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
AI Thread Summary
Archimedes used his principle to investigate whether a goldsmith had defrauded King Hero by replacing gold with silver in a crown. The crown weighed 700g, but the volume of water displaced was 42.35 cm³, indicating a discrepancy. The expected volume for pure gold would be 36.27 mL based on its density of 19.3 g/cm³. This difference suggests that the goldsmith added silver, which has a lower density of 10.5 g/cm³. To find the mass of gold stolen, equations for total mass and volume must be established based on the densities of gold and silver.
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)...
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

How Did Archimedes Determine the Crown's Purity?
Replies
1
Views
4K
How Did Archimedes Use His Principle to Compare Densities of Gold and Silver?
Replies
2
Views
7K

Hot Threads

Recent Insights

Back
Top