What are the factors that govern over the path that shrapnel and/or other particles follow upon explosion of explosives(the ones that are planted i.e. stationary ones) etc. Is it possible to predict the path of all the particles ? Also is it possible to make the particles move in desired directions ?
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asked Dec 26, 2013 at 15:38
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$\begingroup$ Please define the following: 1) explosion of a static object? 2)symmetry of the exploding body prior to explosion? 3) homogeneity of the material which is not consumed in the explosion? There are plenty of guided-charge designs. Heck, a rifle bullet is one such! $\endgroup$– Carl WitthoftCommented Dec 26, 2013 at 16:44
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$\begingroup$ en.wikipedia.org/wiki/Gun $\endgroup$– DumpsterDoofusCommented Dec 26, 2013 at 20:18
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4 Answers
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To predict the path of shrapnels one needs to perfectly know how the bomb is built i.e. how it will defragment. So it's theoretically possible but only if we're given the initial conditions.
As Sagnik pointed out what you know is that the total momentum will be conserved. So for a "stationary" bomb the total momentum will be 0, for fireworks the global motion of the shrapnels will be parabolic (if we neglect air resistance).
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I think only one factor governs the path of shrapnels : Conservation of Momentum.
Even when the explosive is planted, the principle of conservation acts, for the total sum of displacement of shrapnels would then equal Zero. Thats why for a stationary explosive, shrapnels scatter in all directions.
It is not "impossible" to predict the path of all particles theoretically. Practically, unless we have a special explosive that defragments along certain parts I dont think its possible to keep account of so many shrapnels, for example : a real life grenade.
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$\begingroup$ Keeping account of the multitude of particles is definitely possible, it may be tedious and time consuming, but definitelg possible. $\endgroup$ Commented Jan 13, 2014 at 15:07
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$\begingroup$ true that. it was just a personal opinion. $\endgroup$– SagnikCommented Jan 13, 2014 at 15:11
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The path is governed by tragectory, initial velocity, collisions, air resistance, gravity and deflection from the ground.
The trajectory is decided by initial position.
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As pointed out in other answers, Conservation of Momentum will be the main and most important factor. However, that isn't the only factor.
Internal Pressure: The explosive may (and IRL will, to varying extents) generate uneven pressure. This may (and IRL will, to varying extents) dictate how other factors related to the acceleration of the shrapnel will apply.
External Pressure: In order to generate outwards acceleration, and explosion and/or shrapnel have to overcome whatever external force acts upon them. Shrapnel acceleration from an explosion in a vaccum will be different to one at atmospheric pressure, which will be different to one underwater, which will be different to one in dense magma.
Fragmentation: Shrapnel often includes or depends upon the fragmentation of the explosive's casing and/or of other fragmentaton elements. You'd need to know the design and material of these elements in order to understand and/or predict how the shrapnel will form, as shrapnel pieces of different shapes, masses and orientations will be accelerated differently upon the explosion, as well as later due to external resistance (assuming the explosion is not in vacuum).
Disregarding all of the factors other than CoM, the shrapnel's initial trajectory will be a vector of whatever momentum was present before the explosion, plus whatever momentum is accquired from the explosion.
