On August 10, 1972, a large meteorite skipped across the atmosphereabove the wes

Question

On August 10, 1972, a large meteorite skipped across the atmosphereabove the western United States and western Canada, much like astone skipped across water. The accompanying fireball was so brightthat it could be seen in the daytime sky and was brighter than theusual meteorite trail. The meteorite's mass was about 3.4 x106 kg; it's speed was about 16 km/s. Had itentered the atmosphere vertically, it would have hit Earth'ssurface with about the samespeed. (a) Calculate the meteorite'sloss of energy (as a positive number, in joules) that would havebeen associated with the verticalimpact. (b) Express the energy as amultiple of the explosive energy of 1 megaton of TNT, which is 4.2x 1015 J. (c) The energyassociated with the atomic bomb explosion over Hiroshima wasequivalent to 13 kilotons of TNT. To how many Hiroshima bombs wouldthe meteorite impact have been equivalent?

Explanation / Answer

   mass, m = 3.4 x 106 kg    velocity, v = 16 km/s = 16000 m/s (a) loss of energy of meteorite = kinetic energy = (1/2)mv2                                                     = (1/2) ( 3.4 x 106 kg ) ( 16000 m/s )2                                                      = 435.2X 10 12 J (b) 1 megaton of TNT = 4.2 x 1015 J       loss of energy of meteorite=  435.2 X 10 12 / 4.2 X 10 15= 0.1 mega tonnes of TNT                                                                          = 10 5 tonnes of TNT (c)   energy of atomic bomb = 13 kilotons ofTNT = 13000 tonnes of TNT         loss of energy ofmeteorite = 10 5 tonnes of TNT                                                 = 10 5 / 13000 times of atomicbomb                                                 = 7.69 times of atomic bomb                                                      = 435.2X 10 12 J (b) 1 megaton of TNT = 4.2 x 1015 J       loss of energy of meteorite=  435.2 X 10 12 / 4.2 X 10 15= 0.1 mega tonnes of TNT                                                                          = 10 5 tonnes of TNT (c)   energy of atomic bomb = 13 kilotons ofTNT = 13000 tonnes of TNT         loss of energy ofmeteorite = 10 5 tonnes of TNT                                                 = 10 5 / 13000 times of atomicbomb                                                 = 7.69 times of atomic bomb

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