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

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SUMMARY

Ben Cohen's demonstration illustrates the overkill of the US nuclear arsenal, estimated at 2,500 MegaTons (MT) of TNT. He uses shotgun pellets, each representing the destructive power of the Hiroshima bomb (13 kiloTons or kT), to visually convey the scale of nuclear weaponry. The calculation involves determining the volume of the pellets, factoring in a packing fraction of 0.80, to find the total liters needed for the demonstration. The volume of a single pellet is calculated using the formula for the volume of a sphere, and the total number of pellets required is derived from the ratio of the bomb's power to that of a single pellet.

PREREQUISITES
  • Understanding of basic geometry, specifically the volume of spheres
  • Familiarity with unit conversions, particularly between metric units (e.g., kT to MT)
  • Knowledge of packing fractions and their implications in volume calculations
  • Basic grasp of nuclear weapon yields and their historical context
NEXT STEPS
  • Calculate the volume of a sphere using the formula V = (4/3)πr³
  • Research the implications of packing fractions in material science
  • Explore the historical context of nuclear arsenals during the Cold War
  • Learn about the conversion between different units of energy (e.g., kT to MT)
USEFUL FOR

Students in physics or engineering, educators discussing nuclear history, and advocates for disarmament seeking to understand the scale of nuclear arsenals.

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Homework Statement



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.)

Homework Equations





The Attempt at a Solution



1 pellet = 4/3 Pi (.2)^3
= 13 KT

1 Pellet X 2500x10^3 / 13 KT
 
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I suggest you convert these to the same unit first.

Bomb: 2500 MT
Pellet: 13 KT

K = x103
M = x106

Volume of sphere: (4/3)(pi)(r3)
Diameter: 4.00mm
(convert to m)
1m3=1000L

Volume of metal = Volume calculated/0.80

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By finding out how many Pellets = 1 Bomb, that gives you the number of pellet. You should be able to solve the rest from here.