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Shanah Carlson (University of Witwatersrand, South Africa (ZA))

Energy question in Mechanics I

Hi guys. I have a question, if someone could explain how to calculate this. The extinction of the dinousaurs is widely believed to be due to the impact of a very massive meteorite striking the sea, land or both. Consider a smaller meteorite of mass 4 million kg entering the atmosphere vertically at 15 km/s and impacting land in a vertical fashion. You are given that: 1 megaton of TNT is equivalent to 4.2 thousand million million joules 20 kilotons of TNT is the energy associated with the explosion of an atomic bomb The number of atomic bombs to which the meteorite impact would have been equivalent is approximately....

September 23 2015, 6:49 pm

ALL ANSWERS
Houston Muzamhindo (University of Cape Town, South Africa (ZA))
Hi Shanah.

This question has a bit of an assumption we are going to make, that this meteorite's speed just before it hits the earth is 15km/s (or that it doesn't lose speed on entering the atmosphere - which is not entirely true but it works for our case).

The process here is this (starting from where we want to go):
- to get number of atomic bombs, we need to get kilotons of TNT;
- to get kilotons of TNT we need to get megatons of TNT;
- to get megatons of TNT, we need to get the joules

So let's reverse this process.
Just before hitting the ground, the meteorite's Total energy is fully Kinetic and can be calculated using 1/2 * m * v^2 and you get something like 4.5x10^14 J.

Now that we have the energy it possesses before hitting the ground, let's convert that to megatons of TNT.
Use proportion: 4.2 thousand million million joules (or 4.2 000 000 000 000 000 J) is equivalent to 1 megaton, what about the energy we have just calculated, 4.5x10^14J?
You get 0.107.. megatons

Great now let's convert these to kilotons.
We know that 1megaton equals 1 000 kilotons, now what about the megatons we have just calculated? Doing direct proportion you get 107.14... kilotons

Now with kilotons, we can get the number of atomic bombs.
20 kilotons equal the energy of one atomic bomb. What about the kilotons we have calculated just now? Again, proportion gives 5.35... atomic bombs.

So the meteorite has energy equivalent to 5.35 atomic bombs.


September 23 2015, 7:16 pm


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