Answer:
a) The object's density measures 1.9302 g/mL
b) The method employed to ascertain the density of a solid utilizes the principle of Archimedes
c) To utilize this method, assumptions regarding the overall volume of the fluid mixture and the fraction of the solid that is submerged must be made
Explanation:
- Assuming the mixture's total volume: vAB = 1000 mL
From which we derive vA = 413.7 mL ∧ vB = 586.3 mL
The density of the mixed solution (A+B) can be calculated as mass AB / volume AB
Thus, mAB = mA + mB
We find mA using vA * dA = 413.7 mL * 2.0514 g/mL = 848.664 g for A
And mB computes as vB * dB = 586.3 mL * 2.6678 g/mL = 1564.13 g for B
Leading to mAB = 2412.795 g for AB
Density of mixture = 2412.795 g / 1000 mL = 2.4127 g/mL for AB
Beginning with Archimedes' principle for finding the density of a solid within a liquid, we state:
- E = dAB * g * Vs........ (1)
Where Vs is the submerged volume;
E is the fluid weight displaced by the solid
dAB is the density of the mixture
g is the acceleration due to gravity
In force equilibrium: ∑F = 0
This gives us E - Wsolid = 0
Thus, E = Wsolid
And Wsolid = msolid * g........... (2)
Equating (1) and (2) gives us msolid * g = dAB * g * Vs
Thus, msolid ultimately equals dsolid * Vs......(3)
In assuming that 80% of the solid is submerged in the mixture, we have:
Vs = 0.8 * Vsolid.....(4)
By substituting (4) into (3):
dsolid * Vsolid = dAB * 0.8 * Vsolid leads us to dsolid = dAB * 0.8
Thus, dsolid = 2.4127 g/mL * 0.8 = 1.9302 g/mL
