2
$\begingroup$

I’m trying to understand the nature and amount of energy/force generated in an explosion. Take, for example, the explosion that results from the complete annihilation of one gram of matter, releasing 8.9876E+13 Joules. Let’s say that the initial volume of the explosive material is one cubic centimeter, shaped into a sphere with an area of .2244 square meters. Working through the inverse square law I end up with an output of 4.0050E+14, and this is where I begin to get confused.

I get that having an area measuring less than 1.0 means that my final energy value will be greater than my original energy value, but while this might be mathematically correct it doesn’t reflect what would happen in the real world (making an explosive smaller does not make it more powerful). I suspect I’m missing something fundamental here, but being neither a mathematician nor a scientist I’m not sure what it is.

My second point of confusion has to do with something I came across when I was reading up on the inverse square law. In the description I found the following statement: "At large distances from the source (compared to the size of the source)…”. What I’m wondering is what constitutes a “large” distance compared to the source. Is it twice the size? Ten times?

Thank you for any help you can give me.

Improve this question
$\endgroup$
2
  • 1
    $\begingroup$ Which inverse square law are you talking about? If the energy output is $8.9876\times 10^{13}\;\mathrm{J}$ it will always result in an output of $8.9876\times 10^{13}\;\mathrm{J}$, and never $4.0050\times 10^{14}\;\mathrm{J}$. Neither the inverse square law for electric fields, nor the inverse square law for gravity, nor sound attenuation, nor any of the others can possibly affect that. $\endgroup$
    – N. Virgo
    Commented May 6, 2014 at 6:09
  • $\begingroup$ Also, note the dimensions. You're most likely comparing apples and oranges right now. Energy and energy density have different dimensions. $\endgroup$
    – Ruslan
    Commented May 6, 2014 at 8:58

1 Answer 1

Reset to default
4
$\begingroup$

If the total energy is $E$, then what you've worked out is the energy density $E/A$ i.e. the energy per unit area. There's no problem with the energy density being greater than the total energy because they are different quantities.

You say:

making an explosive smaller does not make it more powerful

and that's true, but compressing the energy from the explosive into a smaller area does make the energy per unit area greater.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.