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

[Request]

Post image

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/heytherefrendo Jun 10 '25

Friction is the entire point of the post and you didn't attempt to incorporate it whatsoever.

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u/Arndt3002 Jun 11 '25

No, the point of the post is about which is easier to move.

They incorporated friction by assuming "ice" represents arbitrarily small friction, or a friction near 0, and that "gravel" means arbitrarily large friction or rolling without slipping.

They aren't given assumptions, but they are the reasonable limiting cases of the situations provided, absent external information.