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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 —

( 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 —

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