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# 8: Frictional Forces

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Today we're going to talk about friction, something...

( *students murmuring* )

Please, I have a terrible cold.

My voice is down.

Help me to get through this with my voice--

thank you.

We're going to talk about friction which we have never dealt with.

Friction is a tricky thing, not as easy as you may think.

I have an object on a horizontal surface.

The object has a mass, m, gravitational force, mg.

This is the y direction.

This could be the x direction.

There must be a force pushing upwards from the surface to cancel out mg because there's no acceleration in the y direction.

We normally call that the "normal force" because it's normal to this surface and it must be the same as mg.

Otherwise there would be an acceleration in the y direction.

Now I am going to push on this object with a force--

force Walter Lewin.

And we know that the object in the beginning will not start accelerating.

Why is that? That's only possible because there is a frictional force which adjusts itself to exactly counter my force.

I push harder and harder and harder and there comes a time that I win and the object begins to accelerate.

It means that the frictional force--

which is growing all the time as I push harder--

reaches a maximum value which it cannot exceed.

And that maximum value that the friction can achieve--

this is an experimental fact--

is what's called the friction coefficient mu which has no dimension, times this normal force.

We make a distinction between static friction coefficients and kinetic.

This is to break it loose, to get it going.

This is to keep it going when it already has a certain velocity.

The static is always larger than the kinetic for reasons that are quite obvious.

It's a little harder to break it loose.

Once it's going, it's easier to *keep* it going.

It is fairly easy to measure a friction coefficient by putting an object on an incline and by changing the angle of the incline, increasing it.

This is the angle alpha.

You increase it to the point that the objects start to slide down.

Here is the object.

This is the gravitational force, mg which I will decompose in two forces: one in the y direction--

which I always choose perpendicular to the surface--

and another one in an x direction.

You are free to choose this plus or this plus.

I will now choose this the plus direction.

I am going to decompose them, so I have one component here and this component equals mg times the cosine of alpha.

And I have a component in the x direction which is mg sine alpha.

There is no acceleration in the y direction, so I can be sure that the surface pushes back with a normal force, N and that normal force N must be exactly mg cosine alpha because those are the only two forces in the y direction.

And there is no acceleration in the y direction so this one must be mg cosine alpha.

Now this object wants to slide downhill.

Friction prevents it from doing so so there's going to be a frictional force in this direction.

And as I increase the tilt this frictional force will get larger and larger and larger and then there comes a time that the object will start to slide.

Let us evaluate that very moment that it's just about to break loose.

I'm applying Newton's Second Law.

In this direction, now, the acceleration is still zero but the frictional force has now just reached the maximum value--

because I increase alpha--

so this component will get larger and this component will get larger.

This component will get larger.

This component is still holding its own but then all of a sudden it can't grow any further and it starts to accelerate.

So Newton's Second Law tells me that mg sine alpha minus F f maximum at this point is zero.

And this one is mu static times N, which is mg cosine alpha.

This one is mg sine alpha.

This equals zero.

I lose my mg, and you see that mu of s equals the tangent of alpha.

It's that easy to measure.

So you increase the tilt.

We will do that later until it starts to slip and then at that critical angle that it starts to slip you have a value for mu of s for the static friction coefficient.

It is very nonintuitive that this friction coefficient is completely independent of the mass.

The mass has disappeared.

Think about it--

it's very nonintuitive.

If you double the mass, the angle would be the same given the fact that you have the same kind of object.

The friction coefficient only depends on the materials that you have the materials that are rubbing over each other.

It's also independent of the surface area that is in contact with this incline which is equally nonintuitive.

It's very nonintuitive, but we will see that that's quite accurate within the uncertainties that we can measure it.

If you have a car and you park your car you throw it on the brakes and you put it at an angle and you increase the angle of the slope the friction coefficient for rubber on concrete is about one so the tangent is one, so the angle is about 45 degrees.

So if the road were 45 degrees, the car would start to slide independent of the mass of the car--

no matter whether it's a truck or whether it is a small car--

independent of the width of the tires.

It doesn't enter into it even though you may think it does.

They would both start to slide at the same angle given the fact, of course the same road and the same kind of rubber.

I first want to show you some of this which is at first very qualitative.

I don't want it to become quantitative yet.

The difficulty with these experiments are--

I'm going to use this plank here--

that the moment that my fingers touch this plank or touch the bottom of any of the objects that I'm going to slide, then all hell breaks loose.

A little bit of water on the plank would locally make the friction coefficients larger.

My fingers have chalk on them.

A little bit of chalk on a local place would make the friction coefficient go down.

That's why, at this point, we'll keep it a little qualitative.

The first thing I want to show you is, if I take a rubber puck and I put the rubber puck on this incline and I have a plastic bin--

this is quite smooth, I put it on here--

that it's immediately intuitive that the friction coefficient of this plastic bin will be lower than of the rubber puck.

So when I increase the angle, you expect that first the plastic bin will start to slide and then the rubber puck.

And if I gave you the angles at which that happens you could actually calculate the two values for the friction coefficient--

which I will not do now, but I will do that later.

So all I want you to see--

I hope--

Terima Kasih Semoga Bermanfaat dan mohon Maaf apabila ada kesalahan.

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