Answer to Question #106565 in Mechanics | Relativity for Adam Yaacoub

Question

A pirate in a movie is carrying a chest (0.30 m × 0.30 m × 0.20 m) that is supposed to be filled with gold. To see how ridiculous this is, determine the mass of the gold. The mass density of gold is 19300 kg/m3. To judge how large this is by converting to lbs., using the fact that 1 kg has a weight of 2.2 lbs.

Answer 1

To determine the mass of gold we should first determine the chest volume

(1) $V=0.30\cdot 0.30\cdot 0.2 m^3=1.8\cdot 10^{-2} m^3$

Then we multiply (1) by the mass density of gold $\rho=1.93\cdot 10^4 kgm^{-3}$

(2) $W=V\cdot \rho=1.8\cdot 10^{-2}m^3 \cdot 1.93\cdot 10^4 kgm^{-3}=3.47\cdot 10^2kg$

Converting to lbs. we have

(3) $Wlbs=W\cdot 2.2=3.47\cdot 10^2 \cdot 2.2 lbs=764 lbs$

Answer: The weight of gold in chest is 347 kg or 764 lbs.