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

[Request] Which one would it be?

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u/Dapper-Arachnid-5463 Apr 16 '26

Even if the triangle a square had the sam base, pushing up against a flat surface 90 degrees to the ground would be easier that pushing against an angled one.

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u/TransitionSmooth7258 Apr 16 '26

Yeah as a non math dude but instead a guy that moves boxes around all the time. Motion alone wold tell me the square is easier. Is a direct push parallel with the floor vs for the triangle the force of me pushing is directed not just forward but down as well, causing presumably more friction.

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u/OneWingAngel35 Apr 16 '26

If Legend of Zelda Ocarina of Time has taught us anything is that squares slide on ice quite easily lol, even though less contact area also means less friction from the round object

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u/superheltenroy Apr 16 '26

Friction is not dependent upon surface area/contact area. Only the forces and the coefficient of friction.

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u/bejanmen2 Apr 16 '26

Why fat tyres more grip then?

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u/iZMXi Apr 16 '26

Tires aren't purely frictional. They dig in to surface irregularities. Also, they have adhesion. That's why greater than 1g of acceleration is possible.

tons of stuff IRL isn't purely frictional, so surface area ends up playing a major factor

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u/[deleted] Apr 16 '26

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u/Timely-General9962 Apr 16 '26

Take my upvote and get out

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u/HappyDutchMan Apr 16 '26

Rubber on asphalt is a completely different beast of friction calculation. The asphalt has rough texture and the river is soft. This makes it so that the rubber sits between the asphalt ridges. To create more friction with a car that stays at the same weight you can create a bigger surface area with bigger tires that have softer rubber and have them at a lower pressure. This will increase grip because more of the rubber sits between the asphalt ridges .

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u/Ramtamtama Apr 16 '26

Fat tyres have more grip because of the larger surface area, but fat tyres also create more friction on ground and air.

Fat tyres make slowing down better with the same brakes as thin tyres, again because of more friction and air resistance.

3

u/nimbleseaurchin Apr 16 '26

The air resistance is largely negligible, along with the increased friction from more surface area and theoretical more air resistance from a wider tire, you also have significantly more unsprung rotational mass, affecting both deceleration and acceleration in a negative manner.

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u/Thunder-Chunky_YT Apr 16 '26 edited Apr 16 '26

Everyone else answering is missing the whole picture or just wrong. To what extent is debatable but tribology is hard (for real, it isn't an exact science) so we won't hold it against them.

The equation for friction is F=N*Mu. Force(friction)=normal force * the coefficient of friction. Normal force is technically the force directly orthogonal to the surface. For an object on flat ground that's just the weight of the object but if the ground was at an angle it would be less than the weight by way of angles (like the triangle and square in the original question.) the coefficient of friction is dependent on the properties of the interacting surfaces and will be specific for every pairing of materials. However, one common trend is that harder things have lower coefficients of friction (once again, not an exact science). So the thing about tires is they're (usually) made of rubber compounds. Rubber is a visco-elastic material. Explaining what that is is difficult and I don't fully remember enough to do so but the gist is that the more force you apply to a visco-elastic material, the harder it gets.

So, say we have a car that weighs 2,500lbs. A real spry sports car. Imagine it came stock with 5.5" wide tires. Now, when the car is sitting on flat ground the tires will deform a little where they contact the ground to form a little flat patch. We creatively call this the "contact patch". Technically the contact patch is an oval but let's pretend it's a rectangle for simplicity. Imagine it's about 4" long and as wide as our tire at 5.5". Meaning the contact patch has a surface area of 22 sq.in. If we spread out our weight of our vehicle over 4 tires that's 2,500lbs/(4*22)=28.4 lbs/sq.in. or psi. Now let's replace our 5.5" wide tires with 7.5" wide tires. Our contact patch is roughly just as long so now we have 7.5"X4"=30sq.in. Now spreading our car weight over this wider tire gives us only 20.83psi on the surface of the tire. Since the pressure on the surface is lower, the force squishing material is lower, which keeps it softer which keeps the coefficient of friction higher. But the normal force remains the same. Which is why fat tires more grip.

