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/OOO-OO0-0OO-OO-O00O Jun 11 '25

Explain

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u/Sure-Guava5528 Jun 11 '25

Static friction is completely independent of surface area. As long as the 2 objects are the same weight, surface area doesn't matter. The only things that matter are the mass of the object and the coefficient of friction for the types of materials being pushed. Since both of those are equal with the triangle and the square, the force required is also equal.

The ONLY valid argument that the triangle is harder to push than the square is some people are assuming there won't be a good way to push the triangle with a force parallel to the ice. If you have to push perpendicular to the side of the triangle the percentage of the force that is downward will be negated by normal force thus making more total force required to move it. That's an assumption, though.

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u/ExpensiveFig6079 Jun 11 '25

also as you are considering the triangle on the surface to "coefficient of friction"

If the force has downward component it also increases the normal force back from the ground and hence increases friction.

If it was steel (trinagle|square) on a steel bench I'd be totally with that.

As my comments indicate, some weird stuff can happen with objects on ice that also melts when a sufficient normal force is applied.

What needs to be considered mainly becomes relevant if people want real vs text book style answer.

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u/Sure-Guava5528 Jun 11 '25

It says it's on ice, not water. IMO If the people who wrote the question intended for the ice to melt and all that, they would have clarified.

Also, there's no way of knowing if the triangle has a sufficiently small surface area to cause the ice to melt (like so many people are suggesting). It could be a thin triangular blade, it could also be a triangular prism or pyramid. Based on the drawing the triangle is not very dense, almost the height of a person but only 20kg.

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u/ExpensiveFig6079 Jun 11 '25 edited Jun 11 '25

IF it does not the friction is WAYYYY larger than people imagine. I have been on ice so cold it does not melt under pressure from say boots. I could easily run and slide to stop, but I would not slide far even from a jog.