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 object
starts 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-- that this one will go earlier
than that one. So I am going to increase
the tilt... I do it very slowly. I try not to... rock the boat
too much, very slowly. We must be approaching the
critical angle for the plastic. Boy, it's holding on to itself. There it goes... and the rubber
goes a little later. The rubber can be made rough
by rubbing it on one side in which case the angle
will be even larger. I told you that
the friction coefficient is independent
of the mass of the object. I have
two identical bins here... well, as far
as they can be identical. Maybe one at the bottom is
a little rougher than the other. But in one,
I'm going to put 200 grams which is about five times
the weight of the bin. And then, within reason when I tilt them,
they will go at the same angle because it's independent
of the mass. So let's try that again
and see how close they are. It may be off by half a degree
or one degree, of course because the plank is
not uniform everywhere. And now it's 18 degrees...
19½... 20... 20½... 21, and the other one is 21.2. So they almost go
at the same time, so you've seen that apparently the mass has
very small if any effect. Now comes something that I always find
very, very nonintuitive and that is surface area. I have two pieces of wood
and they're identical-- whatever that means,
"identical"; you can never make them exactly
the same in terms of roughness. This surface we prepared as well as we prepared
this bottom surface. But this bottom surface here is
four times smaller in area than this surface area here,
the flat part. I'm going to put
the flat one here and I'm going to put
the same object-- but with its small area-- here. If indeed the friction
coefficient is independent of surface area,
then when I tilt them they should start to slide
roughly at the same angle. There we go. 14 degrees... 16... 18... one
goes and the other one follows. It was in two-tenths
of a degree. And the reason why there's
always some difference-- of course, the plank is
not exactly uniform. I have to be careful that I don't touch
the critical surfaces. So you have seen difference
in friction coefficients and you have seen there's
almost no effect on surface area and there's no effect
on the mass. And that is both
very nonintuitive. The width of the tires
of your car does not matter. And that... I ask you
the question to explain-- in your assignment
number three-- why race cars have
very wide tires. There must be a reason for that. I want you to think about that. There is another way that one can measure
the friction coefficient which is way more complicated and really, that's not the
reason why I want you to see it. The reason why I want you to go
with me through these arguments is that you begin to see how subtle and how really
difficult friction is. I'm going to put an object now on an incline again,
as we did before and instead of having it
sit on its own I'm going to attach to it
a string. So here is that object
and here is the string and a pulley and here a string. And here is an object mass m2,
and this object has mass m1 and the angle here... alpha. I'm looking for my green chalk. I want to use
the same color convention. Now let's look at all the forces
that we can think of. Here is m1 g. Let's decompose that
in y and x direction. And I will call this direction
y, as I always do perpendicular to the surface. So we call this y and I will call this direction
now the positive x direction. You're free to choose it
any way you want to. The force here is m2 g... and now comes a major problem. The biggest problem is
that you do not know in advance whether this system will start
to accelerate in this direction or whether it will start
to accelerate in this direction or whether it will
not accelerate at all-- it's quite possible. And all these three cases,
as you will see have to be dealt with
independently. You cannot do it with one
equation, as you will see. Let's first decompose this force as we did before,
in the y direction. So this one equals
m1 g cosine alpha and this one, the x component-- which is in
the minus x direction now-- equals m1 g sine alpha. Clearly, this one--
m1 g cosine alpha-- we never have to worry about. There is no acceleration
in the y direction so this normal force N
will kill this one and this is m1 g cosine alpha. So you never have to worry
about the y direction; we know there's no acceleration. We only deal with forces
in the x direction that are of interest. There is a tension
in this string and now comes the problem: I do not know in what direction
the frictional force is. If this object has
the tendency to go uphill-- which I don't know yet-- then the frictional force is
in this direction because it opposes always the direction in which
the object wants to go. If, however, this object wants
to go in this direction-- which I do not know-- then the frictional force has
to be put in this direction. And I don't know that. The only thing I do know is that the maximum value
of the friction will be mu static times N,
which is what we had there. Remember, that's
the maximum value that the friction can have
times m1 g cosine alpha. That I know. So now, if I want
to deal with this I have to look at three
complete different situations: acceleration in this direction in which the friction is
pointing here; acceleration in this direction in which the friction is
pointing there; or no acceleration at all. There is also, of course,
