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

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(students murmuring )

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Please, I have a terrible cold.

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My voice is down.

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Help me to get through this
with my voice-- thank you.

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We're going to talk
about friction

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which we have never dealt with.

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

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I have an object
on a horizontal surface.

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

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This is the y direction.

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This could be the x direction.

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There must be a force

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pushing upwards from the surface
to cancel out mg

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because there's no acceleration
in the y direction.

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We normally call that
the "normal force"

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because it's normal
to this surface

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and it must be the same as mg.

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Otherwise there would be an
acceleration in the y direction.

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

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force Walter Lewin.

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And we know that the object
in the beginning

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will not start accelerating.

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Why is that?

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That's only possible because
there is a frictional force

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which adjusts itself
to exactly counter my force.

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I push harder
and harder and harder

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and there comes a time
that I win

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and the object begins
to accelerate.

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It means that
the frictional force--

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

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reaches a maximum value
which it cannot exceed.

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And that maximum value
that the friction can achieve--

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this is an experimental fact--

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is what's called
the friction coefficient mu

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which has no dimension,
times this normal force.

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We make a distinction

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between static friction
coefficients and kinetic.

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

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This is to keep it going

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when it already has
a certain velocity.

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The static is always larger
than the kinetic

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for reasons
that are quite obvious.

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It's a little harder
to break it loose.

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Once it's going, it's easier
tokeep it going.

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It is fairly easy to measure
a friction coefficient

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by putting an object
on an incline

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and by changing the angle
of the incline, increasing it.

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This is the angle alpha.

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You increase it

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to the point that the objects
start to slide down.

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Here is the object.

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This is
the gravitational force, mg

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which I will decompose
in two forces:

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one in the y direction--

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which I always choose
perpendicular to the surface--

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and another one
in an x direction.

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You are free to choose
this plus or this plus.

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I will now choose this
the plus direction.

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I am going to decompose them,
so I have one component here

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and this component equals
mg times the cosine of alpha.

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And I have a component
in the x direction

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which is mg sine alpha.

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There is no acceleration in the
y direction, so I can be sure

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that the surface pushes back
with a normal force, N

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and that normal force N must be
exactly mg cosine alpha

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because those are the only
two forces in the y direction.

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And there is no acceleration
in the y direction

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so this one must be
mg cosine alpha.

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Now this object wants
to slide downhill.

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Friction prevents it
from doing so

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so there's going to be
a frictional force

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in this direction.

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And as I increase the tilt

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this frictional force will get
larger and larger and larger

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and then there comes a time that
the object will start to slide.

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Let us evaluate

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

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I'm applying
Newton's Second Law.

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In this direction, now,
the acceleration is still zero

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but the frictional force has now
just reached the maximum value--

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because I increase alpha-- so
this component will get larger

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and this component
will get larger.

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This component will get larger.

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This component is
still holding its own

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but then all of a sudden
it can't grow any further

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and it starts to accelerate.

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So Newton's Second Law tells me

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that mg sine alpha minus F
f maximum at this point is zero.

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

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This one is mg sine alpha.

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This equals zero.

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I lose my mg, and you see

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that mu of s equals
the tangent of alpha.

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It's that easy to measure.

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So you increase the tilt.

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We will do that later
until it starts to slip

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and then at that critical angle
that it starts to slip

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you have a value for mu of s

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for the static
friction coefficient.

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It is very nonintuitive
that this friction coefficient

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is completely independent
of the mass.

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The mass has disappeared.

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Think about it--
it's very nonintuitive.

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If you double the mass,
the angle would be the same

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given the fact that you have
the same kind of object.

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The friction coefficient
only depends

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on the materials that you have

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the materials that are rubbing
over each other.

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It's also independent
of the surface area

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that is in contact
with this incline

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which is equally nonintuitive.

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It's very nonintuitive,
but we will see

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that that's quite accurate

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within the uncertainties
that we can measure it.

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If you have a car
and you park your car

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you throw it on the brakes
and you put it at an angle

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and you increase
the angle of the slope

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the friction coefficient for
rubber on concrete is about one

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so the tangent is one, so
the angle is about 45 degrees.

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So if the road were 45 degrees,
the car would start to slide

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independent of the mass
of the car--

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

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independent of the width
of the tires.

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

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They would both start to slide
at the same angle

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given the fact, of course

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the same road
and the same kind of rubber.

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I first want to show you
some of this

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which is at first
very qualitative.

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I don't want it
to become quantitative yet.

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The difficulty
with these experiments are--

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I'm going to use
this plank here--

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that the moment
that my fingers touch this plank

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or touch the bottom
of any of the objects

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that I'm going to slide,
then all hell breaks loose.

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A little bit of water
on the plank

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would locally make the
friction coefficients larger.

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My fingers have chalk on them.

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A little bit of chalk
on a local place

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would make the friction
coefficient go down.

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

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The first thing I want to show
you is, if I take a rubber puck

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and I put the rubber puck
on this incline

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and I have a plastic bin--

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

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that it's immediately intuitive

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that the friction coefficient
of this plastic bin

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will be lower than
of the rubber puck.

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So when I increase the angle,
you expect

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that first the plastic bin
will start to slide

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and then the rubber puck.

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And if I gave you the angles
at which that happens

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you could actually
calculate the two values

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for the friction coefficient--

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

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So all I want you to see--
I hope--

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that this one will go earlier
than that one.

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So I am going to increase
the tilt... I do it very slowly.

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I try not to... rock the boat
too much, very slowly.

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We must be approaching the
critical angle for the plastic.

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Boy, it's holding on to itself.

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There it goes... and the rubber
goes a little later.

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The rubber can be made rough
by rubbing it on one side

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in which case the angle
will be even larger.

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I told you that
the friction coefficient

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is independent
of the mass of the object.

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I have
two identical bins here...

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well, as far
as they can be identical.

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Maybe one at the bottom is
a little rougher than the other.

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But in one,
I'm going to put 200 grams

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which is about five times
the weight of the bin.

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And then, within reason

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when I tilt them,
they will go at the same angle

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because it's independent
of the mass.

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So let's try that again
and see how close they are.

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It may be off by half a degree
or one degree, of course

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because the plank is
not uniform everywhere.

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And now it's 18 degrees...
19½... 20... 20½...

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21, and the other one is 21.2.

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So they almost go
at the same time, so you've seen

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that apparently the mass has
very small if any effect.

