SOLUTIONS TO EXERCISE 4


(a) The density of the asteroid is 7.9 g/cm^3, or 7900 kg/m^3 put
into MKS units.  The spherical asteroid is 10 km across, so its radius
is 5 km or 5000 m.  So the asteroid's mass is its density times volume:

                          4 * pi
  m = DV = 7900 kg/m^3 *  ------ * (5000 m)^3 = 4.1 * 10^15 kg
                             3

Thus the asteroid's kinetic energy is (0.5) * mv^2, or

  E = (0.5) * (4.1 * 10^15 kg) * (30,000 m/s)^2 = 1.9 * 10^24 Joule.

(b) What's the most destructive thing on Earth that I'm aware of?  
I would probably have to say an atomic bomb.  I suspect that the total
explosive power of all the nuclear weapons in the world could be
enough to cause mass extinction.  So I will compare the total energy
output of these weapons with the kinetic energy carried by this meteorite.

Estimates vary, but numerous sources on the WWW and elsewhere put
the total amount of explosive power in nuclear weapons worldwide at
about 500,000 times the power of the atomic bomb detonated over
Hiroshima on August 6, 1945.  That bomb had an explosive yield of
about 18 kilotons of TNT; and one kiloton of TNT is equivalent to one
trillion Joules (10^12 J) of energy.  Thus, this asteroid carried an
amount of kinetic energy roughly equivalent to

     1.9 * 10^24 Joule
 --------------------------- = 210,000 times more energy than all the
 500,000 * 18 * 10^12 Joule

nuclear weapons in the world today.  It's not hard to imagine that this
impact could indeed have wiped out the dinosaurs.