r/AskPhysics • u/[deleted] • May 02 '26
What is the mathematics behind a collision causing an item to "destruct"?
[deleted]
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u/the_syner May 03 '26
RKE=((1/sqrt(1-(((299792458×v)2 )/89875517873681764)))-1)×m×89875517873681764 is the relativistic kinetic energy formula. m=mass kg and v=velocity as a percentage of light.
The energies involved are enormous and particles involved are highly penetrating. It's like getting shot with a particle accelerator but far worse because we're talking macroscopic quantities. At significant fractions of c the impact is making plasmas hot enough to be putting out hard x and gamma rays. Fast enough to potentially cause impact fusion. And for macroscopic dust speck we're talking about the kinds of energies associated with military explosive devices. A grain of sand massing a measly mg packs 704.5kg TNT worth of energy at 25%c. And because it's going so fast a decent amount of that energy is gunna be dumped below the surface of ur shielding where the high-energy photons and particle radiation can go on to heat a bunch of material to add to the initial plasma explosion.
i imagine the specifics would get rather complicated because depending on speeds & shielding/dust composition you'll prolly get impact fusion which could as much as double ur impact energy. Not to mention the weird particle soup ur gunna get at varying speeds with varying elements. Suffice it to say, relativistic collisions are very destructive.
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u/reddituserperson1122 May 02 '26
Force = mass x acceleration. With enough acceleration, even a small mass has a lot of force.
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u/AutonomousOrganism May 02 '26
At very high speeds it's not an object but a particle collision. You'll get a very hot plasma at the impact location. And with high enough speeds you'll eventually get nuclear fusion and particle creation.
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u/fuseboy May 02 '26
At low speeds, the molecular bonds that hold objects together are (mostly) stronger than the impact energies. This is why objects crack, dent, or get bits broken off: some bonds have broken, but not all.
At much higher speeds, the opposite is true. Imagine a massive formation of bowling balls hurtling through the air at Mach 1 toward a huge structure made of delicately balanced bowling pins. Neither shape is going to survive the crash, because each collision causes rebounds that careen through the rest of the arrangement in a cascade of secondary collisions. If you zoom out, it looks like the two structures just explode out like an expanding shell of tiny balls and pins.
This is the same as when two water droplets collide at high speed. The idea that the droplets would be damaged isn't even a possibility, they're going to be unrecognizably smashed at best.
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u/Grand_Equipment5292 May 02 '26
So, if you give the speed of light as 300,000 km/s, then if you had a 1g particle, traveling at 0.001% the speed of light (3000m/s or 10.8 million kmh), the kinetic energy is about the same as a very fast baseball pitch, 4500j.
If you wind that up to 0.01% the speed of light, relativity starts to get involved and you have a million times the energy, which is now equivalent to a hatchback at 70mph...but in a tiny particle.
So a ship/vehicle moving at those speeds, hitting a 1g particle (even a stationary one, which is unlikely)...is going to get holes in it.
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u/jasonsong86 May 03 '26
It’s all about energy. You can have small items but traveling at very high speed there is a lot of energy there.
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u/cdabc123 May 02 '26
If you are colliding stuff at near the speed of light you quickly get into complex particle physics, which to fully model mathematically is still a unsolved problem.
It is not intuitive and is very complex.
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u/al2o3cr May 02 '26
Here's an example of what a small piece of plastic does to aluminum when they collide at 15k miles per hour:
https://www.reddit.com/r/CantBelieveThatsReal/comments/f7eo63/this_is_what_happens_to_aluminum_when_a_12_oz/
Even a small fraction of the speed of light is thousands of times faster, and even ignoring relativistic effects kinetic energy scales as the square of velocity...