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Now comes something

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that I always find
very, very nonintuitive

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and that is surface area.

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I have two pieces of wood
and they're identical--

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whatever that means,
"identical";

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you can never make them exactly
the same in terms of roughness.

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This surface we prepared

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as well as we prepared
this bottom surface.

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But this bottom surface here is
four times smaller in area

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than this surface area here,
the flat part.

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I'm going to put
the flat one here

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and I'm going to put
the same object--

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but with its small area-- here.

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If indeed the friction
coefficient is independent

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of surface area,
then when I tilt them

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they should start to slide
roughly at the same angle.

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There we go.

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14 degrees... 16... 18... one
goes and the other one follows.

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It was in two-tenths
of a degree.

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And the reason why there's
always some difference--

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of course, the plank is
not exactly uniform.

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I have to be careful

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that I don't touch
the critical surfaces.

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So you have seen difference
in friction coefficients

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and you have seen there's
almost no effect on surface area

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and there's no effect
on the mass.

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And that is both
very nonintuitive.

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The width of the tires
of your car does not matter.

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And that... I ask you
the question to explain--

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in your assignment
number three--

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why race cars have
very wide tires.

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There must be a reason for that.

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I want you to think about that.

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There is another way

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that one can measure
the friction coefficient

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which is way more complicated

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and really, that's not the
reason why I want you to see it.

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The reason why I want you to go
with me through these arguments

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is that you begin to see

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how subtle and how really
difficult friction is.

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I'm going to put an object now

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on an incline again,
as we did before

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and instead of having it
sit on its own

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I'm going to attach to it
a string.

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So here is that object
and here is the string

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and a pulley and here a string.

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And here is an object mass m2,
and this object has mass m1

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and the angle here... alpha.

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I'm looking for my green chalk.

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I want to use
the same color convention.

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Now let's look at all the forces
that we can think of.

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Here is m1 g.

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Let's decompose that
in y and x direction.

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And I will call this direction
y, as I always do

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perpendicular to the surface.

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So we call this y

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and I will call this direction
now the positive x direction.

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You're free to choose it
any way you want to.

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00:13:15 --> 00:13:21

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The force here is m2 g...

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00:13:22 --> 00:13:28

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and now comes a major problem.

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The biggest problem is
that you do not know in advance

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whether this system will start
to accelerate in this direction

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or whether it will start
to accelerate in this direction

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or whether it will
not accelerate at all--

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it's quite possible.

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And all these three cases,
as you will see

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have to be dealt with
independently.

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You cannot do it with one
equation, as you will see.

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Let's first decompose this force

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as we did before,
in the y direction.

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So this one equals
m1 g cosine alpha

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and this one, the x component--

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which is in
the minus x direction now--

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equals m1 g sine alpha.

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Clearly, this one--
m1 g cosine alpha--

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we never have to worry about.

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There is no acceleration
in the y direction

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so this normal force N
will kill this one

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and this is m1 g cosine alpha.

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So you never have to worry
about the y direction;

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we know there's no acceleration.

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We only deal with forces
in the x direction

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that are of interest.

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There is a tension
in this string

272
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and now comes the problem:

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I do not know in what direction
the frictional force is.

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If this object has
the tendency to go uphill--

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which I don't know yet--

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then the frictional force is
in this direction

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because it opposes always

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the direction in which
the object wants to go.

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If, however, this object wants
to go in this direction--

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which I do not know--

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then the frictional force has
to be put in this direction.

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And I don't know that.

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The only thing I do know

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is that the maximum value
of the friction will be

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mu static times N,
which is what we had there.

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Remember, that's
the maximum value

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that the friction can have
times m1 g cosine alpha.

288
00:15:31 --> 00:15:37
That I know.

289
00:15:33 --> 00:15:39
So now, if I want
to deal with this

290
00:15:36 --> 00:15:42
I have to look at three
complete different situations:

291
00:15:40 --> 00:15:46
acceleration in this direction

292
00:15:43 --> 00:15:49
in which the friction is
pointing here;

293
00:15:46 --> 00:15:52
acceleration in this direction

294
00:15:48 --> 00:15:54
in which the friction is
pointing there;

295
00:15:51 --> 00:15:57
or no acceleration at all.

296
00:15:52 --> 00:15:58
There is also, of course,
the tension here...

297
00:15:56 --> 00:16:02

298
00:15:59 --> 00:16:05
and this tension is exactly
the same as that tension.

299
00:16:02 --> 00:16:08
We discussed that last time.

300
00:16:04 --> 00:16:10
I will not go over that
because this is an ideal

301
00:16:06 --> 00:16:12
and, of course,
an unphysical situation.

302
00:16:09 --> 00:16:15
The pulley has no mass

303
00:16:10 --> 00:16:16
the pulley is
completely frictionless

304
00:16:12 --> 00:16:18
and the string has no mass--
it's a massless string.

305
00:16:16 --> 00:16:22
And I argued last time

306
00:16:17 --> 00:16:23
that therefore the tension here
must be the same

307
00:16:20 --> 00:16:26
as the tension there.

308
00:16:21 --> 00:16:27
We even know the tension.

309
00:16:23 --> 00:16:29
I'm going to evaluate, for now

310
00:16:26 --> 00:16:32
only situations
that the system is at rest.

311
00:16:30 --> 00:16:36
It's not yet moving.

312
00:16:31 --> 00:16:37
If the system is at rest,
T must be m2 g

313
00:16:34 --> 00:16:40
because this object is
not being accelerated.

314
00:16:38 --> 00:16:44
So we already know

315
00:16:39 --> 00:16:45
that all situations
where the system is at rest

316
00:16:42 --> 00:16:48
T must be m2 g--
that's nonnegotiable.

317
00:16:46 --> 00:16:52
It's this T as well as that T.

318
00:16:50 --> 00:16:56
Now I have to start splitting in
the following situation.

319
00:16:55 --> 00:17:01
My first option is

320
00:16:57 --> 00:17:03
that I make the assumption
that the system is just...

321
00:17:02 --> 00:17:08
just about to start
accelerating upwards.

322
00:17:06 --> 00:17:12
It isn't doing it\yet;
it is just about to do that.

323
00:17:11 --> 00:17:17
If that's the case, then I know

324
00:17:14 --> 00:17:20
that the frictional force
will be in this direction

325
00:17:17 --> 00:17:23
and it will have reached
the maximum value

326
00:17:21 --> 00:17:27
with the static
friction coefficient.

