Question

4. Kinetic energy is the energy of motion. How much kinetic energy does a spherical asteroid with a 1 km diameter have if it is made out of iron (has density of about 8 kg m-3) and hits Earth at a relative velocity of 10 km s-1? Convert your answer to megatons of TNT (1 megaton of TNT = 4.18 x 1015 joules).

Answer 1

Kinetic energy = 1/2 m V2

V is the velocity of the object

m is the mass of the object

density of the asteroid(given) = 8kg/m3

density = mass / volume

volume of sphere= 4/3 r3, where r is the radius of the sphere

radius of asteroid = 1km/2 = 0.5 km =500 m

volume of sphere= 4/3 (500)3

= 1.33 * 3.14 * 125*106

= 522.025 * 106 m3

mass= density * volume  

= 8 * 522.025 *106 [ (kg/m3) * m3]

= 4176.2 * 106 kg

velocity of asteroid = 10km/sec = 104m/sec

Kinetic energy = 1/2 mV2

= 0.5 * (4176.2 * 106) * (10000)2 kg* (m/sec)2

= 2088.1 * 106 * 108 kgm/sec2 * m

= 2.088.1 * 1014 N * m

= 2088.1 * 1014 joules

1 megaton of TNT = 4.18 * 1015joules

2088.1 * 1014 joules = (1/ 4.18 * 1015) * 2088.1 * 1014 megaton of TNT

= 0.4995 * 100

= 49.95 megaton of TNT