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

Question #106565
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.
Expert's answer

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.

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