327
00:17:23 --> 00:17:29
Now I can write down, in the x
direction, Newton's Second Law.

328
00:17:28 --> 00:17:34
Now I have T, which is
in the positive direction

329
00:17:33 --> 00:17:39
minus m1 g sine alpha
minus F f max.

330
00:17:42 --> 00:17:48
That now has to be zero,
just at the moment

331
00:17:46 --> 00:17:52
that it is just about to change
its mind and start accelerating.
 

332
00:17:52 --> 00:17:58
Now, I know what T is,
that is, m2 g

333
00:17:55 --> 00:18:01
so m2 g equals m1 g sine alpha

334
00:18:03 --> 00:18:09
plus the maximum frictional
force, which is this value.

335
00:18:09 --> 00:18:15
So this is just at the moment
that it wants to start sliding.

336
00:18:17 --> 00:18:23
Therefore, if I make mass m2
a hair larger, just a hair

337
00:18:23 --> 00:18:29
it will go.

338
00:18:25 --> 00:18:31
And therefore the moment
that I make this a larger sign

339
00:18:29 --> 00:18:35
I know that it's going
to accelerate uphill.

340
00:18:32 --> 00:18:38
That's the criterion
for going uphill.

341
00:18:36 --> 00:18:42
Now I look at situation two.

342
00:18:40 --> 00:18:46
Now I make the assumption that
the object, still standing still

343
00:18:46 --> 00:18:52
is just about
to start accelerating downhill.

344
00:18:50 --> 00:18:56
Aha! If that's the case, I know

345
00:18:52 --> 00:18:58
that the maximum force is
now pointing upwards--

346
00:18:55 --> 00:19:01
the same magnitude, but it
has now a different direction.

347
00:18:59 --> 00:19:05
So now I can write down
Newton's Second Law.

348
00:19:02 --> 00:19:08
So the frictional force is
nowhelping T.

349
00:19:05 --> 00:19:11
So now we get

350
00:19:07 --> 00:19:13
T plus F f max minus
m1 g sine alpha equals zero.

351
00:19:21 --> 00:19:27
We know that this is m2 g

352
00:19:26 --> 00:19:32
so m2 g equals
m1 g sine alpha minus F f max.

353
00:19:37 --> 00:19:43
Notice the difference:

354
00:19:39 --> 00:19:45
there's a plus sign here;
there's a minus sign here.

355
00:19:43 --> 00:19:49
This is... the object
is still not moving

356
00:19:47 --> 00:19:53
but if I make m2 g a hair less,
just a teeny-weeny little less

357
00:19:51 --> 00:19:57
it will definitely start
to accelerate downwards.

358
00:19:55 --> 00:20:01
So if I make this
"smaller than" sign

359
00:19:59 --> 00:20:05
the object will start
accelerating downhill.

360
00:20:04 --> 00:20:10
This is condition one,
this is condition two.

361
00:20:07 --> 00:20:13
If the condition is
neither one nor two...

362
00:20:10 --> 00:20:16

363
00:20:14 --> 00:20:20
what do you think
will happen then?

364
00:20:16 --> 00:20:22
Very possible
that you don't meet

365
00:20:18 --> 00:20:24
any one of these two conditions.

366
00:20:20 --> 00:20:26
What do you think will happen?

367
00:20:23 --> 00:20:29
(class murmurs )

368
00:20:24 --> 00:20:30
LEWIN:
Can't hear you.

369
00:20:25 --> 00:20:31
(student replies )

370
00:20:26 --> 00:20:32
LEWIN:
It won't move-- a is zero.

371
00:20:29 --> 00:20:35
Because this... both cases
are going to accelerate

372
00:20:33 --> 00:20:39
so in all other cases,
the acceleration equals zero.

373
00:20:37 --> 00:20:43
And the frictional force,
in this case

374
00:20:40 --> 00:20:46
will adjust itself
just the right way

375
00:20:42 --> 00:20:48
so that Newton's Second Law
in the x direction

376
00:20:46 --> 00:20:52
will give you,
for the force, a zero.

377
00:20:50 --> 00:20:56

378
00:20:53 --> 00:20:59
Let us take
a very simple example

379
00:20:56 --> 00:21:02
so that you see this at work.

380
00:20:59 --> 00:21:05
So, we have an example here,
and in my example

381
00:21:05 --> 00:21:11
I have m1 equals 1 kilogram,
m2 equals 2 kilograms.

382
00:21:10 --> 00:21:16
Can't make the numbers
much simpler.

383
00:21:14 --> 00:21:20
I take alpha equals 30 degrees.

384
00:21:18 --> 00:21:24
I take a static friction
coefficient which is 0.5

385
00:21:25 --> 00:21:31
and I take
a kinetic friction coefficient

386
00:21:29 --> 00:21:35
which is a little less,
which is 0.4.

387
00:21:33 --> 00:21:39
The question is now, is it going
to be accelerated uphill

388
00:21:36 --> 00:21:42
or accelerated downhill
or no acceleration at all?

389
00:21:39 --> 00:21:45
What it comes down to

390
00:21:41 --> 00:21:47
is that we have to evaluate
these three terms.

391
00:21:45 --> 00:21:51
Let's first take m2 g--
m2 g equals 20.

392
00:21:49 --> 00:21:55
We'll just take, for g, 10--
that is just easier.

393
00:21:54 --> 00:22:00
M1 g sine alpha...

394
00:21:56 --> 00:22:02
The sine of alpha is a half,
so that is five.

395
00:22:02 --> 00:22:08
M1 g sine alpha equals five.

396
00:22:08 --> 00:22:14
And what is F f maximum?

397
00:22:11 --> 00:22:17
I have to use, for
my friction coefficient, .5.

398
00:22:16 --> 00:22:22
I have to use, for m1, one

399
00:22:19 --> 00:22:25
here, a 10, and have
the cosine for 30 degrees.

400
00:22:22 --> 00:22:28
And what I find-- you have
to take my word for it--

401
00:22:26 --> 00:22:32
that this is about 4.33,
and I want to remind you

402
00:22:30 --> 00:22:36
I have used the static
friction coefficient.

403
00:22:33 --> 00:22:39
This is in newtons.

404
00:22:34 --> 00:22:40
I never put a capital N
for newtons

405
00:22:36 --> 00:22:42
because that is very confusing
with this normal force.

