An explosion at ground level leaves a crater with a diameter that is proportiona

Question

An explosion at ground level leaves a crater with a diameter that is proportional to the energy of the explosion raised to the 1/3 power; an explosion of 1 megaton of TNT leaves a crater with a 1 km diameter. An ancient impact crater is found with a 60 km diameter. What was the kinetic energy associated with that impact, in terms of (a) megatons of TNT (1 megaton yields 4.2 × 1015 J) and (b) Hiroshima bomb equivalents (13 kilotons of TNT each)? (Ancient meteorite or comet impacts may have significantly altered Earth's climate and contributed to the extinction of the dinosaurs and other life-forms.)

Explanation / Answer

Let D be the diameter of the crater and E be the energy

D E1/3

To remove the proportionality and make it an equation, let us introduce a constant, K

D = KE1/3   where K is some constant and E, the Energy.

To compare the two Scenarios, we write

D1 / D2 = (E1 / E2)1/3

D1 = 1000 m , D2 = 60000 m , E1 = 1 x 4.2 x 1015 J , E2 = n x 4.2 x 1015 J

1000 / 60000 = (1 / n)1/3

1/ 603 = 1/n

n = 603 = 216000 megatons of TNT (answer to a )

1 Hiroshima bomb equivalents 13 kilotons = 13000 tons of TNT

number of Hiroshima bomb equivalent to this ancient explosion = 216000 x 106 / 13000

= 16615384.62 Hiroshima bomb equivalents

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.