Kings Crown Part 1

Classical Mechanics Level 2

The King asks Archimedes if his crown is made of pure gold. He knows that the crown is either pure gold or it may have some silver in it.

Archimedes figures out that the volume of the crown is $\SI[per-mode=symbol]{125}{\centi\meter\cubed}$ and that its mass is $\SI[per-mode=symbol]{1.8}{\kilo\gram}$ . He also knows that $\SI[per-mode=symbol]{1}{\kilo\gram}$ of gold has a volume of about $\SI[per-mode=symbol]{50}{\centi\meter\cubed}$ and $\SI[per-mode=symbol]{1}{\kilo\gram}$ of silver has a volume of about $\SI[per-mode=symbol]{100}{\centi\meter\cubed}$ .

Is the crown pure gold, or does it have some silver in it?

It is all made from silver It has some silver in it It is not made from either silver nor gold but another element It is all made from gold

1 solution

Terry Yu
May 12, 2017

You have to find out the density of the crown and compare it with the density of the other objects. It cannot have been made from another element, so to find the density,

$\rho=\frac{m}{v}$ .

The mass it 1.8 and the volume is 125, so $\rho=\frac{1.8}{125}=0.0144$

The volume of gold is $\rho=\frac{1}{50}=0.02$

And the volume of silver is $\rho=\frac{1}{100}=0.01$

As you can see, the density of the crown is right in between the density of the silver and the density of the gold. That means, it's mixed with some silver, and the king has not gotten cheated (thanks to Archimedes).

Is Part 2 going to have us find the actual volumes?

Steven Chase - 4 years ago

@Steven Chase - yes it is, but the actual masses.

Terry Yu - 4 years ago

Kings Crown Part 1

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