406
00:22:40 --> 00:22:46
All my units are always
in S.I. units

407
00:22:42 --> 00:22:48
so the force is always
in newtons.

408
00:22:45 --> 00:22:51
Aha! We are well on our way.

409
00:22:48 --> 00:22:54
Let's first test
whether condition one is met.

410
00:22:52 --> 00:22:58
Is 20 larger than 5 plus 4.33?

411
00:22:58 --> 00:23:04

412
00:23:00 --> 00:23:06
And the answer is yes, it is.

413
00:23:03 --> 00:23:09
So we know that it's going
to be accelerated uphill.

414
00:23:07 --> 00:23:13
That is nonnegotiable.

415
00:23:09 --> 00:23:15
So now I could ask you
a simple question:

416
00:23:13 --> 00:23:19
What is the acceleration

417
00:23:15 --> 00:23:21
and what is the tension
in the string?

418
00:23:18 --> 00:23:24
And so you will think

419
00:23:20 --> 00:23:26
"Oh, well, that is
within arm's reach."

420
00:23:23 --> 00:23:29
Not quite, because things are
now going to change.

421
00:23:27 --> 00:23:33
If it is going
to be accelerated uphill

422
00:23:31 --> 00:23:37
then at least I know one thing

423
00:23:34 --> 00:23:40
which I am going to put
in this drawing now.

424
00:23:38 --> 00:23:44
I know that this is
the maximum friction possible

425
00:23:43 --> 00:23:49
which now becomes mu kinetic--
because it's going to move--

426
00:23:48 --> 00:23:54
times m1 times g
times cosine alpha.

427
00:23:55 --> 00:24:01
So that is already one change.

428
00:23:57 --> 00:24:03
It is moving, so sure,
it's going to be accelerated

429
00:24:00 --> 00:24:06
so the frictional force is in
this direction, has this value.

430
00:24:04 --> 00:24:10
So let's write down now

431
00:24:06 --> 00:24:12
Newton's Second Law
in the x direction.

432
00:24:10 --> 00:24:16
So we have T in the positive
direction minus m1 g sine alpha

433
00:24:19 --> 00:24:25
minus this maximum force--
minus mu k m1 g cosine alpha--

434
00:24:29 --> 00:24:35
and that, now, according
to Newton's Law, must be

435
00:24:33 --> 00:24:39
m1 times a, if a is
T acceleration uphill.

436
00:24:37 --> 00:24:43
One equation with two unknowns.

437
00:24:41 --> 00:24:47
You don't know a
and you don't know T.

438
00:24:45 --> 00:24:51
Or do you know T? What is T?
What is the tension?

439
00:24:52 --> 00:24:58
What is the tension

440
00:24:54 --> 00:25:00
when that thing is
being accelerated uphill?

441
00:24:57 --> 00:25:03
Anyone has the courage to try?

442
00:24:59 --> 00:25:05
(student responds )

443
00:25:01 --> 00:25:07
LEWIN:
You think "m2 g"--
you couldn't be more wrong.

444
00:25:05 --> 00:25:11
It's now moving,
it's being accelerated.

445
00:25:08 --> 00:25:14
That means this object is going
to be accelerated down

446
00:25:12 --> 00:25:18
and if this force is
the same as this

447
00:25:15 --> 00:25:21
it can never accelerate down.

448
00:25:17 --> 00:25:23
This T must get smaller.

449
00:25:20 --> 00:25:26
Remember, an object in an
elevator being accelerated down

450
00:25:25 --> 00:25:31
loses weight--
it's losing weight.

451
00:25:28 --> 00:25:34
This object must
be accelerated down.

452
00:25:31 --> 00:25:37
We have to take that
into account.

453
00:25:33 --> 00:25:39
So the tension, once it starts
accelerating, will go down.

454
00:25:36 --> 00:25:42
So I have the second equation
for object number two.

455
00:25:39 --> 00:25:45
I call this the plus direction,
so for object number two

456
00:25:44 --> 00:25:50
I have m2 g minus T equals
m2 times a.

457
00:25:52 --> 00:25:58
It is very important
that you see

458
00:25:54 --> 00:26:00
that the tension will change.

459
00:25:56 --> 00:26:02
Now I have two equations
with two unknowns

460
00:25:59 --> 00:26:05
and now I can solve.

461
00:26:02 --> 00:26:08
It's very easy-- you just add
them, and I leave you with that.

462
00:26:06 --> 00:26:12
I'll just give you the results.

463
00:26:08 --> 00:26:14
I find that the acceleration, a,
equals plus... I think 3.85.

464
00:26:15 --> 00:26:21
That is correct-- plus 3.85
meters per second squared.

465
00:26:21 --> 00:26:27
And I find that the tension
equals 12.3 newtons.

466
00:26:30 --> 00:26:36
I want to dwell on this
a little bit.

467
00:26:33 --> 00:26:39
I find, for the acceleration,
a plus sign.

468
00:26:36 --> 00:26:42
Had I found a minus sign,
I would...

469
00:26:39 --> 00:26:45
I'm sure I would have made
a mistake.

470
00:26:41 --> 00:26:47
Why is itmandatory
that I find a plus sign?

471
00:26:45 --> 00:26:51
Absolutely mandatory!

472
00:26:46 --> 00:26:52
Who wants to try that one?

473
00:26:48 --> 00:26:54
Yeah?

474
00:26:49 --> 00:26:55
(student making explanation )

475
00:26:55 --> 00:27:01
LEWIN:
Yeah, you say...
you say it well.

476
00:26:58 --> 00:27:04
I would have said it
slightly differently.

477
00:27:01 --> 00:27:07
We know that the acceleration is
in this direction.

478
00:27:03 --> 00:27:09
We derived that.

479
00:27:04 --> 00:27:10
Therefore the acceleration

480
00:27:05 --> 00:27:11
since I call that
the "plus x direction"--

481
00:27:06 --> 00:27:12
that was my plus sign--
must come out plus.

482
00:27:10 --> 00:27:16
So if this comes out negative,
you've made a mistake.

483
00:27:14 --> 00:27:20
I also want this number
to be less than 20.

484
00:27:18 --> 00:27:24
If not, I've made a mistake.

485
00:27:20 --> 00:27:26
Why does that number
have to be less than 20?

486
00:27:24 --> 00:27:30
(student making explanation )

487
00:27:26 --> 00:27:32
LEWIN:
Exactly--
this object is goingdown.

