Kings Crown Part 2

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 $\SI[per-mode=symbol]{100}{\centi\meter\cubed}$ .

What is the product of the mass of gold and the mass of silver in the crown?

Submit your answer in $\text{kg}^2$ to 2 decimal places.

The answer is 0.77.

1 solution

Terry Yu
May 12, 2017

We could write an algebraic equation, with x=gold and y=silver.

$x+y=1.8$ ------------- 1

$50x+100y=125$ ---------- 2

For equation 2 , we could change it into $x+2y=2.5$ , then subtract that with equation 1 , getting y=0.7. Then you can find out that x=1.1.

That means there is 1.1 kg of gold and 0.7 kg of silver, and when you multiply it you get $\color{#D61F06}\boxed{0.77kg^2}$ .

Hey give the units in $kg^2$

Md Zuhair - 4 years ago

Kings Crown Part 2

The answer is 0.77.

1 solution

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