the tension here... and this tension is exactly
the same as that tension. We discussed that last time. I will not go over that
because this is an ideal and, of course,
an unphysical situation. The pulley has no mass the pulley is
completely frictionless and the string has no mass--
it's a massless string. And I argued last time that therefore the tension here
must be the same as the tension there. We even know the tension. I'm going to evaluate, for now only situations
that the system is at rest. It's not yet moving. If the system is at rest,
T must be m2 g because this object is
not being accelerated. So we already know that all situations
where the system is at rest T must be m2 g--
that's nonnegotiable. It's this T as well as that T. Now I have to start splitting in
the following situation. My first option is that I make the assumption
that the system is just... just about to start
accelerating upwards. It isn't doing it yet;
it is just about to do that. If that's the case, then I know that the frictional force
will be in this direction and it will have reached
the maximum value with the static
friction coefficient. Now I can write down, in the x
direction, Newton's Second Law. Now I have T, which is
in the positive direction minus m1 g sine alpha
minus F f max. That now has to be zero,
just at the moment that it is just about to change
its mind and start accelerating. Now, I know what T is,
that is, m2 g so m2 g equals m1 g sine alpha plus the maximum frictional
force, which is this value. So this is just at the moment
that it wants to start sliding. Therefore, if I make mass m2
a hair larger, just a hair it will go. And therefore the moment
that I make this a larger sign I know that it's going
to accelerate uphill. That's the criterion
for going uphill. Now I look at situation two. Now I make the assumption that
the object, still standing still is just about
to start accelerating downhill. Aha! If that's the case, I know that the maximum force is
now pointing upwards-- the same magnitude, but it
has now a different direction. So now I can write down
Newton's Second Law. So the frictional force is
now helping T. So now we get T... plus F f max minus
m1 g sine alpha equals zero. We know that this is m2 g so m2 g equals
m1 g sine alpha minus F f max. Notice the difference: there's a plus sign here;
there's a minus sign here. This is... the object
is still not moving but if I make m2 g a hair less,
just a teeny-weeny little less it will definitely start
to accelerate downwards. So if I make this
"smaller than" sign the object will start
accelerating downhill. This is condition one,
this is condition two. If the condition is
neither one nor two... what do you think
will happen then? Very possible
that you don't meet any one of these two conditions. What do you think will happen? (class murmurs) LEWIN:
Can't hear you. (student replies) LEWIN:
It, it won't move-- a is zero. Because this... both cases
are going to accelerate so in all other cases,
the acceleration equals zero. And the frictional force,
in this case will adjust itself
just the right way so that Newton's Second Law
in the x direction will give you,
for the force, a zero. Let us take
a very simple example so that you see this at work. So, we have an example here,
and in my example I have m1 equals 1 kilogram,
m2 equals 2 kilograms. Can't make the numbers
much simpler. I take alpha equals 30 degrees. I take a static friction
coefficient which is 0.5 and I take
a kinetic friction coefficient which is a little less,
which is 0.4. The question is now, is it going
to be accelerated uphill or accelerated downhill
or no acceleration at all? What it comes down to is that we have to evaluate
these three terms. Let's first take m2 g--
m2 g equals 20. We'll just take, for g, 10--
that is just easier. M1 g sine alpha... The sine of alpha is a half,
so that is five. M1 g sine alpha equals five. And what is F f maximum? I have to use, for
my friction coefficient, .5. I have to use, for m1, one here, a 10, and have
the cosine for 30 degrees. And what I find-- you have
to take my word for it-- that this is about 4.33,
and I want to remind you I have used the static
friction coefficient. This is in newtons. I never put a capital N
for newtons because that is very confusing
with this normal force. All my units are always
in S.I. units so the force is always
in newtons. Aha! We are well on our way. Let's first test
whether condition one is met. Is 20 larger than 5 plus 4.33? And the answer is yes, it is. So we know that it's going
to be accelerated uphill. That is nonnegotiable. So now I could ask you
a simple question: What is the acceleration and what is the tension
in the string? And so you will think "Oh, well, that is
within arm's reach." Not quite, because things are
now going to change. If it is going
to be accelerated uphill then at least I know one thing which I am going to put
in this drawing now. I know that this is
the maximum friction possible which now becomes mu kinetic--
because it's going to move-- times m1 times g
times cosine alpha. So that is already one change. It is moving, so sure,
it's going to be accelerated so the frictional force is in
this direction, has this value. So let's write down now Newton's Second Law
in the x direction. So we have T in the positive
direction minus m1 g sine alpha minus this maximum force--
minus mu k m1 g cosine alpha-- and that, now, according
to Newton's Law, must be m1 times a, if a is
T acceleration uphill. One equation with two unknowns. You don't know a
and you don't know T. Or do you know T? What is T?
