Assuming the person is durable enough to not break his hand, how fast would he have to move his fist to punch completely through a solid steel door that is 1 inch thick?
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2$\begingroup$ If you assume the hand ist hard enough to do that, it is not a matter of speed but mainly of force. If you don't apply enough force, your hand just pushes against the steel without moving anything. If the force is high enough, your hand will break through the steel even if you move it slow. The form of the broken steel will just be different. So you have to specify how you want to break the steel. $\endgroup$– CharisturcearOct 20, 2020 at 18:13
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$\begingroup$ A clean hole punched in it like aluminum foil. $\endgroup$– PraearcturusOct 20, 2020 at 18:18
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$\begingroup$ Unfortunately, I doubt you'll get a clear answer to this. There is a sad lack of concrete science dedicated to punching through things, I've found. (worldbuilding.stackexchange.com/questions/142841/…) A bummer for those of us who are curious about the actual specifications of our super powered characters, lol. $\endgroup$– MarielSOct 20, 2020 at 18:32
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$\begingroup$ Are the fist arm of normal human mass, or this mass is somehow increased? $\endgroup$– AlexanderOct 20, 2020 at 18:32
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$\begingroup$ If you ask here, folks don't know the answer (it's apparently REALLY complicated to figure out, since so many variables are involved) and if you ask the hard science stacks (physics SE, etc.) they shut your question down for being too unrealistic due to any handwaving (like assuming your super powered character won't break his fist in the first place). Oh well. I hope you do get what you're looking for anyway... $\endgroup$– MarielSOct 20, 2020 at 18:36
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1 Answer
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As clarified in the comments, the door is an ideal immovable door and we are to ignore that in a normal door the hinges or bolts which hold it closed will shear long before a big fat projectile like a human fist will punch a hole.
In this idealized case, we can compute an approximation of the necessary velocity of an non-deformable human fist backed up by the entire weight of the unbreakable unbendable human to punch through:
The shear strength of steel is about 350 to 1400 MPa (50,000 to 200,000 psi). Let's assume 1000 MPa. (To get an idea of how much this is, 1000 MPa is about 10,000 atmospheres.)
To punch a neat hole, we must apply enough force to overcome the shear strength of the 25 mm of steel along the circumference of the hole; let's say that the circumference of the fist is about 400mm (it's a big fist but not huge).
400 mm circumference times 25 mm depth is 10,000 square mm, or 0.01 square meters.
0.01 square meters times 1000 megapascal is 10 meganewton. (For a rough idea of bigness, that's about 1000 tons-force.)
10 meganewton of force applied on a 100 kg body (big fist, big man) gives an acceleration of 100,000 meters per second squared.
With a uniform acceleration $a$, a body will come to rest in a given space $S$ (= the thickness of the door in our case) when it starts with a velocity $v = \sqrt{2aS}$. Plugging in the numbers, we find that $v = \sqrt{2 \times 100,000 \times 0.025} = 71 \,\text{m/s}$. That's about 250 km/h or 155 mph.
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$\begingroup$ @Praearcturus: It's the thickness of the door. The fist must travel at least one inch. (If the initial speed is higher then the fist won't come to a stop and will continue moving after punching clean through the door; but it must travel at least a distance equal to the thickness of the door, or else it won't punch completely through.) $\endgroup$– AlexPOct 21, 2020 at 4:59
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$\begingroup$ This seems suspect. Ignoring that they would pulverize their fist, 155mph doesn't seem as far away from peak human athleticism as I assumed this would be. And you didn't even choose the lowest number for steel's shear strength. $\endgroup$– John OOct 21, 2020 at 13:46
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$\begingroup$ @JohnO: (It has no relationship with reality. In reality, the human would go splash. The strength in compression of human bones is very very much inferior to the strength of steel; and the bones in the hand are tiny. In fact, a human can easily break their bones if they hit a steel door running at full speed.) It's a 100 kg indestructible body hitting an one inch steel plate at 250 km/h over a small area (about 127 cm² or 20 sq.in.). For a mental picture, imagine a 100 kg (200 pound) cannon ball hitting the plate. Have you seen how a car looks like after hitting a wall at 250 km/h? $\endgroup$– AlexPOct 21, 2020 at 14:24
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$\begingroup$ @JohnO if you had read the question you would know that he is indestructible. $\endgroup$ Oct 21, 2020 at 14:39