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In the sequel to the original movie, Tremors 2: Aftershocks, Earl Basset and team resort to a very strange method of killing graboids.

A piece of dynamite or other explosive is placed on a remote-controlled toy car. As the car moves, the sound attracts the graboids and they supposedly gobble it up. Once they have eaten the car, a detonator with the hunters is operated and the bomb explodes inside the graboid, killing it.

I have two, perhaps, silly questions.

  1. How can a bomb that can sometimes be scratched/damaged from pressure, in a creature's belly, underground, be signalled with an overground detonator?
  2. Even if the signal could get through, how would the bomb explode underground, in the absence of any oxygen?
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Let's start with..

How would the bomb explode underground, in the absence of any oxygen?

Bombs don't require oxygen to explode, they just need an explosive material and some form of detonator. Fire requires oxygen to continue burning but explosive materials do not.

An explosive material, also called an explosive, is a reactive substance that contains a great amount of potential energy that can produce an explosion if released suddenly, usually accompanied by the production of light, heat, sound, and pressure.

Explosive materials may be categorized by the speed at which they expand. Materials that detonate (the front of the chemical reaction moves faster through the material than the speed of sound) are said to be "high explosives" and materials that deflagrate are said to be "low explosives". Explosives may also be categorized by their sensitivity. Sensitive materials that can be initiated by a relatively small amount of heat or pressure are primary explosives and materials that are relatively insensitive are secondary or tertiary explosives.

Wikipedia

On to

How can a bomb that can sometimes be scratched/damaged from pressure, in a creature's belly, underground, be signalled with an overground detonator?

There's a certain amount of "plot magic" here but the bombs aren't really under any pressure underground since they have been swallowed whole.

As for the radio signals, it's true that these don't propogate very far underground, usually just a few feet but, in this case, that's exactly how deep the graboids are. You can tell since the explosions make it to the surface with relatively small amounts of explosive per device

enter image description here

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    To clarify on the "bombs don't need oxygen" point: a chemical explosion of this sort is, to grossly simplify things, a process of extremely rapid combustion. To be that rapid, you simply cannot rely on atmospheric oxygen, so explosive materials generally contain oxygen somewhere in their chemical makeup. All they need then is something (like a spark) that starts the reaction. The effect of the presence or absence of atmospheric oxygen on this process is small enough to be more or less unnoticeable. – anaximander May 4 '18 at 13:29
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    Random sidenote, Fuel Air Explosives do need oxygen and are very cool: youtube.com/watch?v=i20zvZ-3MMw Of course, this doesn't impact the explosives described in answer. – NPSF3000 May 4 '18 at 16:24
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    Alternative solution for the signal could be a dead-man switch style. The signal is constantly being sent and, once it stops, the explosive is triggered. – David Starkey May 4 '18 at 16:31
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    @KonradRudolph Not all explosives need oxygen. See for example copper(I) acetylides, benzvalene, cyanuric triazide, disulfur diazide, octaazacubane, and silver nitride. All of those have no oxygen, but are primary high explosives even in a completely oxygen free environment. None of them combust when they detonate either, which is what requires oxygen. All of them have high energy bonds that take very little energy to break (and as a result most are shock sensitive). – Austin Hemmelgarn May 4 '18 at 18:14
  • @AustinHemmelgarn It was a complete brain fart. They need an oxidiser, not oxygen. – Konrad Rudolph May 4 '18 at 18:38

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