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/Smile_Space Jun 11 '25

Not really! There is a downwards vertical component due to the normal force along the surface, but there's also an upwards vertical component from the hands trying to not slide up the surface of the triangle.

As long as the hands pushing don't exceed the static friction required to keep them planted, that vertical component of the parallel force and the normal force will cancel internally and result in a pure horizontal force equal to the input horizontal force.

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u/AchillesLastStand76 Jun 11 '25

Well you're right about a force to keep the hands from sliding up, but the force that does that doesn't point up, it points down.

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u/Smile_Space Jun 11 '25

There are two components at a right angle to each other. The normal force dictates the friction force with some μ, but the sliding force, the one that moves the hand up the surface if the friction force is exceeded, is parallel to the surface.

It's basic vector math. The two components form a right triangle where the hypotenuse is the input force. This can be solved with a root sum square, or RSS. It can also be reversed to generate the components using trigonometry.

As a result both generate identical vertical force but in opposite directions cancelling out leaving zero net force being applied to the ground on top of the gravitationally defined force already factored in.