Solving a Royal Mystery: Archimedes & the Crown

AI Thread Summary
To determine if a crown is made of pure gold or contains silver, measuring its density by calculating mass and volume is essential. The density of the crown can then be compared to the known density of gold. If the density is lower than that of pure gold, it indicates the presence of silver. The shape of the crown can be approximated to find its volume using Archimedes' principle. This method allows for a non-destructive evaluation of the crown's composition.
dami
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Homework Statement


Once upon a time the famous archimedes was given a problem to determine if a crown supposedly made of pure gold actually contained some silver. If Archimedes was your lab partner, explain how the two of you could quickly determine if the crown were gold or not without damaging or destroying it.


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The Attempt at a Solution


I thought of getting the density (by measuring the mass, volume of the crown) and comparing it to the density of gold. But what if the density of gold has not be defined (found). Also, if i may ask, what do you call the shape of a crown and how do i find the volume.
 
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Well there are only a few properties that differ greatly between gold and silver. For example atomic weight/number and therefore its specific gravity, boiling point...

I'm guessing the solution will be of some relevance to Archimedes... So I feel that you're on the right track by measuring the crowns volume...
 
I used archimedes and solved it.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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