Backspace NumLk 7 8 0 PHYS1114 Benton Spring 2018 OSU Physics Dept. Physics 1114

Question

Backspace NumLk 7 8 0 PHYS1114 Benton Spring 2018 OSU Physics Dept. Physics 1114: College Physics I Solutions to Homework Assignment 5 l. Astronomers predict that on Friday 13 April 2029 the asteroid 99942 Apophis is going to pass within 30,000 km of the Earth. Given the fact that, on average, the Moon is 385,000 km distant from the Earth, this asteroid is going to pass pretty darn close. 99942 Apophis has a mass of 2.7 × 1010 kg and is expected to be traveling at a speed of 12.6 km/s relative to the Earth at the time of closest approach. What if the astronomers goofed in their calculations and the asteroid is actually going to hit the Earth? With what kinetic energy would 99942 Apophis impact the Earth in terms of megatons of TNT. A detonation of 1 megaton of TNT releases 4.2 × 1015 J of energy. The largest nuclear weapon ever detonated (the Tsar Bomba test by the former Soviet Union) was about 50 megatons, while the largest nuclear weapon the U.S. ever detonated (the Castle/Bravo test) was 15 megatons.

Explanation / Answer

given
mass of asteroid, M = 2.7*10^10 kg
speed, v = 12,600 m/s
hecne
energy transferred on impact = 0.5Mv^2 = 2143260000000000000 J = 0.0214326*10^20 J

now, 1 megaton TNT = 4.2*10^15
hence this asteroid will transfer 510.3 megaton TNT equivalent energy

which is 10 times the largest weapon ever detonated

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