What is the tension? What is the tension when that thing is
being accelerated uphill? Anyone has the courage to try? (student responds) LEWIN:
You think "m2 g"-- you couldn't be more wrong. It's now moving,
it's being accelerated. That means this object is going
to be accelerated down and if this force is
the same as this it can never accelerate down. This T must get smaller. Remember, an object in an
elevator being accelerated down loses weight--
it's losing weight. This object must
be accelerated down. We have to take that
into account. So the tension, once it starts
accelerating, will go down. So I have the second equation
for object number two. I call this the plus direction,
so for object number two I have m2 g minus T equals
m2 times a. It is very important
that you see that the tension will change. Now I have two equations
with two unknowns and now I can solve. It's very easy-- you just add
them, and I leave you with that. I'll just give you the results. I find that the acceleration, a,
equals plus... I think 3.85. That is correct-- plus 3.85
meters per second squared. And I find that the tension
equals 12.3 newtons. I want to dwell on this
a little bit. I find, for the acceleration,
a plus sign. Had I found a minus sign,
I would... I'm sure I would have made
a mistake. Why is it mandatory
that I find a plus sign? Absolutely mandatory! Who wants to try that one? Yeah? (student making explanation) LEWIN:
Yeah, you say... you say it well. I would have said it
slightly differently. We know that the acceleration is
in this direction. We derived that. Therefore the acceleration since I call that
the "plus x direction"-- that was my plus sign--
must come out plus. So if this comes out negative,
you've made a mistake. I also want this number
to be less than 20. If not, I've made a mistake. Why does that number
have to be less than 20? (student making explanation) LEWIN:
Exactly-- this object is going down. To put it
the way we put it last time it lost weight,
it's accelerated downwards. This Nt g, which is 20,
better wins it from T; otherwise it would
never be accelerated down. So this plus sign is a must,
and this is a must. And if you find not a plus sign
but a minus sign you have to go back
to your calculation because you've made a mistake. Now we take the same situation,
I leave everything unchanged but I make the second mass, m2,
I make it 0.4 kilograms. So now all the numbers remain
the same that we have there except that m2 g now becomes 4. Now I'm going to test again. This m2 g, which is 4-- is that larger than 5 plus the
frictional force static, 4.33? The answer is no. I'm going to test
for my second case. Is m2 g smaller
than 5 minus 4.33? The answer is no,
so what do we conclude? What must be our conclusion? Condition one is not met,
condition two is not met. The conclusion is a is zero. The object will
not be accelerated and the frictional force
is going to adjust along the x direction so that
the acceleration indeed is zero. How does
the frictional force do that? This is that slope,
here is that object. I will only put in the forces
along the x direction. I don't bother
about the y direction. I know that there is m1 g
sine alpha, and that one is 5. So we have here
a component of gravity which is the m1 g sine alpha,
and we know that that is 5. We have it there. I also know
that we have tension here and the tension must be m2 g because the object is
not being accelerated. We're back where we were. Number two is
not being accelerated. The tension is four. Five newtons downhill,
four newtons uphill. What will the friction be, how
large, and in what direction? Uphill, how large? One, exactly. The friction will adjust itself
so that there is equilibrium that nothing is going. All right, I now would like
to do a few demonstrations whereby I want you to calculate the friction coefficients
for me. So we're going to put a particular object
on that incline and I'm first going to raise
the angle until it breaks loose. So you should be able
to calculate what the friction
coefficient is using the equation
tangent alpha equals mu s. And the object that I use
for that is this... this box. In this box is a little weight
that's not very important. It makes the whole thing
361 grams. So I want you to know that the weight
of this object is 361 grams. I'll write it down for you here. So, the mass
of the object is 361; I'm sure that the uncertainty is
at least 1 gram. You have to trust me
when I give you the angles. I'm going to increase
the incline and there comes a moment
that it will start to slide. I'll give you the angle and I want you to calculate
that friction coefficient. So we'll do that first...
there we go. It's now 10 degrees, 11...