488
00:27:30 --> 00:27:36
To put it
the way we put it last time

489
00:27:33 --> 00:27:39
it lost weight,
it's accelerated downwards.

490
00:27:36 --> 00:27:42
This Nt g, which is 20,
better wins it from T;

491
00:27:39 --> 00:27:45
otherwise it would
never be accelerated down.

492
00:27:41 --> 00:27:47
So this plus sign is a must,
and this is a must.

493
00:27:44 --> 00:27:50
And if you find not a plus sign
but a minus sign

494
00:27:48 --> 00:27:54
you have to go back
to your calculation

495
00:27:50 --> 00:27:56
because you've made a mistake.

496
00:27:53 --> 00:27:59
Now we take the same situation,
I leave everything unchanged

497
00:27:58 --> 00:28:04
but I make the second mass, m2,
I make it 0.4 kilograms.

498
00:28:07 --> 00:28:13
So now all the numbers remain
the same that we have there

499
00:28:12 --> 00:28:18
except that m2 g now becomes 4.

500
00:28:15 --> 00:28:21
Now I'm going to test again.

501
00:28:18 --> 00:28:24
This m2 g, which is 4--

502
00:28:21 --> 00:28:27
is that larger than 5 plus the
frictional force static, 4.33?

503
00:28:32 --> 00:28:38
The answer is no.

504
00:28:34 --> 00:28:40
I'm going to test
for my second case.

505
00:28:37 --> 00:28:43
Is m2 g smaller
than 5 minus 4.33?

506
00:28:44 --> 00:28:50
The answer is no,
so what do we conclude?

507
00:28:51 --> 00:28:57
What must be our conclusion?

508
00:28:54 --> 00:29:00
Condition one is not met,
condition two is not met.

509
00:28:58 --> 00:29:04
The conclusion is a is zero.

510
00:29:02 --> 00:29:08
The object will
not be accelerated

511
00:29:07 --> 00:29:13
and the frictional force
is going to adjust

512
00:29:11 --> 00:29:17
along the x direction so that
the acceleration indeed is zero.

513
00:29:16 --> 00:29:22
How does
the frictional force do that?

514
00:29:18 --> 00:29:24
This is that slope,
here is that object.

515
00:29:21 --> 00:29:27
I will only put in the forces
along the x direction.

516
00:29:25 --> 00:29:31
I don't bother
about the y direction.

517
00:29:27 --> 00:29:33
I know that there is m1 g
sine alpha, and that one is 5.

518
00:29:33 --> 00:29:39
So we have here
a component of gravity

519
00:29:37 --> 00:29:43
which is the m1 g sine alpha,
and we know that that is 5.

520
00:29:44 --> 00:29:50
We have it there.

521
00:29:45 --> 00:29:51
I also know
that we have tension here

522
00:29:48 --> 00:29:54
and the tension must be m2 g

523
00:29:50 --> 00:29:56
because the object is
not being accelerated.

524
00:29:54 --> 00:30:00
We're back where we were.

525
00:29:56 --> 00:30:02
Number two is
not being accelerated.

526
00:29:59 --> 00:30:05
The tension is 20...
sorry, not 20, what is my m2?

527
00:30:02 --> 00:30:08
The tension is... mg is 4.

528
00:30:08 --> 00:30:14
Five newtons downhill,
four newtons uphill.

529
00:30:11 --> 00:30:17
What will the friction be, how
large, and in what direction?

530
00:30:16 --> 00:30:22
Uphill, how large? One, exactly.

531
00:30:21 --> 00:30:27
The friction will adjust itself
so that there is equilibrium

532
00:30:27 --> 00:30:33
if nothing is going.

533
00:30:28 --> 00:30:34
All right, I now would like
to do a few demonstrations

534
00:30:32 --> 00:30:38
whereby I want you to calculate

535
00:30:34 --> 00:30:40
the friction coefficients
for me.

536
00:30:37 --> 00:30:43
So we're going to put

537
00:30:38 --> 00:30:44
a particular object
on that incline

538
00:30:41 --> 00:30:47
and I'm first going to raise
the angle until it breaks loose.

539
00:30:47 --> 00:30:53
So you should be able
to calculate

540
00:30:50 --> 00:30:56
what the friction
coefficient is

541
00:30:51 --> 00:30:57
using the equation
tangent alpha equals mu s.

542
00:30:56 --> 00:31:02
And the object that I use
for that is this... this box.

543
00:31:02 --> 00:31:08
In this box is a little weight
that's not very important.

544
00:31:05 --> 00:31:11
It makes the whole thing
361 grams.

545
00:31:10 --> 00:31:16
I want you to know

546
00:31:12 --> 00:31:18
that the weight
of this object is 361 grams.

547
00:31:16 --> 00:31:22
I'll write it down for you here.

548
00:31:19 --> 00:31:25
So, the mass
of the object is 361; 

549
00:31:24 --> 00:31:30
I'm sure that the uncertainty is
at least 1 gram.

550
00:31:29 --> 00:31:35
You have to trust me
when I give you the angles.

551
00:31:31 --> 00:31:37
I'm going to increase
the incline

552
00:31:33 --> 00:31:39
and there comes a moment
that it will start to slide.

553
00:31:36 --> 00:31:42
I'll give you the angle

554
00:31:38 --> 00:31:44
and I want you to calculate
that friction coefficient.

555
00:31:41 --> 00:31:47
So we'll do that first...
there we go.

556
00:31:44 --> 00:31:50

557
00:31:47 --> 00:31:53
It's now 10 degrees, 11...
12½, 13... 14, 15... 16

558
00:31:59 --> 00:32:05
17... 17½, 18, 19,
19½, 20-- 20 degrees.

559
00:32:08 --> 00:32:14
It starts to slide at about
20 degrees-- write that down.

560
00:32:13 --> 00:32:19
Now I'm going to do
exactly this experiment:

561
00:32:19 --> 00:32:25
Put a rope over it, with a
pulley, and put m2 on this side.

562
00:32:25 --> 00:32:31
And now I'm going
to load down m2

563
00:32:27 --> 00:32:33
to the point that it starts
to slide uphill.

564
00:32:31 --> 00:32:37
That should allow you

565
00:32:33 --> 00:32:39
to also calculate
the friction coefficient.

