Answer to Question #147271 in Mechanics | Relativity for Akilo tohimat

Question

An alloy of gold and quartz has a mass of 150g.Determine the mass of the gold in the alloy. Relative density of gold is 19.3 of quartz is 2.6 and of the alloy 6.5. Assume that there is no change in volume when the metals form the alloy

Answer 1

$\rho = \frac{m}{V};V=\frac{m}{\rho};V_{alloy}=\frac{m_{alloy}}{\rho_{alloy}}=\frac{150}{6.5}\approx23.1$

$m_{gold}+m_{quartz}=150;m_{quartz}= 150 -m_{gold}$

$V_{alloy} = V_{gold}+V_{quartz}$

$V_{gold}+V_{quartz} = \frac{m_{gold}}{\rho_{gold}}+\frac{m_{quartz}}{\rho_{quqrtz}}=$ $\frac{m_{gold}}{\rho_{gold}}+\frac{m_{allow}-m_{gold}}{\rho_{quartz}}$

$V_{alloy}*\rho_{gold}*\rho_{quartz} = m_{gold}*\rho_{quartz}+m_{allow}*\rho_{gold}-m_{gold}*\rho_{gold}$

$m_{gold}= \frac{V_{alloy}*\rho_{gold}*\rho_{quartz} -m_{allow}*\rho_{gold}}{\rho_{quartz}-\rho_{gold}}\approx103.9$

Answer:$m_{gold}\approx103.9g$