A crown is given to a king as a gift. The king believes the gift to be a fraud a
ID: 1472877 • Letter: A
Question
A crown is given to a king as a gift. The king believes the gift to be a fraud and asks you investigate. You weight the crown in air and find it to have a mass of 3.2 kg. You fully submerge the crown in water and use a scale to measure its apparent mass, which you read off as being 2.75 kg.
A.) Find the buoyant force on the crown.
B.)Find the volume of the water that is displaced by the crown.
C.) Find the density of the crown. Hint: The crown is fully submerged, so what is its volume relative to your answer in part ‘b’ above?
D.) Look up the density of gold. Was the king right to be suspicious?
Explanation / Answer
buoyant force = (actual mass - apparent mass) * g
buoyant force = (3.2 - 2.75) * 9.8
buoyant force = 4.41 N
density of water = 1000 kg / m^3
density = mass / volume
1000 = (3.2 - 2.75) / volume
volume of water displaced = 0.00045 m^3
density of crown = mass / volume
density of crown = 3.2 / 0.00045
density of crown = 7111.1 kg/m^3
density of gold = 193200 kg/m^3
since the densities are different king was right to be suspicious