An object floats on water with 84% of its volume below the surface. The same object when placed in another liquid floats on that liquid with 74% of its volume below the surface. Determine the density of the unknown fluid
v * density of object * g = .84v *1(density of water) *g
density of object = .84
v*density of object(.84) * g = .74v * density of unknown liquid * g
= density of unknown liquid is .84/.74
To determine the density of the unknown fluid, we can use Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid displaced by the object.
Let's assume the volume of the object is V and its weight is W.
In the first scenario, 84% of the object's volume is below the surface of the water. Therefore, the volume of water displaced is 84% of V.
Buoyant force in water = Weight of water displaced
Since the object floats, the buoyant force is equal to its weight:
W = (Density of water) * (Volume of water displaced)
In the second scenario, 74% of the object's volume is below the surface of the unknown fluid. Therefore, the volume of the unknown fluid displaced is 74% of V.
Buoyant force in unknown fluid = Weight of unknown fluid displaced
Similar to the first scenario, the buoyant force equals the object's weight:
W = (Density of unknown fluid) * (Volume of unknown fluid displaced)
Since the object is the same in both scenarios, its weight remains the same. Therefore, we can equate the two expressions for W:
(Density of water) * (Volume of water displaced) = (Density of unknown fluid) * (Volume of unknown fluid displaced)
Since we are looking to determine the density of the unknown fluid, we can rearrange the equation:
Density of unknown fluid = (Density of water) * (Volume of water displaced) / (Volume of unknown fluid displaced)
Substituting the given percentages for the volume ratios, we have:
Density of unknown fluid = (Density of water) * 0.84 / 0.74
The density of water is approximately 1000 kg/m^3. Substituting this value, we get:
Density of unknown fluid = 1000 * 0.84 / 0.74
Simplifying this expression:
Density of unknown fluid ≈ 1135.14 kg/m^3
Therefore, the approximate density of the unknown fluid is 1135.14 kg/m^3.
To determine the density of the unknown fluid, we need to compare its density with that of water.
Let's start by assigning some variables:
- Let V be the total volume of the object
- Let Vw be the volume of the object below the surface when it floats in water
- Let Vf be the volume of the object below the surface when it floats in the unknown fluid
- Let Dw be the density of water
- Let Df be the density of the unknown fluid
We are given that the object floats on water with 84% of its volume below the surface. This means that Vw/ V = 0.84 or Vw = 0.84V.
Similarly, the object floats on the unknown fluid with 74% of its volume below the surface. So, Vf/ V = 0.74 or Vf = 0.74V.
Now, let's compare the densities:
Density = Mass / Volume
The mass of the object cancels out in this comparison, so we can say:
Dw = V / Vw (density of water)
Df = V / Vf (density of the unknown fluid)
We can rearrange these equations to solve for Vw and Vf:
Vw = V / Dw
Vf = V / Df
Substituting the given values and rearranging the equations, we get:
0.84V = V / Dw
0.74V = V / Df
Now, let's compare these equations:
0.84 / Dw = 0.74 / Df
Cross-multiplying, we have:
0.84 * Df = 0.74 * Dw
Dividing both sides by 0.74 and solving for Df, we get:
Df = (0.84 / 0.74) * Dw
Based on the given information and calculations, the density of the unknown fluid is (0.84 / 0.74) times the density of water.
Do/Dw = 0.84
Do/1 = 0.84
Do = 0.84 g/cm^3 = Density of the object
Do/Df = 0.74
0.84/Df = 0.74
0.74Df = 0.84
Df = 1.135 g/cm^3 = Density of the fluid.