In this problem you\'ll compare the energy of an asteroid impact with those of t

Question

In this problem you'll compare the energy of an asteroid impact with those of the Hiroshima bomb (yield 15kt TNT) and the Castle Bravo bomb (the largest nuclear test by the US with the yield of 15Mt TNT). Energy yield of 1 ton of TNT is equivalent to 109cal = 4.184 times 109J. In this problem you can assume that the asteroid is perfectly spherical in shape and made of stony material with the mean density of rho = 3.5g / cm3. Consider a low speed asteroid with impact speed of 15km/s. Calculate its impact energy for the asteroid radius of 10m, 100m and 1km and express it in terms of energy yields of the Hiroshima and Castle Bravo bombs.

Explanation / Answer

(1) Radius 10 m

volume = 4/3*(103) = 4.19e03 m3 , mass = V = (3500 kg/m3)(4.19e03) = 1.47e07 kg

compact energy come from kinetice energy = 0.5mv2 = 0.5(1.47e07)(15000)2 = 1.65e15 J

which is equivalent to 3.94e05 ton of TNT = 26.28 Hiroshima bomb = 0.026 Castle Bravo bomb

(2) Radius 100 m

volume = 4/3*(1003) = 4.19e06 m3 , mass = V = (3500 kg/m3)(4.19e06) = 1.47e10 kg

compact energy come from kinetice energy = 0.5mv2 = 0.5(1.47e10)(15000)2 = 1.65e18 J

which is equivalent to 3.94e08 ton of TNT = 2.63e04 Hiroshima bomb = 26.28 Castle Bravo bomb

(3) Radius 1000 m

volume = 4/3*(10003) = 4.19e09 m3 , mass = V = (3500 kg/m3)(4.19e09) = 1.47e13 kg

compact energy come from kinetice energy = 0.5mv2 = 0.5(1.47e13)(15000)2 = 1.65e21 J

which is equivalent to 3.94e11 ton of TNT = 2.63e07 Hiroshima bomb = 2.63e04 Castle Bravo bomb

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