How much gold did the goldsmith steal from King Hero's crown?

  • Thread starter Thread starter Workout
  • Start date Start date
  • Tags Tags
    Archimedes Gold
Click For Summary
SUMMARY

The discussion centers on a problem involving King Hero's crown, which was suspected to contain silver instead of pure gold. The goldsmith was given 700g of gold, but Archimedes used water displacement to determine the crown's actual composition. The crown displaced 42.35 cm³ of water, while the expected volume for pure gold was calculated to be 36.27 mL. This discrepancy indicates that the goldsmith stole a certain mass of gold, which can be calculated using the densities of gold (19.3 g/cm³) and silver (10.5 g/cm³).

PREREQUISITES
  • Understanding of density and its formula (density = mass/volume)
  • Familiarity with water displacement method for volume measurement
  • Basic algebra for solving equations
  • Knowledge of the properties of gold and silver
NEXT STEPS
  • Calculate the mass of gold stolen using the equation derived from the volume discrepancy.
  • Explore the implications of Archimedes' principle in modern physics.
  • Learn about the historical context of Archimedes' work and its impact on science.
  • Investigate methods for verifying the purity of precious metals in modern applications.
USEFUL FOR

Students studying physics or mathematics, jewelers verifying metal purity, and anyone interested in historical scientific methods.

Workout
Messages
38
Reaction score
0

Homework Statement


Legend has it that Archimedes first used his discovery to help out his boss King Hero of Syracuse. The king had given 700g of gold to a goldsmith to make him a crown. When the goldsmith brought him the finished crown the King was suspicious that he had defrauded him by replacing some of the gold with silver and keeping the leftover gold. However, the crown still had a mass of 700 g. Archimedes placed the crown in a cylindrical barrel full to the brim with water and collected the water that overflowed. He measured the volume of the displaced water as 42.35cm3 and concluded the goldsmith was guilty. The density of gold is 19.3g/cm3 and the density of silver is 10.5 g/cm3.

(b) What mass of gold had the goldsmith stolen?


Homework Equations


m=dv



The Attempt at a Solution



Ok So I figured out how much water should have been displaced by the gold crown using v=m/d
(0.7kg)/19300kg/m^3

v = 36.27 mL

But the actual amount of water displaced was 42.35 ml. So I know the Vs + Vg = 45.35 mL
Vs = volume of silver, Vg = volume of gold.

I don't know where to go from there...
 
Physics news on Phys.org
So you know that there's a discrepancy in the volume displaced, and therefor the goldsmith's done something fishy.

Suppose the actual mass of gold used in the crown is mg, and that an amount ms of silver was added. Write an equation for the total mass and another for the total volume (given the densities of gold and silver)...
 

Similar threads

Archimedes' Principle-Gold Crown problem
  • · Replies 4 ·
Replies
4
Views
18K
High School How Did Archimedes Determine the Crown's Purity?
  • · Replies 1 ·
Replies
1
Views
4K
How Did Archimedes Use His Principle to Compare Densities of Gold and Silver?
  • · Replies 2 ·
Replies
2
Views
7K