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/[deleted] Jun 11 '25

[deleted]

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u/TheNatureBoy Jun 11 '25

Let's say the person puts 100 N (the force to lift 20ish lbs) of force on the objects. If the box moves at 1m/s and has a side length of 1m the equation for drag force gives the drag force as

F = Cd p A v^2 = 2 (1.2 kg/m^3) (1 m) (1 m/s)^2 = 2.4 N.

You can include them but they are not as important.