A probe sent to the surface of Mars uncovers a pure platinum

A probe sent to the surface of Mars uncovers a pure platinum disc inscribed with the message, \"We\'ll be right back\" (in Martian, of course!). The disc is 2 inches thick and 0.6 meters in diameter. The density of platinum is 21,450 kg/m3. What is the mass of the platinum disc in pounds (lbm) The Martian acceleration due to gravity is 3.61 m/s2 while Earth\'s gravitational constant is 32.2 ft/s2. What is the Earth weight of the disc in Newtons?

Solution

The disc is 2 inches thick and 0.6 meters in diameter.

Find volume of disc ( shape of cylinder ) = pi*r^2*h where h is height and r is radius

r= 0.6/2 = 0.3 mt ;; h = 2*2.54/100 = 0.0508 mt

Volume = pi*r^2*h =pi*(0.3)^2*(0.0508) = 0.01436m^3

density =21,450 kg/m3

mass = densityx volume = 21,450 x 0.01436 = 308 kg =  308 x2.20 =677.64 pounds

Earth\'s gravitational constant:32 ft/sec^2

Earth weight of the disc in Newtons= massx acc due to gravity = 677.64 pounds x 32 ft/sec^2 = 21689.82 slug

( 1 kilogram is equal to 0.068521765562 slug) = 3104188.46 Newton