A block of wood with volume V floats in water with 0.68V submerged. In oil the block floats with 0.86V of its volume submerged.
What's the density of the wood?
All you need to answer that is the amount submerged in water, and the density of water.
According to Archimedes Principle:
(Water density) * 0.68 V
= (wood density)* V
Cancel out the V and use the density of water
1.00 g/cm^3 * 0.68 = wood density
To find the density of the wood, we can use Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Let's assume the density of water is ρw and the density of oil is ρo.
When the block is submerged in water with 0.68V submerged, the buoyant force is equal to the weight of water displaced:
Buoyant force_water = weight_of_water_displaced
The weight of water displaced can be calculated as the volume of water displaced (0.68V) multiplied by the density of water (ρw):
Weight_of_water_displaced = ρw * (0.68V) -----------(1)
Similarly, when the block is submerged in oil with 0.86V submerged, the buoyant force is equal to the weight of oil displaced:
Buoyant force_oil = weight_of_oil_displaced
The weight of oil displaced can be calculated as the volume of oil displaced (0.86V) multiplied by the density of oil (ρo):
Weight_of_oil_displaced = ρo * (0.86V) -----------(2)
Since the block is floating, the weight of the block is equal to the buoyant force in both cases. Therefore, we have:
Weight_of_block = ρw * (0.68V) = ρo * (0.86V)
Dividing both sides of the equation by V, we get:
ρw * 0.68 = ρo * 0.86
Now, we can solve this equation to find the density of the wood (ρw).
ρw = (ρo * 0.86) / 0.68
Therefore, the density of the wood is (ρo * 0.86) / 0.68.
To find the density of the wood, we can use the principle of buoyancy. The buoyant force acting on the block of wood will be equal to the weight of the water (or oil) displaced by the submerged part of the block.
Let's assume the density of water is ρw and the density of oil is ρo. We can use the following equation:
Buoyant force = Weight of displaced liquid
In water:
Buoyant force in water = Weight of water displaced
= Density of water × Volume of water displaced (0.68V)
Similarly, in oil:
Buoyant force in oil = Weight of oil displaced
= Density of oil × Volume of oil displaced (0.86V)
Since the block is floating, the buoyant force in both cases will be equal to the weight of the block.
Weight of block = Buoyant force in water = Buoyant force in oil
Therefore, we can set up an equation where the weight of the block equals the buoyant forces in both water and oil:
Density of water × Volume of water displaced = Density of oil × Volume of oil displaced
Let's solve for the density of wood (ρw):
ρw = (Density of oil × Volume of oil displaced) / (Volume of water displaced)
Substituting the given values:
ρw = (ρo × 0.86V) / (0.68V)
Simplifying the equation:
ρw = ρo × 0.86 / 0.68
Now, if you have the density of the oil (ρo), you can simply substitute it into the equation to find the density of the wood (ρw).