566
00:32:36 --> 00:32:42
You have all the tools for it,
because once you know

567
00:32:40 --> 00:32:46
that it is just at the point
of breaking and going uphill

568
00:32:43 --> 00:32:49
you know that that equals sign
of that equation holds

569
00:32:47 --> 00:32:53
and so you should be able
to calculate

570
00:32:49 --> 00:32:55
the friction coefficient.

571
00:32:51 --> 00:32:57
Would you find
exactly the same number

572
00:32:54 --> 00:33:00
as you find
from this experiment?

573
00:32:56 --> 00:33:02
Not very likely.

574
00:32:57 --> 00:33:03
You have to think
about that for yourself.

575
00:32:59 --> 00:33:05
Wood has grain, and the grain
in this direction

576
00:33:02 --> 00:33:08
could be very different from
the grain in this direction.

577
00:33:04 --> 00:33:10
But it would be interesting
to compare the two numbers

578
00:33:07 --> 00:33:13
to see how much they're off.

579
00:33:10 --> 00:33:16
So I'm going to put here
this rope over here

580
00:33:14 --> 00:33:20
and I'm going to set the angle
now at a given value

581
00:33:18 --> 00:33:24
so this is now not negotiable.

582
00:33:21 --> 00:33:27
I set it at 20.

583
00:33:25 --> 00:33:31

584
00:33:28 --> 00:33:34
I could be off by half a degree.

585
00:33:31 --> 00:33:37
Again, you see, it wants to go.

586
00:33:33 --> 00:33:39
You just saw that-- at 20
degrees, it wants to go.

587
00:33:36 --> 00:33:42
So I prevent it from going

588
00:33:38 --> 00:33:44
and so I'm going to put
a little weight on here.

589
00:33:42 --> 00:33:48
Now there is 100 grams,
and it's not going.

590
00:33:46 --> 00:33:52
It's happy
and it's sitting there.

591
00:33:49 --> 00:33:55
A is zero.

592
00:33:50 --> 00:33:56
That condition isn't met
and this condition isn't met.

593
00:33:53 --> 00:33:59
So now you must write down
in your notebook

594
00:33:56 --> 00:34:02
that alpha now-- it's
an independent experiment--

595
00:33:59 --> 00:34:05
equals 20.0,
maybe plus or minus 1.

596
00:34:06 --> 00:34:12
I think it's about 1 degree
accuracy that I can do.

597
00:34:10 --> 00:34:16
Okay, I'm going to load here
more weight--

598
00:34:13 --> 00:34:19
more mass, I should say-- at m2

599
00:34:15 --> 00:34:21
and I'll give you the numbers

600
00:34:16 --> 00:34:22
and when it breaks loose,
you will see it.

601
00:34:18 --> 00:34:24
I will give you the numbers.

602
00:34:20 --> 00:34:26
Now, I have done this
many times, believe me

603
00:34:22 --> 00:34:28
and the breaking point is
not always at the same mass.

604
00:34:27 --> 00:34:33
The mass could differ
by 20, 25 grams easily.

605
00:34:30 --> 00:34:36
So whatever number
we're going to find for m2

606
00:34:34 --> 00:34:40
I would say you should
at least allow an uncertainty

607
00:34:38 --> 00:34:44
of about something
like 25 grams

608
00:34:43 --> 00:34:49
just because I've done
it many times...

609
00:34:45 --> 00:34:51
and I know it could
even be worse at times.

610
00:34:47 --> 00:34:53
The humidity could change
in the room

611
00:34:50 --> 00:34:56
and that could change
the friction coefficient.

612
00:34:52 --> 00:34:58
Okay, we have 100 grams on it...
we have 200 grams on it...

613
00:34:57 --> 00:35:03
250... 260... 270,
and it goes at 270.

614
00:35:05 --> 00:35:11
Did you see it go?

615
00:35:07 --> 00:35:13
It started to slide at 270.

616
00:35:10 --> 00:35:16
So at 270 grams, I met
exactly that condition.

617
00:35:16 --> 00:35:22
It was an equals sign.

618
00:35:17 --> 00:35:23
That should allow you
to calculate

619
00:35:19 --> 00:35:25
the static friction coefficient

620
00:35:21 --> 00:35:27
and you'll get a chance to do
that in your third assignment.

621
00:35:26 --> 00:35:32

622
00:35:30 --> 00:35:36
When I had this thing up here,
and when I was loading this down

623
00:35:34 --> 00:35:40
making it heavier and heavier,
I hope you realize

624
00:35:37 --> 00:35:43
that at first it wanted
to slide in this direction.

625
00:35:40 --> 00:35:46
So at first the friction was
in this direction.

626
00:35:43 --> 00:35:49
As I loaded it down
more and more

627
00:35:45 --> 00:35:51
the friction became less
and less and less.

628
00:35:47 --> 00:35:53
There comes even a time
that the friction becomes zero.

629
00:35:52 --> 00:35:58
I loaded more and more and more.

630
00:35:54 --> 00:36:00
The friction flips over
to the other side.

631
00:35:57 --> 00:36:03
The friction grows
and grows and grows

632
00:35:59 --> 00:36:05
fights an heroic battle
to not make it go uphill

633
00:36:03 --> 00:36:09
loses the battle at one point,
reaches the maximum value.

634
00:36:07 --> 00:36:13
I put a little bit more on here
and it goes.

635
00:36:10 --> 00:36:16
So this frictional force is
really having a rough time

636
00:36:13 --> 00:36:19
starting off in this direction,
slowly becoming less

637
00:36:16 --> 00:36:22
becoming zero, changing
direction, reaching the maximum

638
00:36:20 --> 00:36:26
and finally losing the battle.

639
00:36:22 --> 00:36:28
Friction is often a pain
in the neck, as we all know.

640
00:36:26 --> 00:36:32
Friction causes wear, it causes
tear and it costs fuel.

641
00:36:31 --> 00:36:37
With a car, there's a lot
of friction with the road.

642
00:36:35 --> 00:36:41
You pay for that, and
people try to reduce friction

643
00:36:39 --> 00:36:45
with bearings and
with lubrication, oil.

644
00:36:42 --> 00:36:48
Water is an amazing lubricant.

645
00:36:45 --> 00:36:51
If it starts raining

646
00:36:47 --> 00:36:53
and there is a little bit
of dust on the road

647
00:36:50 --> 00:36:56
the friction coefficient
between your tires and road

648
00:36:53 --> 00:36:59
can become so low
that you begin to hydroplane

649
00:36:56 --> 00:37:02
and that you literally...
(makes whooshing sound )

650
00:36:58 --> 00:37:04
that your friction coefficient
goes almost to zero.