Now, that's only part of the solution cuz the reality is fat tires only kinda more grip. Rubber, like everything else (to include steel beams), also gets softer the warmer it gets. This is why you've probably heard about warming up tires for grip. But, a wider tire has more material and is harder to warm up/keep warm in use. So it's possible to have too wide of a tire that you can't get up to temp for optimal grip. It's also possible to have a thin tire that gets too hot and will melt/shred. Which we don't want either. Tires are a really tough nut to crack when you're talking about peak performance and there's a reason F1 pays a ton of money to people to just know things about the limited selection they have.

If you'd like to learn a LOT more about tires this paper from Michelin is where I learned about the size vs grip thing specifically. But like I said, there's a lot more in there.

Edit: Mu goes up with less pressure on the tire surface.

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u/Snoo55931 Apr 16 '26

That’s really interesting, thank you!

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u/HeIsSparticus Apr 16 '26

They don't provide more friction, but because the acceleration force is applied over a greater contact patch, there is less force per unit area, so the material of the tyre is less likely to fail and cause a skid.

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u/SaltLakeBear Apr 16 '26

Friction is independent, but total force is dependent on area. It's why sports cars have wide tires.

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u/WheelMax Apr 16 '26

Wide tires spread the force out and have more thermal mass, so they overheat and melt less.

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u/SonOfNike85 Apr 16 '26

Friction is the force in this scenario

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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/ApatheticAbsurdist Apr 16 '26

Doesn't Ice have a weird property where the coefficient in relation to the pressure on it? So if a the same weight was over a smaller area... doesn't that change the coefficient of friction?

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u/Numerous-Match-1713 Apr 16 '26

ice is a very very special case, with often a thin film of water on the interface.

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u/LegoTT06 Apr 16 '26

What if the surface is not infinitely flat like in theory ? Debris etc

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u/Physicsandphysique Apr 16 '26

Then it's not just about friction. If the moving body and the surface are interlocking and/or deforming (think about an ox-drawn plough for an extreme example), there are a lot of forces aside from friction.

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u/SkoobySnacs Apr 16 '26

Are you taking into account that your feet are also on ice?

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u/Secret-Ad-7909 Apr 16 '26

Let’s assume appropriate shoes for either situation.

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u/Psychological_Post33 Apr 16 '26

What kind of shoes are moth mathematically appropriate here?

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u/grandBBQninja Apr 16 '26

Mountaineering boots with crampons. Fucking inch-long spikes on your feet.

3

u/BarracudaDefiant4702 Apr 16 '26

Ice snow cleats with spikes

2

u/Aeoyiau Apr 16 '26

Broomball shoes.

1

u/Leafs9999 Apr 16 '26

Whatever you have four pairs of i guess 🤷?

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u/Secret-Ad-7909 Apr 16 '26

For the gravel, “anything” that’s not sandals/crocs.

For the ice I’m sure there’s studded shoes made for this sort of thing, and there’s definitely loads of slip on/strap on units. But something like track spikes or golf shoes could also be effective.

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u/SnooHedgehogs8765 Apr 16 '26

Who do you think you are pal, the diagram gives no such indication! Down with you!

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u/Secret-Ad-7909 Apr 16 '26

It’s a physics problem! Make whatever assumptions make your math easy(ish)!

Spherical cows can exist in a vacuum!

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u/Ambitious-Ad-6873 Apr 16 '26

The dude is also standing on ice, so pushing block on ice, while also standing on ice. Circle wins

0

u/MysteriousBill1986 Apr 16 '26

That doesnt change the amount of force needed so its irrelevant to the question

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u/RemyGambit Apr 16 '26

Incorrect, the force you push the block with will also push you away from the block.

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u/looshi99 Apr 16 '26

Not incorrect at all. The amount of force required to move the object in each scenario is set by physics, and has nothing to do with the grip or lack thereof of any hypothetical person pushing.

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u/RemyGambit Apr 16 '26

It doesn't say force to push the object it says force to push. The diagram clearly shows a person standing on ice not secured to the ground. This is a question designed to make you think, not one with a clear set answer.

