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SOLUTIONS TO EXERCISE 7

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energy: TOC for Knowledge Concepts, Exercises, and Solutions


(a) E = mc^2, so if m = 0.003 gram = 3 * 10^(-6) kg and c = 3 * 10^8 m/s,

    E = (3 * 10^(-6)) * (3 * 10^8)^2 = 2.7 * 10^11 J

    This is equal to about (2.7 * 10^11)/(10^9) = 270 tons of exploding dynamite.

(b) Again, E = mc^2, and this time m = (2.509 + 4.995 + 2.263 + 5.706) = 15.48 g

    so E = (15.48 * 10^(-3) kg) * (3 * 10^8 m/s)^2 = 1.39 * 10^14 J

    This is about (1.39 * 10^14)/(10^9) = 139,000 tons of exploding dynamite.

(c) From Exercise 6, we know that the atomic bomb detonated over Hiroshima 
converted about 0.2 g of matter completely into energy.  Thus, these four coins
together would produce energy equivalent to about

    (15.48 g) / (0.2 g) = 77 atomic bombs.