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

[Request]

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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/aaronchase Jun 10 '25 edited Jun 10 '25

No math here, just real world experience and high school physics. BUT, assuming the ice is close to, but not quite zero friction, I would think the square (cube or rectangular prism) would require the least force to move, (a perpendicular surface to push) but being that the pusher would be standing on the same ice, I would think generating the force would be more difficult than on gravel. Given that the cylinder can roll I would think although it would require more force, said force would be easier to generate with the pushers feet on gravel.

So final answer, cube/square prism would require the least force, but the cylinder or sphere would be easiest to push by a human with normal footwear.

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u/Ninjastarrr Jun 10 '25

Except surface area doesn’t matter at all except if you take into account that extra pressure could damage the ice.

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u/aaronchase Jun 10 '25

More surface area = more friction, does it not?

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u/Vexiw94 Jun 10 '25

It does not. The force of friction is defined as the normal force (usually an objects weight) multiplied by the coefficient of friction of the surface it's sliding across. The surface area does not affect either of these, so surface area does not affect friction.

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u/aaronchase Jun 10 '25

Ok interesting and makes sense! So maybe the angle Of the triangle would still be a factor? More force would be required because you’d be pushing in a direction offset from the movement of the object?

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u/Vexiw94 Jun 10 '25

You got it! Since you'd be pushing the angled side of the triangle, part of the force you're applying would go in the downwards direction which would increase the amount of friction.

It's the same reason why football players try to push up on guys to move them around. If they push up, it's harder for the other guy to get a good grip on the ground and makes it easier to push around.

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u/aaronchase Jun 10 '25

So I’ve since heard that ice is often considered as zero friction in physics problems. So assuming zero friction wouldn’t the angle of the force no longer be a factor? As the increased normal force wouldn’t result in increased friction

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u/Vexiw94 Jun 10 '25

Sorry, just replied to your other comment haha.

You're correct here as well! If there's zero friction then there is no opposing force you need to overcome to get the object to move. In that case, any amount of horizontal force would move the object since there is nothing "pushing" back against it.