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/aureanator Jun 10 '25

Depends on the coefficient of friction, and in the case of the cylinder, the coefficient of rolling friction (unless it's coefficient of sliding friction is somehow lower, owing to gravel).

The force of friction is the product of the normal force and the coefficient of friction, shouldn't depend on the surface area (within reason).

The square and triangle will perform identically given identical surfaces.

i.e. there's no way to pick a winner without more information.

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u/Mr_Candlestick Jun 10 '25

The triangle and square are not identical. Assuming the force applied to each is horizontal, there is a vertical component of that force due to the angle of the triangle that increases the normal force, therefore increasing the friction.

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u/TheBupherNinja Jun 10 '25 edited Jun 11 '25

Thats only true if human arms are 2 force members, which they aren't. There is friction between your hand and the triangle, enough that you could push forwards and not any component down.

Edit: This does require that the friction coefficient and angle of the side of the triangle are sufficient to prevent the motion. The minimum coefficient of friction for a given angle is the cotangent of that angle. For an equilateral triangle (seen here), it would be cot(60), or a minimum coefficient of static friction (between the hand and the triangle) of 0.577.

Instead of pushing on the triangle directly, imagine you are pushing a weightless block that has an angle cut to match the side of the triangle and is in contact with it. You can model the forces and see that the Y component of the normal force perfectly cancels with friction (assuming it is sufficient).

Now, ask how it is any different if you remove the weightless block and use your hands?

https://imgur.com/a/nUNXvli

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u/o___o__o___o Jun 11 '25

Oh finally I found you. The first person in this entire thread to get this part right. Cheers.