Answer to Question #84572 in Mechanics | Relativity for sim

Question

2. The British gold sovereign coin is an alloy of gold and
copper having a total mass of 7.988 g, and is 22-karat gold.
(a) Find the mass of gold in the sovereign in kilograms
using the fact that the number of karats 5 24 3 (mass
of gold)/(total mass). (b) Calculate the volumes of gold
and copper, respectively, used to manufacture the coin.
(c) Calculate the density of the British sovereign coin.

Answer 1

(a) Look at the formula:

$$N_{karats}=24\frac{M_{gold}}{M_{total}},$$ $$M_{gold}=M_{total}\frac{N_{karats}}{24}=7.988\cdot \frac{22}{24}=7.322 \text{ g},$$

or 0.007322 kg.

(b) Density of gold:

$$19.32\text{ g/cm}^3$$

. Density of copper:

$$8.94\text{ g/cm}^3.$$ $$V=M/\rho:$$ $$V_{gold}=7.322/19.32=0.379 \text{ cm}^3,$$ $$V_{copper}=(7.988-7.322)/8.94=0.074 \text{ cm}^3.$$

(c) The density of the sovereign:

$$\rho_{sovereign}=\frac{M_{total}}{V}=\frac{M_{total}}{V_{gold}+V_{copper}}=\frac{7.988}{0.379+0.074}=17.634 \text{ g/cm}^3.$$