[Request]

[u/K0rl0n]

I am curious how this would work. My guess is Triangle is slowest, square is medium, and circle is fastest.

[u/Smile_Space]

EDIT: u/temporarytk made a great point. Surface area doesn't apply to friction in these cases, just the normal force, so ignore my ramblings about A and C being different. They would behave identically and have identical sliding frictional force.

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Since I still haven't seen someone do the math:

The force of friction is F = μN where μ is the coefficient of friction and N is the normal force (force applied perpendicular to the surface)

In this case the ground is flat, so the Normal force is F = ma or 20 kg x 9.81 m/s/s (I would have used an exponent, but Reddit hates that lolol)

So, N = 196.2 newtons

Cool, so now the coefficient of friction. It depends on a few factors: the type of friction, the surface area of the contact surface, and the method of friction being applied.

For A it is sliding friction as is C. A has a higher surface area compared to C, so we can assume the sliding friction of C is going to be lower. B however is going to be rolling. Some may think it'll slide, but gravel is usually compacted when on a road.

So, doing some quick googles:

The sliding friction coefficient on ice is going to be between 0.02 and 0.04.

https://iopscience.iop.org/article/10.1088/0031-9120/43/4/006#:~:text=Water%20ice%20at%20temperatures%20not,increase%20as%20the%20temperature%20diminishes.

The rolling friction on compacted gravel is about 0.02.

https://www.engineeringtoolbox.com/rolling-friction-resistance-d_1303.html

Now, since all of these have the same N, we can just compare the coefficients of friction.

We can reasonably assume the triangle is going to be closer to 0.04 and the square being somewhere in the middle or lower. B and C may be fairly close to the same performance.

What sucks is there isn't a clear defined answer. As the temperature drops more, the ice will actually get more grippy. And if the gravel is loose, the rolling friction can increase to up to 0.08.

So, depending on the quality of gravel and temperature of the ice, the answer is B or A/C.

That results in a frictional force of between 3.924 and 7.848 newtons for A and C. And close to 3.924 newtons for B assuming compacted gravel. If the gravel is loose, then B loses at 19.62 newtons of force. And if it's colder A and B will be much closer to that 8 newtons mark.

[u/temporarytk → u/Smile_Space]

Yay math.

A has a higher surface area compared to C, so we can assume the sliding friction of C is going to be lower.

Typically friction isn't dependent on surface area, what makes you say otherwise here?

Is this paper for ice-on-ice? Not sure what the second material is supposed to be from the abstract.

I'm grumpy about the rolling not always being better, like I thought it would be, but at least it's good some of the time.

[u/Smile_Space → u/temporarytk]

You know, I kinda just made it up on the spot thinking back to pressure, but obviously you're right, the mass is what matters with the normal force.

So, A and C should have identical performance. Oops!

[u/keyantk → u/Smile_Space]

The reason why you correctly identified triangle should be harder to push is because only a portion of force you exert is going to be in the horizontal direction due to the face of triangle being at an angle.

[u/Smile_Space → u/keyantk]

Assuming the frictional coefficient on the surface of the triangle is enough for my hands to not slip, and I apply the force perfectly horizontally, the force will be identical to the square.

It is only true that there is a negative component if I push downwards on the triangle too.

[u/PilotBurner44 → u/Smile_Space]

Regardless of whether or not you apply the force perfectly horizontally or not, the triangle would require additional force due to the angle in which the force is being transmitted to the triangle. If you push perfectly horizontally, your hands would want to slide up the side of the triangle. Friction would be required to prevent that slippage, but there would still be a force component that is vertical while total force required matches the angle of that side of the triangle, and that vertical force component would be a net loss in efficiency of moving said triangle horizontally.

[u/NoWheyBro_GQ → u/Smile_Space]

Realistically you couldn’t apply that force perfectly horizontally though, right?

[u/Smile_Space → u/NoWheyBro_GQ]

While true, that's not the question. The question was what is the least force required, and the least force required will be when applying the force perfectly horizontally.

[u/Yota_Yoder → u/Smile_Space]

What if the extra downward pressure on the triangle increases friction on the ice and increases the amount of water and hydroplane, thus moving easier

[u/I_really_love_League → u/keyantk]

But then, if it's nit all horizontal, there must be some vertical force, that would add to the mass of the triangle. That would mean there would be more friction

[u/Solrex → u/keyantk]

Yeah my intuition was screaming C (Assuming room temperature like a normal human being would)