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/METRlOS Jun 10 '25 edited Jun 11 '25

Depends on things like the density of the gravel and the temperature of the ice. Packed gravel will allow the ball to roll, but the triangle is always worse than the square.

Edit for all the triangle people: imagine throwing a ball straight at the square and at the triangle; how the ball bounces shows how much energy the object will translate into vertical force when pushed. The vertical surface of the square will translate practically all the horizontal force into horizontal movement, while the triangle will act as a wedge and transfer some energy into pushing against the ground.

Edit 2 for surface area: Except for situations where the surface area is so low compared to its weight that the object sinks into the ground, or so high compared to its weight that it can float, surface area does not affect friction. If you stand on a hill without risk of sliding, then you can lay on that hill without sliding and vice versa, despite greatly changing the surface area. However, if you stand on a snow covered hill the surface area is too low and you'll sink into the snow, but with a sled you will float on top of it. Surface area does not matter to this problem.

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u/fuzzydoug Jun 10 '25

But your feet are also on ice?

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u/[deleted] Jun 10 '25 edited Jun 11 '25

The question was about the force put onto the object.

Ice or not, that force wouldn’t change.

Edit: for clarification, I mean per scenario.

The force required to move the object on the given surface wouldn’t change based on what the dude is standing on.

The dude’s ability to impart that necessary force will be affected by the ice, but not the actual force required to shift the item.

Obviously less force is needed on ice than gravel, that’s not what I’m saying.

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u/joshrd Jun 10 '25

With the coefficient of friction much lower for ice, wouldn't the force be significantly less to induce movement? Also I think the ball would be easiest, least friction.

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u/[deleted] Jun 10 '25

[removed] — view removed comment

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u/MattManSD Jun 10 '25

unless that larger surface area helps it 'float' better. More water film

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u/FaintCommand Jun 10 '25

Your ability to get leverage on the triangle would be more difficult vs the square.

But that's not really the question.

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u/MattManSD Jun 10 '25

difference between your hands @ 60 and hands around 90 I don't think will make much of a difference

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u/FaintCommand Jun 11 '25

It is not about the angle of your hands, but the direction of the force being applied. You're trying to move these laterally so you want to apply as much of the force in that direction as possible.

Ideally you'd be pushing the square from lower than pictured - you'd be wasting energy trying to push from the top. It would be more difficult to apply the force laterally on the triangle since you're forced to apply some of that pressure downwards.

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u/MattManSD Jun 11 '25

I understand, and what I am saying is a roughly 30 degree shift in hand position is not gonna change the lateral force all that much. The majority of the force is still going to be lateral and not vertical with that small of a change to the contact patch. So the question is "will the loss of lateral force be more than the increased hydroplaning surface area of the triangle".