A shell fired into the air explodes into two equal fragments. Which of the following is conserved.
Stacey Warren - Expert brainly.com
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Which do you think it is? Are there any choices you can rule out right away?
I think it's momentum and impulse but I can only choose one
That's good though! You've ruled out energy.
While energy in a closed system is always conserved, there are so many forms that energy can turn into that you generally can't say that only a single type is conserved. You could only say energy is conserved if you consider kinetic, potential, sound, light, etc etc.
You're also right to link impulse and momentum. The important distinction to make here is that while an impulse can add to the momentum of a system, its not really conserved itself. You can apply an impulse to a system but it doesn't hold on to that impulse, it uses the impulse to change its momentum.
If you want a more thorough explanation, I'd recommend this site: http://www.physicsclassroom.com/class/momentum/Lesson-1/Momentum-and-Impulse-Connection