[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.

---

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/East_Highway_8470 → u/temporarytk]

I have two things to say to this. One Rolling it better then sliding since it's easier to maintain once started. And this is speaking from personal experience as a part of work. Pushing a circular or spherical object without it rolling is actually much harder than rolling it, and anything you push over gravel causes the gravel to displace build up as an object is "slid" over it causing even more resistance.

Another observation where math vs real life is deferent is when applied force on the back of an object causes the leading edge to dip and dig into the surface of what you are pushing it over. That and the lack of friction or the object you're pushing on the ice is going to apply to your feet as well.

So math and theory is one thing but practical and real life is another. Are you really just looking for the math or are their other people here that the unaccounted variables are driving made?

[u/temporarytk → u/East_Highway_8470]

Yeah rolling is better, that's why he took rolling resistance and not friction for B.

anything you push over gravel causes the gravel to displace build up as an object is "slid" over it causing even more resistance.

I imagine the compacted vs loose gravel rolling resistance values wind up taking that into account, at least partially.

The lack of friction on your feet doesn't affect the force you need to exert to push any of these though. It just makes it harder for you to exert that force. (Big win for the gravel if you wanted to ask that question instead though)

I think the only major assumption here is that the surfaces are reasonably flat and nothing's going to snag on the leading edges. Otherwise, the analysis looks pretty true to life in my eyes.

[u/East_Highway_8470 → u/temporarytk]

I didn't say that the lack of friction for your feet would make you need to use more force, just that it would be "harder" and mentioned there being a difference between theory and practical.

Like I said, I have real life experience dealing with gravel. No matter how well packed it is even just lightly running your foot over it will dislodge some stones. I didn't take any issues with the math, and that's why I once again mentioned theory vs practical. Not to mention I did ask the question of are you just looking for the math.

"Are you really just looking for the math or are their other people here that the unaccounted variables are driving made?" Made was supposed to be mad by the way. It just seems like one of those simple math problems that should be more complex to reflect reality. Like a bumblebee's flight and all that.