Balancing a Ruler - Numberphile Numberphile English (auto-generated) English

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Science & Technology 360.9K views 10.9K likes 82 dislikes 05 Jan 2017 Show Contributors 5

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Contributed subtitles

English Amy Draper

Kevin Smith

Rishi Kanaujia

Portuguese (Brazil) Hérus Willyan

Slovak Nia Bride

here's a ruler where is the center of gravity well presumably in the middle

Here's a ruler. Where's the center of gravity? Where presumably it's in the middle, and that's certainly true.

and that's certainly true if I put my finger in the middle somewhere there oops it balances so that's the center of

If I put my finger in the middle, and somewhere there, Oops!, It balances.

gravity but suppose that I attach some weight at one end well where is it well

So that's the center of gravity. But suppose I attach some weight at one end, wher-where is it?

it's not so easy to guess right but there is a very nice way of finding a

Well it's not so easy to guess right? But there's a very nice way of finding the center of gravity,

center gravity which I'll start by doing

which i'll start by doing it without weight.

it with that way you simply put two fingers and to support the object and then you bring them toward each other

You simply put two fingers to support the object, and then you bring them toward each other,

and automatically you see one stop someone starts one stops and they meet

and automatically, you see that one stops and one starts and one stops-and then they meet

automatically at the center gravity and I can even do this with eyes closed

automatically at the center of gravity. And I can even do this with my eyes closed

this works in general if I attach for example a mass at one end I don't know

( Opens mouth) This works in general if i attach, for example a mass at one end.

where the center of gravity is but my fingers automatically find the center of

I don't know where the center of gravity is but, my fingers automatically find the center of gravity. (Opens mouth)

gravity and if I put a hefty mass at the

And, if I put a hefty mass at the other end,

other end well the center gravity will be really close to the end and indeed it

well the center of gravity will be really close to that end, and indeed,

finds the center of gravity over here and if I put both of them at the same time where is it well it automatically

it finds the center of gravity over here. And if I put both of them at the same time, where is it? Well aaaa-it automatically

finds the center of gravity again I'm not deliberately controlling the

finds the center of gravity. Again I am not deliberately controlling the movement of my fingers,

movement my fingers I'm just bringing them slowly toward each other and

I'm just bringing slowly towards each other.

automatically one of them starts

And automatically one of them starts sliding and the other stops and the

studying and the other stops and the others start studying and one stops and

other starts sliding and the one stops and they meet always at the center.

they meet always at the center so how

So how does it work?

does it work it works because of a really simple but why do the applicable principle you know when two bodies sliding against each other or they are

It works because of a really simple but, widely applicable principle.

sort of stopped and they want to start sliding there is something that's opposing the slide and that's called

to start sliding, there is something opposing the slide and that's called friction

friction it turns out that the friction is proportional to increases with the force that's pressing the two body

It turns out that the friction is proportional to increases with the force that is pressing the two bodies

against each two bodies against each other but also is proportional to some

against each-against each other but also, is proportional to some coefficient.

coefficient the factor matter it's very very widely established observational

The fact of matter, it's very very widely established observational fact.

fact when you are studying the friction is slightly smaller than when years

When you are sliding, the friction is slightly smaller than when you are stopped and wanted to start sliding.

top ten wanted to start sliding we talked about the difference between the dynamic friction that's the friction that's acting when the ball is already

We talk about the difference between the dynamic friction ( that's the friction that's acting when the bodies already sliding)

sliding versus static friction when these two bodies are stopped at against each other and then they want to start

vs static friction (when the two bodies are stopped against each other and then they wanted to start sliding)

slightly static friction is a little larger than the dynamic friction okay

Static friction is a little larger than dynamic friction. Okay.

suppose that I start bringing those two

Suppose that I start bringing those two fingers toward each other.

fingers toward each other whether they some random error in the beginning so

There will be some random error in the beginning.

first this finger started moving for

So first this finger started moving for some reason. Ok.

