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Q: nuclear physics ( Answered 5 out of 5 stars,   2 Comments )
Question  
Subject: nuclear physics
Category: Science > Physics
Asked by: travis18-ga
List Price: $15.00
Posted: 20 Apr 2005 10:48 PDT
Expires: 20 May 2005 10:48 PDT
Question ID: 511836
How can I convert the kinetic energy of an incoming meteroid to
equivalent Atomic Bomb or Hydrogen Bomb blast?  Basically, I want to
know How much energy is produced by an Atomic or Hydrogen bomb in
Joules.
Answer  
Subject: Re: nuclear physics
Answered By: welte-ga on 20 Apr 2005 16:23 PDT
Rated:5 out of 5 stars
 
Dear Travis,

Thank you for question on meteors and atomic bombs.  The kinetic
energy in the meteor can be expressed as:

K =   mv^2

However, as the object hurtles toward the Earth, it gains kinetic
energy as its potential energy is converted to kinetic.  Therefore,
one must consider the total energy in the object:

E =  mv^2 + mgh

Just before impact, the height will decrease to zero (at impact) and
all of the energy will be kinetic energy.  For simplicity, I will
neglect loss of energy to resistance due to the atmosphere and effects
of heating secondary to friction with the atmosphere during descent. 
Of course, if one could measure the velocity of the object just prior
to impact, these effects would be inherently be taken into account
(the friction has already had its effect at that point), so one can
either calculate the equivalent energy based on the energy of the
object at a height above the impact site, or one  can calculate the
equivalent energy more accurately by measuring the instantaneous
velocity (and mass) must prior to impact.  The math is essentially the
same.

So, the total energy is given above, and is constant (conservation of
energy).  With the units below, the energy calculated will be in
Joules.  To convert to "atomic bomb units," also known as "equivalent
tons of TNT", we use the conversion

 1 megaton (1 million metric tons) of TNT =  4.185 x 10^22 ergs  =
4.185 x 10^15 Joules

or, one can say, there are
 2.39 x 10^-16 megatons per Joule


A very complete physics unit conversion document can be found here:
http://scholar.google.com/url?sa=U&q=http://www.agu.org/reference/gephys/23_moskowitz.pdf

Table 4 on page 5 of the above document give multiple energy unit conversions.


The answer, then, is a matter of substitution of the conversion factor
into the energy equation:
Energy (in megatons TNT) = E * megatons / Joule
               = E * ( 2.39 x 10^-16 megatons / Joule)
               =  ( mv^2 + mgh) * ( 2.39 x 10^-16 megatons / Joule)

An *excellent* resource for both derivations and discussion of the
many ramifications of such an impact is the following article:
"Comet and Asteroid Threat Impact Analysis," by James A. Marusek.
http://scholar.google.com/url?sa=U&q=http://personals.galaxyinternet.net/tunga/TA.pdf
This document includes multiple estimates on the many variables
involved (e.g., object density, velocity, etc.)

Another good article can be found here:
http://scholar.google.com/url?sa=U&q=http://www.geocities.com/elidoro/collaborazione/whitepaper.pdf

____________________________________________________

Here are definitions of all of the variables I've used above with the
units in brackets:
K: Kinetic energy [joules]
m: mass of object [kilograms]
v: velocity of object [meters/second]
E: Total energy of object [joules]
g: gravitational acceleration constant (9.8 m/s^2)
h: height of object from impact site [meters]

____________________________________________________

I hope this was helpful.  Feel free to request clarification.

Best,

           -welte-ga
travis18-ga rated this answer:5 out of 5 stars
exactly what I needed.  great answer and very fast

Comments  
Subject: Re: nuclear physics
From: endersgame-ga on 20 Apr 2005 12:14 PDT
 
From: http://online.unitconverterpro.com/conversion-tables/convert-group/energy.html
and
http://www.onlineconversion.com/energy.htm

1 gigajoule =  	2.3900573613767E-007 megatons
or in easier form for your purposes, 1 megaton = 4,184,000 gigajoules.
 (add another 9 zeros for just joules)

From http://www.cnn.com/SPECIALS/cold.war/experience/the.bomb/history.science/
The two bombs dropped during WW2 were
15kilotons = 6.276 * 10^13 joules

and 
60 kilotons = 2.51*10^14 joules
Subject: Re: nuclear physics
From: hfshaw-ga on 20 Apr 2005 16:35 PDT
 
You might also find the following on-line resources interesting/useful:

<http://www.lpl.arizona.edu/tekton/crater.html> uses scaling relations
"to determine the diameter of a crater given details on the nature of
the projectile, conditions of impact, and state of the target".

and 

<http://www.lpl.arizona.edu/impacteffects/>  which estimates "the
regional environmental consequences of an impact on Earth. This
program will estimate the ejecta distribution, ground shaking,
atmospheric blast wave, and thermal effects of an impact as well as
the size of the crater produced. "  This calculator will also tell you
the both the total kinetic energy (in MT) of a impacting object as
well as the energy deposited during the impact (they are not the
same).

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