Question

You, Archimedes, suspect that the king?s crown is not solid gold but is instead gold-plated lead. To test your theory, you weigh the crown, and find it to weigh 60.0N, and to have an apparent weight of 55.7 N when it is completely submerged in water. Take the density of gold to be 19300 kg/m3, the density of lead to be 11340kg/m3, and the density of water to be 1000 kg/m3. Also, use g = 9.8 m/s2.

(a) What is the average density of the crown?
Correct: Your answer is correct. kg/m3

(b) What percentage (by weight) of this crown is made of gold? The rest, we assume, is lead.
Incorrect: Your answer is incorrect. %

Answer 1

mass of the crown = 60/9.8 = 6.1224
buoyant force = 60-55.7 = 4.3 N

V1*1000*g + V2*1000*g = 4.3
V1 + V2 = .44 x 10^-3

a)
density of crown = mass/total volume = 13914.545 kg.m^3
b)
V1*19300 + V2*11340 = 6.1224
solving
V1 = 1.41 x 10^-4 m^2
mass of gold = V1*19300 = 2.7213 kg
% of gold = (2.7213/6.1224 )x 100 = 44.45 %

Answer 2

Question: where did "V1 = 1.41 x 10^-4 m^2" come from?