651
00:37:01 --> 00:37:07
It happened to me once,
and it's no fun.

652
00:37:03 --> 00:37:09
It can happen instantaneously

653
00:37:05 --> 00:37:11
particularly
when the rain begins--

654
00:37:07 --> 00:37:13
in the very early part
of the rain

655
00:37:08 --> 00:37:14
when the road is dusty

656
00:37:10 --> 00:37:16
so you get the water
with a little bit of dust mixed.

657
00:37:13 --> 00:37:19
It's a very dangerous situation.

658
00:37:16 --> 00:37:22
At home, I have a pan--
this is my pan at home.

659
00:37:19 --> 00:37:25
Actually I have more than
one pan at home, believe me.

660
00:37:23 --> 00:37:29
But this is a very special pan

661
00:37:25 --> 00:37:31
and what is special about it
is something

662
00:37:29 --> 00:37:35
that I discovered
purely by accident

663
00:37:32 --> 00:37:38
and I want to share with you
this remarkable pan.

664
00:37:36 --> 00:37:42

665
00:37:39 --> 00:37:45
You see,
when I rotate this cover

666
00:37:41 --> 00:37:47
there's a lot of friction--
you can hear it.

667
00:37:44 --> 00:37:50
(metal lid grating )

668
00:37:46 --> 00:37:52
And it stops.

669
00:37:47 --> 00:37:53
You can hear it, right?

670
00:37:49 --> 00:37:55
And so one evening
I was boiling potatoes

671
00:37:53 --> 00:37:59
and I was looking at this pan,
and I walked up to it

672
00:37:56 --> 00:38:02
because I wanted to check
the potatoes.

673
00:37:58 --> 00:38:04
And I touched the thing,
and there was no friction.

674
00:38:01 --> 00:38:07
It just went spinning
and spinning and spinning.

675
00:38:04 --> 00:38:10
I couldn't believe my eyes

676
00:38:07 --> 00:38:13
until I realized
what is happening.

677
00:38:11 --> 00:38:17
Water had accumulated
in the rim of this pan

678
00:38:15 --> 00:38:21
and the cover was beginning
to hydroplane.

679
00:38:20 --> 00:38:26
(metal lid skimming freely )

680
00:38:23 --> 00:38:29
I'm putting water in it now.

681
00:38:25 --> 00:38:31
(metal lid skimming
freely, silently )

682
00:38:31 --> 00:38:37
You almost don't hear it
anymore.

683
00:38:33 --> 00:38:39
Isn't that amazing?

684
00:38:35 --> 00:38:41

685
00:38:38 --> 00:38:44
Almost frictionless.

686
00:38:40 --> 00:38:46
So now the water acts
like a lubricant.

687
00:38:43 --> 00:38:49
And you try it with your pan,
it won't work

688
00:38:46 --> 00:38:52
because you need
just the right shape

689
00:38:48 --> 00:38:54
and you need the right edge

690
00:38:50 --> 00:38:56
to be able to lubricate it
that way.

691
00:38:52 --> 00:38:58

692
00:38:56 --> 00:39:02
There are many experiments
that are done

693
00:38:59 --> 00:39:05
and many attempts have been
made by people

694
00:39:02 --> 00:39:08
to reduce friction.

695
00:39:04 --> 00:39:10
You try, if you can, to avoid
contact between two surfaces.

696
00:39:08 --> 00:39:14
That you can do by putting
a lubricant in between.

697
00:39:12 --> 00:39:18
But even better it would be

698
00:39:14 --> 00:39:20
if you could separate
the object completely

699
00:39:18 --> 00:39:24
and only have air in between

700
00:39:21 --> 00:39:27
because air has much
less friction than a liquid.

701
00:39:25 --> 00:39:31
And that's being done
with great success.

702
00:39:28 --> 00:39:34
People use hovercrafts

703
00:39:30 --> 00:39:36
so they blow air out from below
so the craft lifts itself up

704
00:39:34 --> 00:39:40
and now it's no longer
in contact with the water.

705
00:39:38 --> 00:39:44
It's above the water,
so if it moves now

706
00:39:41 --> 00:39:47
all it has to overcome is
the air friction and that's it

707
00:39:44 --> 00:39:50
and that helps tremendously.

708
00:39:46 --> 00:39:52
You will be seeing
in this lecture hall

709
00:39:49 --> 00:39:55
many demonstrations that I
will be doing in the future

710
00:39:53 --> 00:39:59
with what I call an "air track."

711
00:39:55 --> 00:40:01
I will show it to you
in a minute.

712
00:39:57 --> 00:40:03
It is a long...
call it a bar, for now.

713
00:40:02 --> 00:40:08
The cross-section is
a triangular shape

714
00:40:06 --> 00:40:12
and there are holes in here,
and we blow air out of that.

715
00:40:11 --> 00:40:17
And on top of that are devices

716
00:40:14 --> 00:40:20
which have been
specially designed

717
00:40:17 --> 00:40:23
to perfectly fit this triangle.

718
00:40:19 --> 00:40:25
And when you start blowing
the air

719
00:40:22 --> 00:40:28
they are lifted up,
so they float.

720
00:40:25 --> 00:40:31
And so now when you give them
a little tap

721
00:40:28 --> 00:40:34
they can move almost--
not quite, but almost--

722
00:40:32 --> 00:40:38
without friction.

723
00:40:34 --> 00:40:40

724
00:40:35 --> 00:40:41
Here's one... a lot of friction.

725
00:40:40 --> 00:40:46

726
00:40:42 --> 00:40:48
Now I'll turn on the air.

727
00:40:44 --> 00:40:50
(air whooshing )

728
00:40:45 --> 00:40:51

729
00:40:49 --> 00:40:55
Look at the difference.

730
00:40:51 --> 00:40:57
Isn't that amazing?

731
00:40:52 --> 00:40:58
It's floating
on its own air cushion.

732
00:40:55 --> 00:41:01

733
00:41:04 --> 00:41:10
And if I turn it off...

734
00:41:07 --> 00:41:13
(air clicks off )

735
00:41:08 --> 00:41:14
the moment that the air stops,
you will see it stops.

736
00:41:13 --> 00:41:19
So this is the technique

737
00:41:15 --> 00:41:21
that is often used
to do demonstrations

738
00:41:19 --> 00:41:25
if you have to do them
with a minimum of friction.

