a plastic duck floats half-immersedi n water in the bathtub. What fraction of its volume would be immersed in a liquid of relative density 2.0?
If the density of the fluid is twice that of water, you only have to displace half as much to float. If it floats half-submerged in water, 3/4 can be above the denser fluid and 1/4 immersed below.
Well, that's one buoyant duck! If the plastic duck is floating half-immersed in water, it means that the weight of the water displaced by the duck is equal to half of the duck's weight. The relative density of the liquid doesn't really come into play here, but I appreciate the effort in throwing that in! To answer your question, half of the duck's volume would be immersed in the liquid. So, we could say it's a "quack-tacular" 1/2 or 0.5 fraction of its volume!
To determine the fraction of the plastic duck's volume immersed in the liquid, we need to compare the density of the liquid to the density of the duck.
Let's assume that the density of water is 1.0 (since it is not mentioned in the question), and the relative density of the liquid is 2.0.
Since the density of the liquid is twice that of water, the liquid is denser, which means the duck will float with a greater portion of its volume submerged.
Let's represent the fraction of the duck's volume submerged as "x."
According to Archimedes' principle, the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Since the density of water is 1.0, the fraction of the duck's volume submerged in water (x_water) can be calculated as:
x_water = (density of duck) / (density of water)
Similarly, the fraction of the duck's volume submerged in the liquid with a relative density of 2.0 (x_liquid) can be calculated as:
x_liquid = (density of duck) / (density of liquid)
Given that x_water = 0.5 (since the duck is half-immersed in water), we can solve for x_liquid.
0.5 = (density of duck) / 1.0
0.5 = (density of duck)
Now, let's substitute this in the equation for x_liquid.
x_liquid = (0.5) / (2.0) = 0.25
Therefore, the fraction of the plastic duck's volume that would be immersed in the liquid with a relative density of 2.0 is 0.25 or 25%.
To determine what fraction of the plastic duck's volume would be immersed in a liquid of relative density 2.0, we can consider the concept of buoyancy.
The buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. If the object is floating, the buoyant force is equal to its weight, and consequently, the weight of the displaced fluid is also equal to its weight.
Let's assume that the plastic duck has a volume of V and a weight of W. When the duck is floating half-immersed in water, the buoyant force acting on it is equal to its weight, which is W.
Now, the relative density (also known as specific gravity) of a substance is the ratio of its density to the density of another substance (usually water). In this case, the relative density of the liquid (assuming it's not water) is 2.0. This means that the density of the liquid is twice that of water.
To find out what fraction of the duck's volume would be immersed in the liquid, we need to compare the densities. The buoyant force on the duck does not change, but the weight of the displaced fluid depends on the density of the liquid.
Since the density of the liquid is twice that of water, the weight of the displaced fluid would also be twice as much. Therefore, the duck would displace twice its weight in the liquid, which corresponds to twice its volume in the liquid.
Thus, the fraction of the duck's volume immersed in the liquid of relative density 2.0 would be 2/2 or 1 whole unit, meaning it would be completely submerged.
To summarize:
- The plastic duck would float half-immersed in water.
- If the relative density of the liquid is 2.0, the duck would be completely submerged, meaning its entire volume would be immersed.
It's important to note that this explanation assumes uniform densities and neglects other factors such as surface tension, shape irregularities, or any other complexities that may affect the behavior of the plastic duck in the liquid.