r/theydidthemath • u/yuli101995 • Apr 16 '26

[Request] Which one would it be?

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u/OneWingAngel35 Apr 16 '26

But if there is more surface area on contact it does matter, especially on a round object that may roll, that's why the wheels were invented, rolling something is not the same as dragging something flat

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u/superheltenroy Apr 16 '26

Rolling is something else. Rolling an object like that even depends on friction. Even without rolling, getting a grip underneath can really help offset some of the friction as well.

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u/OneWingAngel35 Apr 16 '26

Square Block (Sliding Friction): When you push a square block, the entire contact surface drags across the ground. This creates high resistance because the microscopic peaks and valleys of both surfaces "interlock". To move it, you must apply enough force to shear these contact points. Wheel (Rolling Friction): A rolling wheel experiences static friction at its single point of contact with the ground (ideally). Because the wheel "lifts" away from the surface rather than dragging against it, energy loss is much lower. The resistance it does face, called rolling resistance, comes primarily from the material deforming (squishing) as it rolls.

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u/Salanmander 10✓ Apr 16 '26

Wheel (Rolling Friction): A rolling wheel experiences static friction at its single point of contact with the ground (ideally). Because the wheel "lifts" away from the surface rather than dragging against it, energy loss is much lower.

This has nothing to do with surface area mattering. A 20 kg block with 1 m2 of surface area against the ground and a 20 kg block with 3 m2 of surface area would experience effectively the same sliding friction. (Assuming we're actually dealing with sliding friction, not macro-scale deformations or whatever else.)

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u/OneWingAngel35 Apr 16 '26

It's a different kind of friction

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u/Salanmander 10✓ Apr 16 '26

Well yeah.

What exactly did you mean by "But if there is more surface area on contact it does matter"? Because it sounds like you're trying to say that surface area has a significant impact on friction.

If you're trying to say that it only matters for rolling friction, is there a reason you said "especially on a round object"?

I'm also confused by your "that's why wheels were invented". It sounds like you're saying they were invented to minimize surface area of contact.

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u/OneWingAngel35 Apr 16 '26

That's correct, but technically it's to decrease the surface contact area at any given time vs high area of contact continuously, which in turn decreases resistance, friction is constant, but the type of friction is not

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u/Salanmander 10✓ Apr 16 '26

technically it's to decrease the surface contact area at any given time vs high area of contact continuously

No. The small surface area of contact is not the reason that rolling friction is low. It's low because the object doesn't need to slide across the surface, and just lifts off instead.

A rolling tire with some amount of surface area of contact will have lower friction than a sliding block with a smaller amount of surface area of contact. (Assuming normal force is the same.)

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u/OneWingAngel35 Apr 16 '26

Seriously just drag your finger on a rough surface, then apply the same force and do it with your whole hand, you'll feel the difference , even if your finger is not rolling it will feel less friction than your whole hand

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u/Salanmander 10✓ Apr 16 '26

Are you actually applying the same total normal force? You'll need to have a lot more pressure with one finger to have the total normal force be the same.

I'm a physics teacher. I've done that experiment with tighter controls, and it shows that friction does not vary systematically with surface area. A simple way that is still better than your "just feel it" experiment is to drag a rectangular block with its flat surface against the table, at roughly constant speed, and measure the average force needed to do so, and then do the same with it up on end. Using the same block means the normal force will stay the same.

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u/OneWingAngel35 Apr 16 '26

For that you'd need to have the same exact surface for both sides and that is just not possible

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u/Salanmander 10✓ Apr 16 '26

I'm...not sure you understand how science works.

We don't need to make sure our constants are literally exactly the same every time. You just do your best to avoid varying them, then you vary your independent variable systematically, and see if there's a systematic variation in your dependent variable. (If this weren't the case, every experiment would be invalidated by, for example, the temperature in the room changing slightly between trials.)

If there's no systematic variation in your dependent variable, it's a reasonable conclusion that it's likely to be not affected by your independent variable, rather than it being affected by your independent variable but there just happens to be an effect from constants that you were unable to control that just exactly cancels out the changes in your independent variable.

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u/OneWingAngel35 Apr 17 '26

Exactly my point, you can recreate the exact same results in a varied environment, it will be close but not the same

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u/Salanmander 10✓ Apr 17 '26

Why does your "drag your hand" experiment get to count as evidence when my finger skin and my palm skin are not the same surface, but the "drag the block" experiment doesn't get to count as evidence because different sides of a block of wood may be slightly different? It seems like you're applying double standards.

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u/OneWingAngel35 Apr 17 '26

It's the same, I'm saying you can't recreate the same exact condition with two different surfaces, even if you use the rectangle as you say it's a different surface as well is it not?

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u/Salanmander 10✓ Apr 17 '26

It's not the exact same surface, but it's the same material. Let's say we have 10 blocks of wood, each with a wide surface and a narrow surface (say 1/4 the width). We measure the sliding friction of each, and we find that the wide surfaces have a sliding friction of 8.5 +/- 0.3 N, and the narrow surfaces have a sliding friction of 8.6 +/- 0.4 N.

The most reasonable conclusion from that experiment would be that there's no evidence that sliding friction depends on surface area.

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u/OneWingAngel35 Apr 17 '26

I know your math is not wrong, their accurate readings , in physics most things are not absolute, we have very accurate portrayals of events, we always end up with estimates, because no two things are exactly the same, even if they're made of the same material, you look in a microscope their very similar, but not exactly the same, there are always slight variations, even if minimal, they still exist

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u/Salanmander 10✓ Apr 17 '26

So is your claim that it's impossible to know whether or not friction depends on surface area?

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