A duck is floating on a lake with 22% of its volume beneath the water. What is the average density of the duck?
1000kg/m^3 *.22= 220
To find the average density of the duck, we need to use the equation:
Average Density = Total Mass / Total Volume
However, we are given the percentage of the duck's volume submerged. We need to convert this into a fraction.
Let's assume the total volume of the duck is V.
Given that 22% of the duck's volume is submerged, it means 78% of the duck's volume is above the water.
So, the fraction of the duck's volume submerged is 22% / 100% = 0.22.
The volume of the duck submerged in water is therefore 0.22 * V.
Now, let's assume the density of the duck is ρ and the density of water is ρw.
Since the duck is floating, its average density is equal to the density of water:
Average Density = ρ = ρw
Now, let's find the ratio of the submerged volume and the total volume:
(0.22 * V) / V = 0.22
Since density is mass divided by volume, we can rearrange the equation to solve for mass:
Mass = Density * Volume
Now, let's substitute the values into the equation:
Mass submerged = ρw * (0.22 * V)
Since the average density is equal to the density of water, we have:
Average Density = ρw = Mass / V
Therefore,
ρw = ρw * (0.22 * V) / V
Simplifying the equation:
ρw = ρw * 0.22
Dividing both sides by ρw:
1 = 0.22
Since this equation is not possible, it means there must be an error in the given information. Please double-check the data given.
To find the average density of the duck, we need to know the density of the material it is made of. The average density is calculated by dividing the mass of the duck by its volume.
Since we don't have the mass or volume of the duck, we need to make some assumptions and use some general information for calculations.
Assumption 1: The density of water is 1 gram per cubic centimeter (g/cm³).
Assumption 2: The duck is completely submerged in water, with 22% of its volume below the water surface.
Let's say the duck has a volume of V. Therefore, 22% of V is submerged in water, which means 0.22V is underwater.
The volume of the water displaced by the duck is equal to the volume of the submerged part of the duck. This is given by 0.22V.
The buoyant force acting on the duck is equal to the weight of the water displaced. According to Archimedes' principle, the buoyant force is also equal to the weight of the duck.
Using this information, we can determine that the weight of the duck is equal to the weight of an equivalent volume of water. The weight of the duck can be expressed as W = m × g, where m is the mass and g is the acceleration due to gravity.
Since we assume the density of water is 1 g/cm³, the mass of the water displaced is equal to the volume (0.22V) multiplied by the density of water (1 g/cm³). Therefore, the weight of the duck is W = 0.22V × 1 × g.
Dividing both sides of the equation by g, we obtain m = 0.22V.
Now we can calculate the average density of the duck. Average density is given by ρ = m / V.
Substituting the value of m we found, ρ = (0.22V) / V.
Simplifying the expression, we get ρ = 0.22.
Therefore, the average density of the duck is 0.22, assuming the duck is made of the same material as water and is completely submerged.