A Canada goose floats with 26.1% of its volume below water. What is the average density of the goose?
To find the average density of the goose, we need to understand the concept of density. Density is defined as mass divided by volume. In this case, we have information about the volume of the goose, but not its mass. So, we'll need to use a relationship between mass and volume to determine the density.
The fact that 26.1% of the goose's volume is below water indicates that the buoyant force acting on the goose is equal to its weight. Buoyant force is the force exerted by a fluid (in this case, water) on an immersed object and is equal to the weight of the fluid displaced by the object.
Since the goose is floating, its weight is balanced by the buoyant force:
Weight of the goose = Buoyant force
The weight of an object can be calculated using the equation:
Weight = mass × acceleration due to gravity
Since we're only interested in the relationship between the mass and volume, we can divide both sides by the acceleration due to gravity, which will cancel out from both sides:
Weight / (acceleration due to gravity) = mass
Now, let's consider the density of water. The density of water is approximately 1000 kg/m³.
Since the goose is floating, the amount of water displaced by the goose is equal to its volume below water.
Let's assume the total volume of the goose is V, then the volume below water would be 0.261V (26.1% of the total volume).
The weight of the displaced water is equal to the buoyant force, so:
Weight of the displaced water = Buoyant force
Using the relationship between weight, mass, and density:
Weight of the displaced water = density of water × volume of displaced water
Substituting the values, we get:
density of water × volume of displaced water = Weight / (acceleration due to gravity)
density of water × 0.261V = Weight / (acceleration due to gravity)
We also know that the weight of the goose is equal to the weight of the displaced water:
Weight of the goose = Weight of the displaced water
Hence:
density of goose × V = density of water × 0.261V
Now we can cancel out the V on both sides:
density of goose = density of water × 0.261
Substituting the value of the density of water, approximately 1000 kg/m³, we can calculate the average density of the goose:
density of goose ≈ 1000 kg/m³ × 0.261
density of goose ≈ 261 kg/m³
Therefore, the average density of the Canada goose is approximately 261 kg/m³.