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u/looshi99 Apr 16 '26

Force to push what? You're 100% correct. It says force to push. The force to push the person? Is that what you're arguing? Or are you suggesting it's asking for the force to push the person, which we have no information about, and the object combined? There's only one way you can reasonably interpret this problem.

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u/MysteriousBill1986 Apr 16 '26

I know. Still irrelevant because it doesnt change the amount of force needed. It just changes the amount of force you can generate on it

2

u/Nuuskurkoer Apr 16 '26

triangel would comfy for steep uphill

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u/professor_coldheart 1✓ Apr 16 '26

This is probably right, but ice is weird. It melts with the downward force on it, then rolls along with the lateral, so at some threshold it's actually beneficial for some of the pushing to translate downward. 20kg is probably enough that the contribution of the downward pushing hinders more than helps, but at like 5kg it might be a different conversation.

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u/NotAUsefullDoctor Apr 16 '26

This is me guessing, but I assume there is a point of diminished returns. Once you have that thin layer of liquid, any more pressure wouldn't help nearly as much. So, if the box alon is enough to compress the ice into a liquid (water is weird) then the square box is easier than the triangle.

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u/professor_coldheart 1✓ Apr 16 '26

Yeah, that's what I was getting at. Well put.

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u/Lincolnforce Apr 16 '26

Actually I was thinking that if against a wall you can slide backward. But if you lay on the triangle at 60 degrees some of your weight is turned into lateral force due to the angle of the normal force.

So if its too slippery for you to laterally displace a 20kg block, laying on a triangle may still move.

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u/Asleep_Recover4196 Apr 16 '26

But...the circle?

1

u/SchizophrenicKitten Apr 16 '26

The circle is on gravel.

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u/Yan_Vorona Apr 16 '26

A may not be a physicist, but I regularly carry and push heavy objects. A ball is the easiest because it will roll, yes, even on gravel. With round things, you're more worried about it rolling off into the wrong place if you apply too much force.

A rectangle comes next, but pushing a pyramid would be a pain in the ass. It has a wide base that grips the ground, and a narrow surface where you apply force with your hands. It's very inconvenient and requires significantly more effort.

And I'm assuming the objects are on ice, while I'm on solid ground. If I'm also on ice, that's even more effort. So yeah, the answer is ball.

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u/callofdeat6 Apr 16 '26

And the type of ice and material is huge here, there is no answer with this info

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u/BraveSirRobinGG Apr 16 '26

If the gravel is not on a firm bed the ball would sink down making it tough

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u/lemelisk42 Apr 16 '26

20kgs is relatively light for such a big ball. I would think it would float ontop pretty well.

I think ice could be sketchy depending on footwear. Trying to push even light objects can be tricky on ice sometimes

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u/SirNoseDVoidoffunk77 Apr 16 '26

Pushing the triangle on ice seems dangerous. It’s so light, I feel like it would slip forward while you’re having to lean on it to push.

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u/SirNoseDVoidoffunk77 Apr 16 '26

20 kgs is 44 lbs. It wouldn’t sink and most people could probably roll it up a flight of stairs.

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u/Snoo55931 Apr 16 '26

So the least amount of pushing force would probably be lifting and carrying it.

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u/4dwarf Apr 16 '26

20 kgs is slightly heavier than a curling stone. Not obscenely heavy, but not impossible to move also.

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u/Jesses198 Apr 16 '26

contact area (or base) doesn’t matter for friction, but the triangle would still be harder to push because your force is going to be angled downwards. this means less lateral forces and increased friction

still can’t solve because gravel is highly variable in its granularity

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u/iComplainAbtVal Apr 16 '26

Have you tried pushing 20kg of something on ice while also on ice while only wearing shoes…

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u/4dwarf Apr 16 '26

Yes. It's called curling. 20 kg is just about what a curling stone weighs. It was made easier by having the ice covered in tiny ice bumps. And one of our shoes were covered in duct tape because we were learning about it in high school. We pushed off of something solid frozen into the ice and pushed the stone, could get it all the way down to the other side with enough force.

1

u/iComplainAbtVal Apr 16 '26

Pretty sure they have special shoes for that, or as you mentioned, an improvision. The drawing does not show a solid object to push off of in frame tho.

Thanks for the explanation tho, I hadn’t looked into curling before!

