Buoyancy of a piece of wood floating in water

• Woolyabyss
In summary, the problem involves finding the relative density of a piece of wood that is floating in water. The buoyancy formula is used, but since the wood is only partially submerged, only the weight of the submerged portion is considered. Using a force balance, the weight of the wood is found to be equal to the weight of the water displaced, allowing for the calculation of the wood's density.

Homework Statement

A piece of wood floats in water with 65% of its volume under water.Find the relative density of the wood.

Homework Equations

Buoyancy = (Weight of object) / (Relative density of object)

The Attempt at a Solution

B = W/s

1= .65/s

s = .65/1

s= .65

My book says this is the right answer but I can't understand how? I guess .65 and 1 are ratios.
But how did they get the one?

Look up the density of water.

SteamKing said:
Look up the density of water.

Density of water = 1000 kg/m^3

I'm not sure what I am suppose to do with this?

Last edited:
The buoyancy is given by that formula only if the object is completely submerged.
If not, only the "weight" of the submerged part will enter the formula.
So you will have
B=(0.65*W)/RD where RD is relative density.
But the object is floating so B should balance the entire weight of the object.
So B=W and then is follows the rest.

The problem here is that you are applying a formula without a good understanding of the phenomena involved, I suppose. I don't think this is the best way to describe the buoyant force in introductory physics.

Let V represent the volume of the piece of wood, and let ρw represent the density of the wood. What is the weight of the piece of wood? If 65% of the wood is under water, how much wood volume is under the water (in terms of V)? This is the volume of water displaced. If ρ is the density of water, what is the weight of the water that was displaced? From a force balance on the wood, the weight of the wood (downward force on the wood) must be equal to the weight of the water displaced (upward force on the wood). This should give you enough information to calculate the density of the wood.

chet

nasu said:
The buoyancy is given by that formula only if the object is completely submerged.
If not, only the "weight" of the submerged part will enter the formula.
So you will have
B=(0.65*W)/RD where RD is relative density.
But the object is floating so B should balance the entire weight of the object.
So B=W and then is follows the rest.

The problem here is that you are applying a formula without a good understanding of the phenomena involved, I suppose. I don't think this is the best way to describe the buoyant force in introductory physics.

Alright thanks I understand now.

What is buoyancy?

Buoyancy is the upward force exerted by a fluid on an object that is partially or completely submerged in it. It is the result of the difference in pressure between the top and bottom of the object.

How does buoyancy affect a piece of wood floating in water?

The buoyancy force on a piece of wood floating in water is equal to the weight of the water that it displaces. This allows the wood to float because it is less dense than water.

What factors affect the buoyancy of a piece of wood?

The buoyancy of a piece of wood is affected by its density, shape, and size. A less dense wood will float higher in the water, and a larger or more streamlined shape will displace more water and increase the buoyancy.

Why does a piece of wood float vertically in water?

A piece of wood will float vertically in water because of its center of mass and center of buoyancy. When these two points are aligned, the wood will float in a stable, vertical position.

Can a piece of wood sink in water?

Yes, a piece of wood can sink in water if it is denser than the water it is placed in. This can happen if the wood becomes waterlogged or if it is compressed to increase its density.