some reason okay when this finger is closer to the center of gravity than this finger this finger is taking more

When the-this finger is closer to the center of gravity than this finger, this finger is taking more weight

weight over the ruler than this finger

over the ruler than this finger, so there is more friction there.

so there is more friction there and so because there's more friction on this finger than on this finger naturally the finger that slides is this

And so because there is friction on this finger than on this finger, naturally the finger that slides is this one.

one but you see once this finger starts starting it's starting with dynamic friction whereas this is stopped at

But you see, once this finger starts sliding, it's sliding with dynamic friction, whereas this is stopped at static friction.

static friction so in principle you see when these are at equal distances from it from the center of centre of gravity

So, in principle you see, when these ar-equal distances from the center of-center of gravity.

they take equal weights so they should have equal frictions but that's not true

They take equal weights so they should have equal frictions, but thats not true

because this is already sliding so it's taking the sliding friction dynamic

because this is already sliding, so it's taking the sliding friction (dynamic friction) whereas this is taking

friction whereas this is taking static friction so this one can keep sliding although it's taking more and more weight because

static friction. So, this one can keep sliding although it's taking more and more weight

it's friction is a little less than this one so it overshoots towards the center

because it's friction is a little less than this one, so it overshoots towards the center,

and when it's really close then the other one starts moving and so on that's why they alternate stick-slip mechanism

and when it's really close, than the other one starts moving and so on. That's why they alternate.

this is called slip sticks lip stick and

Stick-slip mechanism this is called-slip-stick slip-stick

then they come toward each other so if you take a weighted version well for a

and then they come toward each other, so if you take a weighted version,

long time this left finger slides because left as seen from your sides because it's of course far from the

well for a long time this left finger slides because, left as seen from you, slides because it's of course it's far from

center of gravity so it has a decimate on it so it has less friction but it overshoots and then the other one starts starting over shoots over shoots over

the center of gravity so it has less weight on it, so it has less friction But, it overshoots and then the other one starts sliding, overshoots overshoots overshoots and then

shoots and then they finally meet in the center so this mechanism is using the slightly difference between the dynamic

they finally meet in the center. So this mechanism is using the slight difference between the dynamic and

and Static frictions and the fact that well when you come at equal distances from the center of gravity the one

static friction and the fact that, well, when you come at equal distances from the center of gravity

that's already sliding come over shoot and then once that stops it stays there for a while and then

the one that's already sliding can overshoot, and then once that stops it stays there for a while and then only when

only when the other starting finger has stopped kunti this one starts sliding again and

the other sliding finger has stopped, can (the) this one start sliding again and then overshoot and then come to

then overshoot and come towards them and

us and that's how they come to a stand

so on they come towards them is there an accepted number of times there will be a

Brady: Is there accepted number of times there will be a slip and a stick,

slip and a stick right over the course of 30 centimeters that is arbitrary that

like over the course of thirty centimeters?(tha-te) that seems arbitrary. Tadashi: that is very very-that is an

is very very that's an excellent question I think it's a case-by-case and you can do a very very precise calculation using a simple model of

excellent question. I think its umm case by case, and you can do a very very precise calculation using a simple

stick slip and so forth but the fact of the matter is that it is a very unstable

model of stickslip and so forth, but the fact of the matter that it-a is a very unstable process.

process I mean depending on tiny tiny regularities of the surface and so on

I mean depending on tiny tiny irregularities of the surface and so on

and the number seems to vary quite a lot

so and I think we have to resort to just experiments and the theoretical

So, I think we have to resort to just experiments and theoretical calculations does give

calculation does give some picture but I don't think it gives really as accurate in a prediction as the numbers suggest

some picture but I don't think it gives really as accurate um you know prediction as the numbers suggest

paper clips is linked with our band but not between themselves let's finish with

paper clips is included in our band but not between themselves. Let's finish with something that is work in

something that is working progress so far we have been linking paper clips together and sometimes we refer to this as addition

progress. So far, we have been linking paper clips together and sometimes we refer to this as addition