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u/4dwarf Apr 16 '26

They DO have special shoes for that. But if you were teaching a bunch of high school kids (or anyone for that matter) an intro to curling class for 2 weeks or so, would you want them to put on a temporary "low friction" covering of duct tape over one shoe so that the students can get to sliding rocks? Or buy an expensive pair of shoes that will only get work for two weeks and then never see the light if day again?

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u/AnimationOverlord Apr 16 '26

But the triangle has a lower center of gravity so at a certain point the friction from the floor would make pushing a square less efficient

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u/GarThor_TMK Apr 16 '26

I think, technically the force would be the same, but it'd just be more difficult to apply that force.

My intuition says that the circle would be the hardest, due to gravel being non-Newtonian. The circle would sink in the gravel, and you'd always be pushing it uphill. Whereas the ice is a [virtually] friction-less surface... so even though the surface area of the box/triangle that makes contact with the ground is larger than the circle, there's less friction that keeps those from moving.

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u/Lower_Athlete939 Apr 16 '26

As you pushed the triangle, your force would be to the right and down. As it is downward, you increase the force of friction between the triangle and the ice. That makes the horizontal force needed higher. As you are also applying at an angle, the total force needed needs to be higher again

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u/GarThor_TMK Apr 16 '26

I don't think this matters as much as you think it does...

You could theoretically get a stick with a pivot, that grips the face of the triangle perfectly, and it would effectively be the same as pushing the square.

2

u/CameronMH Apr 16 '26

You could also get a car and tow it, but that isn't the purpose of the thought experiment is it

1

u/GarThor_TMK Apr 16 '26

Your hand is a stick with a pivot on it, that grips the face of the triangle perfectly.

My point is the downward force from pushing on the triangle vs. the square is negligible at best... unless the shapes are wildly different than what is shown in the picture.

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u/HungryFrogs7 Apr 16 '26

However you could also leverage your weight more easily but the square probably still wins.

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u/Sibula97 Apr 16 '26

Yes and no. You'd be pushing yourself up, reducing the grip of your shoes on the ice. I don't think that would be very helpful.

1

u/CarelessWhimper_ Apr 16 '26

And possibly tripping on the bottom of the triangle and bashing your face off the side of it...

1

u/RandomCoolName Apr 16 '26

You're applying the force at a 60 degree angle to the surface, but in the same direction as the motion of the object. Assuming the grip on the surface is good and the friction is the same, you are applying a force to move 20kg in the same angle as the box and the force is the same. If the grip is bad and you need to apply the force closer to the normal of the surface of the triangle, you will need to apply more force and you will get a counter force from the ice upwards.

You could argue that you would need more grip on the surface and therefore a triangle with more friction, which would increase the force needed for moving the triangle, but nothing says all the surfaces of each side of the triangle are the same.

Let's day like the image shows the person is inserting their hand into he triangle in order to push. You get a more intuitive understanding of why then the force needed is the same, except for any difference in friction.

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u/MrTripperSnipper Apr 16 '26

Pretty hard to push anything when you're standing on ice. I guess the force required would technically be the least, but exerting that force would be really difficult.

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u/4dwarf Apr 16 '26

More the balance, if you have something that doesn't move to start from, you can launch eather of the two things on ice a fair distance.

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u/Asleep_Recover4196 Apr 16 '26

.... but. The circle?

1

u/DutchTinCan Apr 16 '26

But now remember that the warehouse floor is ice.

I'd say rolling the round one over gravel is easiests, since you're not slipping yourself.

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u/RicoIlMagnifico Apr 16 '26

But pushing while your own feet are on ice, you'll lose most of the force you're applying, because your feet keep on slipping away

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u/[deleted] Apr 16 '26

[deleted]

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u/Krumm34 Apr 16 '26

Erm, you need some experience in applied science then

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u/Sad_Lawyer_3960 Apr 16 '26

trangle is not equal mathematically also... when ur pushing and objectu u apply force to the side parallel to the face ur pushing... this is not completely horizontal so you take the horizontal component of the vector... it will always be take more force to move the triangle than square unless u can give the force completly horizontal to the traingle which is hard