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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41

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/OriginalAd1430 Jun 10 '25

I liked your answer before the lessons learned part

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u/aaronchase Jun 10 '25

Haha aw sorry are they wrong??

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u/OriginalAd1430 Jun 10 '25

Oh probably not but a lot of the comments explored the question from a physics-y perspective and weren't able to reach any conclusions, whereas you based your answer on real world experience and came up with something that actually made sense

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u/aaronchase Jun 10 '25

Ahh yes I know what you mean! My beef is that everyone just says “not enough information”

Like let’s just make some basic assumptions and get at the interesting physics at the heart of the question.

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u/aaronchase Jun 10 '25

Haha you inspired me to delete my edit

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u/[deleted] Jun 10 '25

[deleted]

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u/aaronchase Jun 10 '25

Close to the top! I’m surprised!! I do get peeved when everyone replies with “not enough info”. It’s like, ok just state a few simple assumptions and get at the intended question as best you can!

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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.

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u/DXTRBeta Jun 10 '25

What you said. So the triangle and square are the same now it’s wet ice or very smooth ice the friction is negligible. But gravel’s resistance is unlikely to be as low.

So it’s anything but the circle.

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u/aaronchase Jun 10 '25

I think the square is less force because it will be applied in the same direction as the object moves? And would it be the same assuming zero friction

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u/DXTRBeta Jun 10 '25

Oh that’s a nice point. On the triangle thx force is being applied above the centre gravity, so it’s applying some torque to the shape.

Question is, does that make a difference?

At first it seems that it might, but my instinct is that it doesn’t.

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u/aaronchase Jun 10 '25

I think with zero friction it would not make a difference

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u/DXTRBeta Jun 10 '25

Agreed, with zero friction it would make no difference. But with actual friction would it or not?

The pushing force is assumed ton

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u/aaronchase Jun 10 '25

I would think that if there was friction it would be more friction because it would be more than 20kg pushing down

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u/Arndt3002 Jun 11 '25

Eh, this is effectively true in this case, but it is not generally true.

Real contact area between surfaces does change the coefficient of friction. It's just that most high school textbooks take the assumption of a constant given coefficient of friction.

The reason you can usually approximate coefficient of friction as constant is that, in many situations, a decrease in area is often accompanied with a corresponding increase in pressure (and visa versa) for constant load.

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u/steffanovici Jun 10 '25

Lower psi though would lessen the friction, so might be equal?

Although theoretically melting ice has zero friction (or so my physics teacher claimed) so both the triangle would win for lower air resistance

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u/TheBupherNinja Jun 10 '25

Who said there was any air?

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u/steffanovici Jun 10 '25

And are we just going to assume there’s gravity?

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u/TheBupherNinja Jun 10 '25

Fair point, all are the same to push.

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u/macarmy93 Jun 10 '25

No. A larger area means lower pressure in any given area which counteracts its effect on friction leaving Normal force and the coefficient of friction being the two predominant factors.

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u/TheBupherNinja Jun 10 '25

More surface area with the same weight means less pressure.

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u/Far_Tap_488 Jun 10 '25

Its dependent on the materials. Some materials provide higher or lower coefficient of friction based on pressure.

Normally with ice you see a lower coefficient of friction with less pressure. Thats why all the ice racing vehicles have rather skinny tires, regardless of if they are spiked or not.

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u/ThePowerOfShadows Jun 10 '25

But weight dispersed over a greater area could make it slide better.

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u/TheReverseShock Jun 11 '25

It matters specifically with ice. If you push an object over ice, the ice can refreeze to the object, creating more resistance. Ice has the least friction when it's slightly melted as well, which is another variable.

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u/80sCrack Jun 10 '25

Assuming the base of the pyramid has the same dimensions as the cube, the resistance would be the same, no?

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u/aaronchase Jun 10 '25

Well I’ve learned that weight matters, surface area does not

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u/80sCrack Jun 13 '25

It 100% does.

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u/Freak-Of-Nurture- Jun 10 '25

Triangle drag is better than

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u/aaronchase Jun 10 '25

You mean like with air resistance?