Question

The mass of a meteor with a radius of 1 km is about 9 x 1012 kg. The mass of a meteor also is proportional to the cube of its radius. Suppose a meteor with a radius of 8.1 km is moving at 2 x 104m/s when it collides inelastically with the Earth. The Earth has a mass of 5.97 x 1024 kg and assume the Earth is stationary. The kinetic energy lost by the asteroid in this collision will be transferred to non-conservative work in heating the atmosphere and physically destroying the place where it lands. The Tsar Bomb, the largest atomic bomb ever tested, released 2.1 x 1017 J of energy. (Which, by the way, is 1000's of times more energy compared to the atomic bombs dropped in World War II.) How many MILLIONS of equivalent Tsar Bombs is the kinetic energy lost of this meteor?

Answer 1

The density of the meteor is the same.

=> M₂ = 4.7829 x 10¹⁵ kg

this is the mass of the 8.1 km meteor

use momentum conservation for Earth-meteor collision,

M₂v + 0 = (M₂+M')V

=> V = 1.6 x 10^-5 m/s

the kinetic energy at impact for this meteor is:

and final kinetic energy is: U' = (1/2)(M₂+M')V² = 7.664 x 10¹⁴ J

so, energy lost by the meteor is: U - U' = 9.565899 x 10²³ J

Energy released by Tsar bomb = 2.1 x 10¹⁷ J

so, it would require 9.565899 x 10²³ / 2.1 x 10¹⁷ = 4.555 Millions of equivalent Tsar bombs.