Energy distribution between fragments in an explosion

[ISU20CpreE]

Ok so far I have been thinking that an explosion is nothing else than a inelastic collision. So energy is lost and momentum is conserved therefore $$P_i = P_f$$, The problem asks for how much kinetic energy did each piece acquire in the explosion, I also know that there was 7800 J released.

In order to make calculations easier I come up with:

$$m_a=1kg$$

$$m_b=1.5kg$$

$$E=7800J$$

I can set up the problem but I can't see further steps I need a bit of explanation please.

 

[Diane_]

I'm not really sure what your question is, nor the use to which you want to put those numbers. Perhaps this will help:

Momentum conservation certainly applies in an explosion as it does everywhere else. If one imagines a bomb, say, sitting in space before the explosion occurs, with total momentum zero, then calculates the momentum of the individual pieces after the explosion, one could easily predict that the vector sum would also come to zero. I suppose one could also consider it an "inelastic collision", as it's certainly the case that kinetic energy is not conserved. "Collision" is probably not the best word to use, as it implies two things coming together, but I can't think of a better one at the moment.

In any event - can you tell me what your goal is? It would be easier to suggest further steps if I knew where you were going.

 

[Tide]

I think ISU's goal is to determine the kinetic energy of both fragments given their total energy and recognizing their total momentum is zero. Unfortunately, we can't help ISU until s/he shows some work!

 

[ISU20CpreE]

I think ISU's goal is to determine the kinetic energy of both fragments given their total energy and recognizing their total momentum is zero. Unfortunately, we can't help ISU until s/he shows some work!

Reasonable. My work until now is:

$$0=m_1V_1f+1.5m_1V_2f$$ or $$V_1f= -1.5_V_2$$

after that i don't have a clue. I am sorry but I will have to work on this in the morning I have a test in 4 hours I need to rest, thanks for the help. I will be asking further questions, sorry I can't stay.

 

[Diane_]

OK - I'm going to assume that your explosion has left only two fragments, and you're trying to work out what happens. Yes?

So, using momentum conservation, you have a relationship between v1f and v2f. (Side note: Since the initial velocity was zero, why bother with the "f" subscript?) You need another relation to solve for them exactly.

You know that the total energy released was 7800J. Assume it all went into kinetic energy - you should, then, be able to write a second equation relating v1f and v2f. That will give you two equations in two unknowns, which you should be able to solve.

Does that do it?