739
00:41:23 --> 00:41:29
Of course, you could do
experiments in the shuttle

740
00:41:26 --> 00:41:32
very well, where you have,
again, only air around you.

741
00:41:30 --> 00:41:36
But that's, of course,
a very expensive way.

742
00:41:33 --> 00:41:39
In 26.100,
we will use the air track

743
00:41:35 --> 00:41:41
when we start colliding objects

744
00:41:37 --> 00:41:43
and try to see what happens
before and after the collision.

745
00:41:42 --> 00:41:48
There is another device,
which is very intriguing

746
00:41:46 --> 00:41:52
and that also acts on the idea
that it lifts itself up

747
00:41:50 --> 00:41:56
as a result of gas
which is flowing out.

748
00:41:55 --> 00:42:01
In this case, it's a container
of carbon dioxide...

749
00:42:00 --> 00:42:06
with carbon dioxide in here,
which is solid

750
00:42:04 --> 00:42:10
and there is
a small opening here

751
00:42:07 --> 00:42:13
and this is

752
00:42:08 --> 00:42:14
an extremely well machined
flat surface, very flat.

753
00:42:14 --> 00:42:20
And the whole thing rests
on an extremely flat surface.

754
00:42:19 --> 00:42:25
Because of the room temperature

755
00:42:21 --> 00:42:27
the carbon dioxide
will start to evaporate

756
00:42:25 --> 00:42:31
and will start to flow out.

757
00:42:27 --> 00:42:33
And therefore under this thing
comes a film

758
00:42:31 --> 00:42:37
a very thin layer
of carbon dioxide

759
00:42:34 --> 00:42:40
and now you can move this
around in two dimensions.

760
00:42:37 --> 00:42:43
You are not stuck, like you
are there, to one dimension

761
00:42:39 --> 00:42:45
of going back and forth
on what we call the air track.

762
00:42:42 --> 00:42:48
But now you can move it
around over this whole surface.

763
00:42:46 --> 00:42:52
And that allows you to do
very interesting things

764
00:42:52 --> 00:42:58
as I want to show you next.

765
00:42:55 --> 00:43:01
First make it dark.

766
00:42:58 --> 00:43:04

767
00:43:06 --> 00:43:12
FILM NARRATOR:
And we've filled that can
with dry ice

768
00:43:09 --> 00:43:15
that is, solid carbon dioxide.

769
00:43:11 --> 00:43:17
Now, you know solid carbon
dioxide is very cold.

770
00:43:15 --> 00:43:21
This white stuff is just frost

771
00:43:17 --> 00:43:23
that's gathered
on the outside of the can.

772
00:43:20 --> 00:43:26
Now, as the can absorbs heat
from the room

773
00:43:24 --> 00:43:30
the carbon dioxide evaporates
and turns into a gas.

774
00:43:28 --> 00:43:34
The gas takes up more room
than the solid

775
00:43:32 --> 00:43:38
so it has to go somewhere.

776
00:43:33 --> 00:43:39
It can't come out the top

777
00:43:35 --> 00:43:41
so it comes out a little hole
here in the bottom of the disc.

778
00:43:39 --> 00:43:45
Now, you can't see it coming out
the hole, but if I make a flame

779
00:43:45 --> 00:43:51
I think you can see

780
00:43:47 --> 00:43:53
that there's gas coming out
and blowing the flame.

781
00:43:51 --> 00:43:57
Now if we put the disc--

782
00:43:54 --> 00:44:00
with its stream of gas
coming out the bottom--

783
00:44:00 --> 00:44:06
down on our table top

784
00:44:01 --> 00:44:07
which is made of a very
smooth piece of plate glass...

785
00:44:04 --> 00:44:10

786
00:44:06 --> 00:44:12
We can wait a moment

787
00:44:07 --> 00:44:13
while the gas coming out
builds up pressure underneath

788
00:44:10 --> 00:44:16
which it has to do
in order to escape.

789
00:44:15 --> 00:44:21
By now, the disc is floating
on this film of escaping gas.

790
00:44:22 --> 00:44:28
That film is so thin

791
00:44:23 --> 00:44:29
that I'm sure you can't see it
from out there.

792
00:44:26 --> 00:44:32
I can scarcely see a space

793
00:44:28 --> 00:44:34
between the disc
and the glass, myself.

794
00:44:32 --> 00:44:38
But if you'll come
and look over my shoulder

795
00:44:34 --> 00:44:40
I think I can show you
that there is a space

796
00:44:37 --> 00:44:43
by slipping underneath the disc

797
00:44:40 --> 00:44:46
this piece of tinfoil I took
off a chewing gum wrapper.

798
00:44:44 --> 00:44:50
Now, we'll slip the tinfoil
between the disc

799
00:44:47 --> 00:44:53
and the plate glass top
of the table

800
00:44:50 --> 00:44:56
showing that there is indeed
a space, a thin film of gas

801
00:44:56 --> 00:45:02
between the disc and the glass
upon which it's resting.

802
00:45:01 --> 00:45:07
The purpose of this is simply
to reduce the friction

803
00:45:04 --> 00:45:10
to a point where
we won't have to worry about it

804
00:45:07 --> 00:45:13
or measure it
in our experiments today.

805
00:45:09 --> 00:45:15
It's fun to play with
this thing-- let me show you.

806
00:45:13 --> 00:45:19
I'll give it a little push,
just a little one.

807
00:45:19 --> 00:45:25
And there it goes, moving
sedately, no sign of slowing up.

808
00:45:25 --> 00:45:31
Come on back.

809
00:45:28 --> 00:45:34
Same thing
in the other direction.

810
00:45:31 --> 00:45:37
It takes only a very tiny force
to start it in motion.

811
00:45:35 --> 00:45:41
Let me show you that.

812
00:45:37 --> 00:45:43
(triumphant Spanish
dance music playing )

813
00:45:40 --> 00:45:46
(music continues
throughout rest of film )

814
00:45:44 --> 00:45:50

815
00:47:46 --> 00:47:52
(\music ends; applause\)

816
00:47:49 --> 00:47:55

817
00:47:50 --> 00:47:56
LEWIN:
So you see, fleas are
good for something.

818
00:47:53 --> 00:47:59
Have a good weekend.

819
00:47:55 --> 00:48:01
See you Monday.

820
00:47:56 --> 00:48:02

821
00:48:07 --> 00:48:13.000