any further questions,