How Do You Calculate the Sinking Depth of Wood in Water?

[zeronem]

I would like someone to tell me the steps for working out this problem. Specifically I would like to know the Equations needed to use for the problem.

Here is the problem. It seems very simple, but I seen to get lost in converting SI Units and then I get confused.

A Piece of wood is 2cm X 4cm X 2mm. It has a density of 450 kg/m/m. To what Depth will it sink in water?

Anyhow, I don't know exactly what to do. I found the Volume in Meters but I have no clue if it is correct. So I then found the mass from the Density and Calculated Volume. I plug the Volume in the Bouyant Force Equation, then I find the Force of weight of the object. What do I do next? Do I find the apparent Force and divide it by Volume? I have no Idea how to find the Depth. I would like a good Explanation as well. Thanks.

 

[kishtik]

Is density 450kg/m^3?
We don't know your object's rotation? On which side is it sinking?
Since G=F_b
$$V_{sunk}d_{fluid}=V_{object}d_{object}$$
As you will see the volume under water is the same no matter its rotation.

 

[M98Ranger]

To solve this problem, you will need to use the following equations:

1. Volume of the wood: V = l x w x h (where l is the length, w is the width, and h is the height)
2. Mass of the wood: m = ρ x V (where ρ is the density and V is the volume)
3. Buoyant force: Fb = ρf x V (where ρf is the density of the fluid, in this case water)
4. Weight of the wood: W = m x g (where g is the acceleration due to gravity, which is approximately 9.8 m/s^2)
5. Pressure at a given depth: P = ρf x g x h (where h is the depth)

Now, let's go through the steps to solve the problem:

1. First, convert the dimensions of the wood from centimeters to meters. This will give you a length of 0.02m, a width of 0.04m, and a height of 0.002m.

2. Use the volume equation to find the volume of the wood: V = 0.02m x 0.04m x 0.002m = 1.6 x 10^-5 m^3.

3. Next, use the density of the wood to find its mass: m = 450 kg/m^3 x 1.6 x 10^-5 m^3 = 0.0072 kg.

4. Now, use the buoyant force equation to find the buoyant force acting on the wood: Fb = 1000 kg/m^3 x 1.6 x 10^-5 m^3 = 0.016 N.

5. Then, use the weight equation to find the weight of the wood: W = 0.0072 kg x 9.8 m/s^2 = 0.07056 N.

6. Since the wood will sink when its weight is greater than the buoyant force, we can set these two values equal to each other and solve for the depth (h):

0.07056 N = 0.016 N + 1000 kg/m^3 x 9.8 m/s^2 x h

h = (0.07056 N - 0.016 N) / (1000 kg/m^3 x 9