12½, 13... 14, 15... 16 17... 17½, 18, 19,
19½, 20-- 20 degrees. It starts to slide at about
20 degrees-- write that down. Now I'm going to do
exactly this experiment: Put a rope over it, with a
pulley, and put m2 on this side. And now I'm going
to load down m2 to the point that it starts
to slide uphill. That should allow you to also calculate
the friction coefficient. You have all the tools for it,
because once you know that it is just at the point
of breaking and going uphill you know that that equals sign
of that equation holds and so you should be able
to calculate the friction coefficient. Would you find
exactly the same number as you find
from this experiment? Not very likely. You have to think
about that for yourself. Wood has grain, and the grain
in this direction could be very different from
the grain in this direction. But it would be interesting
to compare the two numbers to see how much they're off. So I'm going to put here
this rope over here and I'm going to set the angle
now at a given value so this is now not negotiable. I set it at 20. I could be off by half a degree. Again, you see, it wants to go. You just saw that-- at 20
degrees, it wants to go. So I prevent it from going and so I'm going to put
a little weight on here. Now there is 100 grams,
and it's not going. It's happy
and it's sitting there. A is zero. That condition isn't met
and this condition isn't met. So now you must write down
in your notebook that alpha now-- it's
an independent experiment-- equals 20.0,
maybe plus or minus 1. I think it's about 1 degree
accuracy that I can do. Okay, I'm going to load here
more weight-- more mass, I should say-- at m2 and I'll give you the numbers and when it breaks loose,
you will see it. I will give you the numbers. Now, I have done this
many times, believe me and the breaking point is
not always at the same mass. The mass could differ
by 20, 25 grams easily. So whatever number
we're going to find for m2 I would say you should
at least allow an uncertainty of about something
like 25 grams just because I've done
it many times... and I know it could
even be worse at times. The humidity could change
in the room and that could change
the friction coefficient. Okay, we have 100 grams on it...
we have 200 grams on it... 250... 260... 270 and it goes at 270. Did you see it go? It started to slide at 270. So at 270 grams, I met
exactly that condition. It was an equals sign. That should allow you
to calculate the static friction coefficient and you'll get a chance to do
that in your third assignment. When I had this thing up here,
and when I was loading this down making it heavier and heavier,
I hope you realize that at first it wanted
to slide in this direction. So at first the friction was
in this direction. As I loaded it down
more and more the friction became less
and less and less. There comes even a time
that the friction becomes zero. I loaded more and more and more. The friction flips over
to the other side. The friction grows
and grows and grows fights an heroic battle
to not make it go uphill loses the battle at one point,
reaches the maximum value. I put a little bit more on here
and it goes. So this frictional force is
really having a rough time starting off in this direction,
slowly becoming less becoming zero, changing
direction, reaching the maximum and finally losing the battle. Friction is often a pain
in the neck, as we all know. Friction causes wear, it causes
tear and it costs fuel. With a car, there's a lot
of friction with the road. You pay for that, and
people try to reduce friction with bearings and
with lubrication, oil. Water is an amazing lubricant. If it starts raining and there is a little bit
of dust on the road the friction coefficient
between your tires and road can become so low
that you begin to hydroplane and that you literally...
