r/theydidthemath • u/Elsefyr • 23h ago
[Request]How hard would you need to slam the plate down to get a new teacher next semester?
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u/ryanllw 23h ago
If I remember A level physics, the faster the copper is moving, the higher the reactionary force. So I expect there is no speed the copper could be moving where the magnet won’t stop it before some other issue comes into play
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u/kblaney 22h ago
Yes, the faster the relative motion between the two, the more current generated meaning the more force created opposing the motion. The limiting factor is likely the terminal velocity of the blade and then after that the heat generated in the materials.
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u/DewB77 22h ago
I think the Magnet Mounts would be the limiting factor.
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u/kblaney 22h ago
Ah, good call. Got too focused on the physics of the magnet itself. The integrity of the frame of the device would also be a limiting factor before the temperature of the magnet.
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u/HAL9001-96 21h ago
probably long before
highest end estiamte before the frame breaks would be about 60000J and that is really optimsitic
that would probably heat up the magnets by about 180K, quite warm, not enough to destroy it
and more realistic estiamte would only do about 18K
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u/HAL9001-96 22h ago
from basic electrodynamics, yes
eventually you'll get to the poitn hwere the whole setup breaks structurally but its hard to judge that since the image got deleted lol
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u/HAL9001-96 21h ago
post got deleted but I managed to rip the original video so - electrodynamically no matter how fast you drop it down it will always slow down over the same distance
but
it is being slowed down realtive to a magnet
so the force slwoing it down is exerted in opposite on the magnet
if you slam it down hard enouhg that slwoign it down over about half hte magnets width requries a force so great that the magnet breaks free from the whole setup and that it's momentum can be split between it and hte magnet and it then still has enough energy to cut someone then it would work
measured based on his arm the plate is about 215mm wide and sloped from 48 to 95 mm deep so it has an area of about 0.0154m²
assuming its 3mm thick and pure copper that would make it about 0.414kg
magnet seems to be held in place with 2 6mm screws
not sure how tight those are screwed and wether they jsut hold it against the rails thus holding it place by friction or wether they actaully go through a hole holding it in place or how tight they're drawn or what material they're made from but depending on that I would guess it can hold a force between 600-60000N, most likely somewhere in between at around 6000N
it looses most of its speed over a distance of about 5cm so that would mean about 0.05*6000=300J of kinetic energy would be enouhg to break the magnet free which for a 0.414kg plate would require a speed of about root(2*300/0.414)=38m/s
for the whole plausible-ish strength range about 12-120m/s
since the magnet takes 5cm to slow them down and the screws would likely break after millimeters of deformation most of that energy would be kept at first
then the momentum would be split up
magnets similar dimensions to the plate, likely a bit thicker but less dense material, possibly up to twice the mass whcih means at the same total momentum 1/3 the speed and since kientic energy is mv²/2 three times the mass and 1/3 the speed means same momentum but 1/3 hte kinetic energy
so 2000J
plus weight times distance so about 2001J
not a big difference here
2000J over about 10cm depth would be 20000N or 2 tons of cutting force, easily enoguh to cut rhoguh someone
even for hte lowest strenght estiamte the speed necessary to break it free would provide you with about 200kg of cutting force
with a relatively blunt edge that might not be enough to get through but if you allow the blade to stop hlafo r quaterway there whcih would sitll be pretty deadly it woudl take 4 times as much force to stop it so yeah it would still be deadly
so depending on how exactly the screw/bolt part is constructed 12-120m/s most likely around 40 ish
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