I need help starting this one You are brought in as a consulting physicist to de

Question

I need help starting this one

You are brought in as a consulting physicist to determine if a heavy necklace, ostensibly made of pure gold, is in fact, the real deal. Your client suspects that the gold in the necklace has been alloyed with silver by unscrupulous jewelers. You determine that the necklace weighs 3.150 pounds in air and 2.961 pounds in water. What fraction of the necklace is, in fact, silver? You may assume that the volume of any gold/silver alloy equals the combined volumes of its separate constituents.

Explanation / Answer

in air

M0 =ro*V

in water

M =(ro-ro(water))*V

M0/M = ro/(ro-1000)

(3.150*0.454) / (2.961*0.454) =ro/(ro-1000)

1.0638 =ro/(ro-1000)

1.0638*ro-1063.28 =ro

ro =16674 kg/m^3 is the density of alloy.

now ro(Au) =19300 kg/m^3 (wiki)

ro(Ag) =10490 kg/m^3 (wiki)

if x is the fraction of Au (gold) in the alloy we have

ro = x*ro(Au) +(1-x)*ro(Ag)

16674 =x*19300 +(1-x)*10490

16674 =19300*x +10490 -10490*x

6184 =8810*x

x =0.7019 =70.19% Au

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