A comet with mass 7.85x10^11kg strikes Earth at a speed, relative to Earth of 25km/s.
a) Find the kinetic energy of the comet.
b) Compare the work done on Earth by the comet, with the energy released in exploding the largest nuclear weapon ever built (4.2x10^15 J)
If the kinetic energy of the comet is (1/2) mv^2 , where m is its mass and v is ts speed.
KE = (1/2)(7.85*10^11 kg)(25 km/s)^2
=(1/2)(7.85*10^11 kg)(25000 m/s)^2
The energy of the largest nuclear weapon =4.2*10^15 J.
So, the comets KE interms of the largest nuclear weopn = Comets KE/energy of the largest nuclear weapon = 2.453125*10^20 J/(4.2*10^15 J.) = 5.84077381*10^4 = 58407.7381 times the energy of the largest nuclear weapon.
Mass of comet = m = 7.85*(10^11) kg
Velocity of comet = v = 25 km/s = 25000 m/s
Energy released by largest nuclear weapon = E' = 4.2*10^15 J
a) Kinetic energy of comet
The kinetic energy of the comet is given by the formula:
E = (1/2)*mv^2
Substituting given values of m and v in this equation we get:
E = (1/2)*[7.85*(10^11)]*25000^2 = 2.453125*10^20 J
b) Comparison of energy released by comet.
This total energy is lost by the comet on striking the Earth. Therefor the work done by the comet on the earth is also same, That is 2.453125*10^20 J.
Therefore ratio of work done by comet to energy released by the largest nuclear weapon = E/E'
= 5.84078*10^4 = 58407.8