(makes whooshing sound) that your friction coefficient
goes almost to zero. It happened to me once,
and it's no fun. It can happen instantaneously particularly
when the rain begins-- in the very early part
of the rain when the road is dusty so you get the water
with a little bit of dust mixed. It's a very dangerous situation. At home, I have a pan--
this is my pan at home. Actually I have more than
one pan at home, believe me. But this is a very special pan and what is special about it
is something that I discovered
purely by accident and I want to share with you
this remarkable pan. You see,
when I rotate this cover there's a lot of friction--
you can hear it. (metal lid grating) And it stops. You can hear it, right? And so one evening
I was boiling potatoes and I was looking at this pan,
and I walked up to it because I wanted to check
the potatoes. And I touched the thing,
and there was no friction. It just went spinning
and spinning and spinning. I couldn't believe my eyes until I realized
what is happening. Water had accumulated
in the rim of this pan and the cover was beginning
to hydroplane. (metal lid skimming freely) I'm putting water in it now. (metal lid skimming
freely, silently ) You almost don't hear it
anymore. Isn't that amazing? Almost frictionless. So now the water acts
like a lubricant. And you try it with your pan,
it won't work because you need
just the right shape and you need the right edge to be able to lubricate it
that way. There are many experiments
that are done and many attempts have been
made by people to reduce friction. You try, if you can, to avoid
contact between two surfaces. That you can do by putting
a lubricant in between. But even better it would be if you could separate
the object completely and only have air in between because air has much
less friction than a liquid. And that's being done
with great success. People use hovercrafts so they blow air out from below
so the craft lifts itself up and now it's no longer
in contact with the water. It's above the water,
so if it moves now all it has to overcome is
the air friction and that's it and that helps tremendously. You will be seeing
in this lecture hall many demonstrations that I
will be doing in the future with what I call an "air track." I will show it to you
in a minute. It is a long...
call it a bar, for now. The cross-section is
a triangular shape and there are holes in here,
and we blow air out of that. And on top of that are devices which have been
specially designed to perfectly fit this triangle. And when you start blowing
the air they are lifted up,
so they float. And so now when you give them
a little tap they can move almost--
not quite, but almost-- without friction. Here's one... a lot of friction. Now I'll turn on the air. (air whooshing) Look at the difference. Isn't that amazing? It's floating
on its own air cushion. And if I turn it off...
(air clicks off) the moment that the air stops,
you will see it stops. So this is the technique that is often used
to do demonstrations if you have to do them
with a minimum of friction. Of course, you could do
experiments in the shuttle very well, where you have,
again, only air around you. But that's, of course,
a very expensive way. In 26.100,
we will use the air track when we start colliding objects and try to see what happens
before and after the collision. There is another device,
which is very intriguing and that also acts on the idea
that it lifts itself up as a result of gas
which is flowing out. In this case, it's a container
of carbon dioxide... with carbon dioxide in here,
which is solid and there is
a small opening here and this is a... extremely well machined
flat surface, very flat. And the whole thing rests
on an extremely flat surface. Because of the room temperature the carbon dioxide
will start to evaporate and will start to flow out. And therefore under this thing
comes a film a very thin layer
of carbon dioxide and now you can move this
around in two dimensions. You are not stuck, like you
are there, to one dimension of going back and forth
on what we call the air track. But now you can move it
around over this whole surface. And that allows you to do
very interesting things as I want to show you next. First make it dark. FILM NARRATOR:
And we've filled that can
with dry ice that is, solid carbon dioxide. Now, you know solid carbon
dioxide is very cold. This white stuff is just frost that's gathered
on the outside of the can. Now, as the can absorbs heat
from the room the carbon dioxide evaporates
and turns into a gas. The gas takes up more room
than the solid so it has to go somewhere. It can't come out the top so it comes out a little hole
here in the bottom of the disc. Now, you can't see it coming out
the hole, but if I make a flame I think you can see that there's gas coming out
and blowing the flame. Now if we put the disc-- with its stream of gas
coming out the bottom-- down on our table top which is made of a very
smooth piece of plate glass... We can wait a moment while the gas coming out
builds up pressure underneath which it has to do
in order to escape. By now, the disc is floating
on this film of escaping gas. That film is so thin that I'm sure you can't see it
from out there. I can scarcely see a space between the disc
and the glass, myself. But if you'll come
and look over my shoulder I think I can show you
that there is a space by slipping underneath the disc this piece of tinfoil I took
off a chewing gum wrapper. Now, we'll slip the tinfoil
between the disc and the plate glass top
of the table showing that there is indeed
a space, a thin film of gas between the disc and the glass
upon which it's resting. The purpose of this is simply
to reduce the friction to a point where
we won't have to worry about it or measure it
in our experiments today. It's fun to play with
this thing-- let me show you. I'll give it a little push,
just a little one. And there it goes, moving
sedately, no sign of slowing up. Come on back. Same thing
in the other direction. It takes only a very tiny force
to start it in motion. Let me show you that. (triumphant Spanish
dance music playing) (music continues
throughout rest of film) (music ends; applause) LEWIN:
So you see-- fleas are
good for something. Have a good weekend. See you Monday.
