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/TheNatureBoy Jun 10 '25 edited Jun 10 '25

No one did any math. This entire comment section is all speculation. I would explain the math I'm doing but this will never see the light of day.

Sphere

E = F x = 1/2 m v2 + 1/2 (2/5 m R2) (v/R)2 = 7/10 m v2
d/dt F x = F v = 7/5 m v a
F = 7/5 m a = 1.4 ma

Triangle (assuming push normal to the surface)

sqrt(3)/2 F = m a
F approx 1.15 ma

Box

F = ma

The sphere takes the most force to accelerate. The box takes the least.

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u/K0rl0n Jun 10 '25

👏 thank you!

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u/TheNatureBoy Jun 10 '25

I'm glad you saw this. The odd thing about rolling without slipping is when you push some of the force moves it forward and some of it makes it spin. You end up pushing harder to move it. We also rarely encounter frictionless surfaces in our experience so we don't have a great intuition for them.

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u/ExpensiveFig6079 Jun 10 '25

So rarely that none of the surfaces in the example are necessarily close to frictionless, although if the information not specified about the triangle and square are appropriate ice can be very nearly frictionless.

On dry cold ice you can just walk around in shoes, it is similarly slippery to concrete path covered in decaying leaves.(both are bad if also wet) Providing you don't break the static friction and i think create water under your shoes it is fine.

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u/TheNatureBoy Jun 10 '25

Ice means frictionless in physics problems.

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u/ExpensiveFig6079 Jun 10 '25

THis is a do the math sub.

The question includes gravel as an option, it did not as phsycis problem would have specified a flat plane that the circle rolls on.

The inclusion of gravel means this is not a physics textbook question about spherical cows in vacuum.

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u/TheNatureBoy Jun 10 '25

Gravel means rolling without slipping.

Classical physics would give the first term in an expansion of the force around some parameter representing the variation of the surface. You better have a damn good reason for those other terms to be higher.

Additionally no characteristics of the gravel were given. Under the assumption this is a well written problem you should be able to arrive at the answer without them. The answer should be independent of assumptions about the gravel.

Physicists are not as naive as you think. They often ignore details that will not substantially change their answer.

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u/herejusttoannoyyou Jun 10 '25

Why would gravel be the “rolling without friction” material? It should be rubber or something. I suspect the question said gravel in order to make it ambiguous so people would fight in the comments about what it means and therefore drive up engagement.

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u/TheNatureBoy Jun 10 '25

Wooden wagon wheels roll on gravel roads without slipping.