Question

During the Cold War the US and the former Soviet Union built up enormous arsenals of nuclear weapons. Although the exact amounts are not known, particularly for the USSR, the stockpile of the US arsenal alone is knowledgeably estimated to have a total destructive power of about 2, 500 Mt (MegaTons) of TNT. Ben Cohen, of "Ben and Jerry's" ice-cream, who is a vocal advocate of diverting military expenditures to things such as education, has a very vivid demonstration of the overkill of the US nuclear arsenal. He takes a single shot-gun pellet to represent the power of the A-bomb that destroyed Hiroshima (about 13 kT) and drops it into a metal bucket, making sure the audience hears the little ping. He then takes a handful of about fifty such pellets and slowly pours them into the bucket, pointing out that the sound against the bottom of the bucket now represents the power of a single ICBM warhead. He then takes cup after cup of shot pellets and pours them into the bucket until he has the equivalent of the US nuclear arsenal. If the shot pellets are spheres of diameter 4.00mm, and the packing fraction of spheres is 0.80, how many liters of shot does Ben need to carry out his demonstration? (The 'packing fraction' embodies the idea that there is empty space -air-between shapes. If the packing fraction is 0.80, then 1 liter of shot really only contains 0.80 L of metal, with the rest being the space between the pellets.)

Answer 1

Given that :

Diameter of the sphere pellet, D = 4 x 10^-3 m

radius of the sphere pellet, r = 2 x 10^-3 m

packing fraction of sphere, P_Frac = 0.8

Volume of sphere pellet is given by, V_P = (4/3) $\pi$ r³

V_P = (4/3) (3.14) (2 x 10^-3 m)³

V_P = 3.35 x 10^-8 m³

How many liters of shot does Ben need to carry out his demonstration?

Volume of metal is given by,   V_m = V_P / (0.8)

V_m = (3.35 x 10^-8 m³) / (0.8)

V_m = 4.18 x 10^-8 m³

Convert m³ into L :

V = 4.18 x 10^-5 Liter