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In my Physics textbook there is sample problem in which a firecracker placed inside a coconut of mass M, initially at rest on a frictionless floor, blows the coconut into three pieces (A, B and C) that slide across the floor. Mass of piece C is 0.30M and its final velocity is 5.0 m/s. We have to find speed of piece B, with mass 0.20M

The author made some conclusions before solving the problem:

  1. The coconut and its pieces form a closed system

  2. The explosion forces are internal to that system

  3. No net external force acts on the system and Therefore the linear momentum of the system is conserved

My question: If Coconut and its pieces form a closed system then the explosion forces are external forces doing work on the system. How can linear momentum be conserved when an external force is doing work in that system? How can the sum of linear momentum of all its pieces be zero when an external force is doing work on the system?

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  • $\begingroup$ I have made an answer, but just to be sure can you please quote the example exactly? Often users post questions about what they think the example is saying rather than what it is actually saying, and so details are missed that are essential to the issue. $\endgroup$
    – BioPhysicist
    Commented Jul 7, 2020 at 15:09
  • $\begingroup$ @BioPhysicist I edited my question and added more details $\endgroup$
    – Forex007
    Commented Jul 7, 2020 at 15:17
  • $\begingroup$ If you have included everything word-for-word then my answer still stands as is. However, the best option would be to just quote the example exactly rather than giving what you think are the relevant details, just in case. $\endgroup$
    – BioPhysicist
    Commented Jul 7, 2020 at 15:24

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You are right to question this. Technically the system consisting of the coconut and the firecracker form a closed system$^*$, so that the entire momentum of this system is then conserved (assuming nothing flies into the air of course).

If you just considered the coconut as the system, then the force from the explosion is external (since the explosion is not the coconut pieces repelling each other), and the coconut could end up with a net momentum in one direction (with the fire cracker having an equal net momentum in the other direction). However, if we were told that the firecracker pieces had a total momentum of $0$ after the explosion, then we could also conclude the coconut pieces have a total momentum of $0$ as well. The same conclusion about just the coconut could then be arrived at using momentum conservation, but this extra information about the firecracker would be needed.

$^*$ Technically I suppose you would need to consider the air in the coconut too? Really what you want to have in your system is the coconut and whatever is pushing on the pieces of the coconut in order to say the momentum is conserved. But let's just assume here that it's the firecracker pieces pushing on the coconut pieces.

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