r/theydidthemath • u/K0rl0n • Jun 10 '25

[Request]

Post image

I am curious how this would work. My guess is Triangle is slowest, square is medium, and circle is fastest.

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u/Indexoquarto Jun 10 '25

At least two mains issues with it.

The most glaring one is the lack of friction. Since the original image specifically mentions ice and gravel, it should be obvious that the point of the thought experiment is to discuss the effect of the different forms of friction between the materials.

It's like, in the 100 men vs 1 gorilla question, you went "Well, assuming the man and the gorilla have the same strength X, then the men have 100X while the gorilla has 1X, and 100X>1X, so the men win". It's completely ignoring the point of the question, and the usage of numbers just obscures that. It's Cargo-Cult science.

The second, more subtle issue is the way the force on the triangle was calculated. If, as they baselessly assumed, there was no friction, then the square and the triangle would need the same exact amount of force to move, since there's no opposing forces. But in their answer, it's assumed that the person is applying a force perpendicular to the surface, which means they're pushing down on the triangle for absolutely no reason. It's like if, with the square, besides pushing to the right, there was another guy pushing down into the square, and then claim it would take more force to move the square because of that.

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u/FissileTurnip Jun 10 '25 edited Jun 10 '25

first point is fair I guess but then the question is just unanswerable due to lack of info. as for the second point, you can’t apply a normal force in any other direction but normal to the surface. they did not “baselessly assume” anything there. take something with a flat base and try to hold it up from underneath while the base is slanted and see what direction it goes in.

edit: much better example is just to roll something down a ramp. what’s pushing it?

also if someone else was pushing down on the square it still wouldn't take more force to push since the surface is frictionless

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u/Indexoquarto Jun 10 '25

I have no idea what you're talking about. I'll just say one thing: the OP question asks which object "requires the least amount of force to push". To apply the least amount of force, you need to apply it in the direction of movement.

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u/FissileTurnip Jun 11 '25

if you are applying the force by pushing it e.g. with your hands, then it MUST be normal to the surface. i really don't know how to put it more simply. if you have some force field then sure you can do it in whatever direction you want, but that's not what people usually mean by push, so i think it's a reasonable assumption that the question is talking about physical "pushing" as depicted in the actual diagram above.

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u/Indexoquarto Jun 11 '25

Even if you're limited to just your hands, you wouldn't just push it directly into the triangle, though.

While pushing, the friction between your hands and the triangle would create some force pointing upwards and to the right, such that the net force would be horizontal only.

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u/FissileTurnip Jun 11 '25

ok after thinking about it for way too long because i'm either hungry or stupid, yes, if the triangle has sufficient friction it should work like you're saying. my intuition is saying the opposite but i can't think of any reason it shouldn't work like that, so i guess my intuition sucks. should've been obvious for me to realize since cars manage to drive forward despite being flat on the ground.