Suppose you made your own hydrometer. The lower part of a hydrometer has a volume of 7.0 g/cm3 and the upper part is 5.0 cm long and has a cross-sectional area of 0.62 cm2. What length of the upper part of the hydrometer will be submerged?
To determine the length of the upper part of the hydrometer that will be submerged, we need to consider the principles of buoyancy and Archimedes' principle.
First, we need to understand that the hydrometer will sink until the weight of the volume of liquid displaced by the submerged part of the hydrometer equals the weight of the hydrometer itself. This is based on Archimedes' principle, which states that any object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.
To calculate the weight of the hydrometer, we need to find the volume of the hydrometer and multiply it by the density of the material it is made from.
The lower part of the hydrometer has a density of 7.0 g/cm^3. Let's assume the volume of the lower part is V1.
V1 = 7.0 g/cm^3 * V1
We don't have enough information to determine V1, so we'll need to find another way to calculate the weight of the hydrometer.
Next, we need to calculate the weight of the liquid displaced by the submerged part of the hydrometer. This can be done by finding the volume of the submerged part and multiplying it by the density of the liquid.
Let's assume the length of the submerged part of the hydrometer is L cm. The volume of the submerged part is given by V2 = L * A, where A is the cross-sectional area of the upper part of the hydrometer.
The weight of the displaced liquid is given by W = density of the liquid * V2 = density of the liquid * (L * A)
To achieve equilibrium, the weight of the hydrometer is equal to the weight of the displaced liquid:
W = weight of the hydrometer
density of the liquid * (L * A) = weight of the hydrometer
Now we have an equation that allows us to solve for L, the length of the upper part of the hydrometer that will be submerged. We'll need to know the density of the liquid to proceed with the calculation.