A slab of wood with mass m = 1.7 kg floats 78% submerged.The density of water is 1000
kg/m3
. What is the density of the wood?
You can read the response to the previous post and try to work out the answer.
To find the density of the wood, we need to use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
First, let's determine the weight of the water displaced by the submerged portion of the wood slab. We know that the wood slab is 78% submerged, so the volume of the water displaced is 78% of the total volume of the slab.
Since the density of water is 1000 kg/m^3, the weight of the water displaced by the submerged portion of the slab can be calculated using the following equation:
Weight of water displaced = Density of water * Volume of water displaced * Acceleration due to gravity
Now, the weight of the water displaced is equal to the buoyant force acting on the submerged slab. This buoyant force is counteracting the weight of the slab, so it is given by:
Buoyant force = Mass of the slab * Acceleration due to gravity
Since the slab is floating, the buoyant force is equal to the weight of the slab:
Buoyant force = Weight of the slab
Therefore, equating the equations for the weight of the water displaced and the weight of the slab, we can solve for the density of the wood:
Density of wood = Mass of the slab / Volume of water displaced
To find the volume of water displaced by the submerged portion of the slab, we can use the fact that the volume of an object is equal to its mass divided by its density.
Volume of water displaced = Mass of water displaced / Density of water
Reorganizing the equation for the density of wood, we get:
Density of wood = Mass of the slab / (Mass of water displaced / Density of water)
Plugging in the given values:
Density of wood = 1.7 kg / (0.78 * 1.7 kg / 1000 kg/m^3)
Simplifying the equation:
Density of wood = 1000 kg/m^3 / 0.78
Density of wood ≈ 1282.05 kg/m^3
Therefore, the density of the wood is approximately 1282.05 kg/m^3.