Conservation of Energy and Momentum in an Explosion

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Discussion Overview

The discussion revolves around the conservation of energy and momentum during explosions, particularly focusing on the kinetic energy changes before and after an explosion. Participants explore theoretical aspects, calculations, and implications of energy conservation in explosive events.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant questions the calculations of kinetic energy (KE) after an explosion, noting a discrepancy in equating total KE after the explosion to 4m.
  • Another participant provides a calculation of KE before the explosion and suggests subtracting it from the KE after the explosion to analyze energy changes.
  • A participant discusses the behavior of combustion gases in an explosion, suggesting that the original KE is not lost but becomes insignificant due to the mass of the surrounding atmosphere.
  • One participant presents specific numerical examples of KE for bomb pieces before and after detonation, showing a total KE that appears consistent with the stationary state of the bomb.

Areas of Agreement / Disagreement

Participants express differing views on the calculations and implications of KE in explosions. There is no consensus on the interpretations or the correctness of the calculations presented.

Contextual Notes

Some calculations and assumptions regarding mass, velocity, and energy transformations are not fully detailed, leading to potential ambiguities in the discussion. The dependence on specific definitions of energy conservation in explosive contexts is also noted.

JamesG23
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Hey, I have a question about explosions and how kinetic energy works during them. I have outlined my question on the attached image. Please let me know if something is wrong or needs clarifying. Thank you.

IMG_2061.png
 
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It would be easier to comment if you had typed up your work. But anyway:

Viewed from the lab frame, you calculated the total KE after the explosion = (26m)/4. Sounds good. Not sure why you set that equal to 4m.

The KE before explosion = (1/2)m(9) = (18m)/4. Subtract that from the KE after the explosion and see what you get.
 
Doc Al said:
It would be easier to comment if you had typed up your work. But anyway:

Viewed from the lab frame, you calculated the total KE after the explosion = (26m)/4. Sounds good. Not sure why you set that equal to 4m.

The KE before explosion = (1/2)m(9) = (18m)/4. Subtract that from the KE after the explosion and see what you get.
Oh shoot I don't know why I simplified like that. Maybe I thought it was 24/6. Thank you
 
JamesG23 said:
I have a question about explosions and how kinetic energy works during them.
In an atmosphere, the explosion of a flying bomb produces a sphere of hot combustion gas that has a very low density compared to the original explosive charge.
That sphere is effectively stopped immediately by it's low mass and the area of it's greater cross-section.
The original KE is not lost, it is just insignificant when applied to the huge mass of atmosphere that encloses the explosion.
 
Let's say the bomb pieces are 10kg each.
KE of each piece at ±2 m/s: 1/2mv2=20J
Total KE of bomb pieces: 40 J

KE of both bomb pieces at +3 m/s before detonation: 90 J
KE of bomb piece at +5m/s: 125 J
KE of bomb piece at +1 m/s: 5 J
Total KE of bomb pieces after explosion: 130 J

But look. 125+5-90 = 40 J
The same as when the bomb is stationary!
 

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