So far in these lectures we've talked about mass, about
acceleration and about forces, but we never used the word
"weight," and weight is a very nonintuitive
and a very tricky thing which is the entire subject
of today's lecture. What is weight? Here you stand
on a bathroom scale. Gravity is acting upon you,
the force is mg, your mass is m. The bathroom scale is pushing
on you with a force F scale and that F scale--
which in this case if the system
is not being accelerated is the same as mg-- that force from
the bathroom scale on you we define as weight. When I stand
on the bathroom scale I could see
my weight is about 165 pounds. Now, it may be
calibrated in newtons but that's, of course,
very unusual. If I weigh myself on the moon where the gravitational
acceleration is six times less then I would weigh six times
less-- so far, so good. Now I'm going to put you
in an elevator and I'm going
to accelerate you upwards and you're standing
on your bathroom scale. Acceleration is
in this direction and I will call this "plus"
and I will call this "minus." Gravity is acting upon you, mg and the bathroom scale is
pushing on you with a force F. That force,
by definition, is weight. Before I write down some
equations, I want you to realize that whenever, whenever you see
in any of my equations "g" g is always plus 9.8. And my signs, my minus signs
take care of the directions but g isalways plus 9.8
or plus 10, if you prefer that. Okay, it's clear that
if this is accelerated upwards that F of s must be
larger than mg; otherwise I
cannot be accelerated. And so we get
Newton's Second Law: F of s is in plus direction... minus mg-- it's in this
direction-- equals m times a and so the bathroom scale
indicates m times a plus g. And I have gained weight. If this acceleration is five meters per second squared
in this direction I am one and a half times
my normal weight. If I look on the bathroom scale,
that's what I see. Seeing is believing--
that is my weight. If I accelerate upwards, with 30
meters per second squared 30 plus 10 is 40-- I am
four times my normal weight. Instead of my 165 pounds, I
would weigh close to 700 pounds. I see that--
seeing is believing. That is my weight. Now I am going to put you
in the elevator-- here you are-- and I'm going to accelerate
you down. This is now a. And just for my convenience I call this now
the plus direction just for my convenience--
it doesn't really matter. So now we have here mg--
that is gravity acting upon you. And now you have the force
from the bathroom scale. Clearly, mg must be
larger than F of s; otherwise you couldn't go
being accelerated downwards. So if now we write down
Newton's Second Law then we get mg minus F of s
must be m times a. This holds for acceleration down and so I get F of s
equals m times g minus a. This is one way of doing it and you put
in positive values for a. If a is five meters
per second squared you get ten minus five is five--
your weight is half. You've lost weight. Being accelerated down,
you've lost weight. You could also
have used this equation and not go through this trouble of setting up
Newton's Law again. You could simply have said "Okay, this a is minus
in this coordinate system" and so you put in
a minus five and a plus ten-- you get the same answer. So you have lost weight
when you accelerate downwards. Suppose now I cut the cable...
cut it. Then this a is ten meters
per second squared if we round it off. You go down with ten meters
per second squared so g minus a is zero. You are now weightless,
you are free-falling. You have no longer any weight. You look at the bathroom scale and the bathroom scale
will indicate zero. You're floating, everything
in the elevator is floating. If you had a glass with water you could turn it over and
the water would not fall out. It's like having
the shuttle in orbit with the astronauts
being weightless. There is a great similarity between the astronauts
in the shuttle and a free-falling elevator. The only difference is that the elevator
will crash, will kill you. In the case of the shuttle it never hits the earth
because of its high speed. We'll talk about this much later when we deal with orbits
and with Kepler's Law. What exactly is free fall? Free fall is when the forces acting upon you
are exclusively gravitational. Nothing is pushing on you; no seat is pushing on you,
no string is pushing on you. Nothing is pulling on you,
only gravity. I will return
to this weightlessness very shortly in great detail but before I do that, I would
like to address the issue-- how could I determine
your weight if I hang you from a string? So now, instead of standing
on a bathroom scale you are here. Here is a string. You might even have
in the string a tension meter as we have seen earlier
in lectures. And you are holding desperately
onto that string. Just like that. The system is not being
accelerated, gravity is mg and so there must be tension
in the string, T which is pulling you up which, if there is no
acceleration, must be mg. I read the scale
and I read my weight. This scale indicates,
in my case, 165 pounds. While I'm hanging,
I can see my weight. So you see,
it makes very little difference whether I am standing
on a bathroom scale and read the force with which the bathroom scale
pushes up on me or whether I hang from a scale extend a spring
and read that value. It makes no difference. The tension here
would indicate my weight. There is a complete similarity
with the bathroom scale except in one case,
something is pulling on me; in the other case, something is
pushing on me from below. Now let's accelerate this system
upwards with an acceleration a-- and I call this plus. Then, of course,
this T must grow; otherwise you
cannot be accelerated. Newton's Second Law,
T minus mg must be ma. The tension in the string
equals m times a plus g. Ah! We've seen that before. No difference with the elevator. You accelerate the system,
the tension will increase and you will see that,
you will read that on the scale. Your weight has increased,
you weigh more. Needless to say, of course, if
you accelerate the system down that you will weigh less-- we
just went through that argument. And if I cut
the cable completely you go into free fall. T will go to zero, a become
minus ten plus ten is zero. You're in free fall. The scale reads zero,
you are completely weightless. If we accept the idea of weight being indicated
by the tension in a string then there is a very
interesting consequence of that. I have here a pin which
is completely frictionless and I have on both sides
a string and this string has
negligibly small mass. Now, just assume
that it is massless. And there is here an object m1
and there is here an object m2 and I am telling you
that m2 is larger than m1. So we all know
what's going to happen. The system is going
to accelerate in this direction. M2 will be accelerated down
and m1 will be accelerated up. What comes now is important,
that you grasp that. I claim that the tension on
the left side must be the same as the tension in this string
on the right side. T Left must be T Right. Why is that? It is because the pin
is frictionless and it is because
the string is massless. Take a little section
of the string here a teeny-weeny little section. If there is a tension on it-- that is, a force
in this direction and there is a force
in this direction-- these two could
never be different because then
this massless string would get
an infinite acceleration. So there can never be
a change in tension from this side of the string
to the other. If you take a little section
of the string here-- there it is,
teeny-weeny little section so there is tension
on the string and there is tension
on the string-- this one could
never be larger than that because this little piece
of string would get
an infinite acceleration. So because there is
no friction on the pin and because the strings
are massless-- only because of that must the
tension be everywhere the same. If there is friction in the
pin-- which we will do later-- then that's not the case. Given the fact
that the tension left and the tension right
are the same I must now conclude that these
two objects have the same weight because didn't we agree that tension is an indication
of weight? So these objects have now
the same weight. And some people may say "Oh, that's a lot of nonsense,
you must be kidding. "If m2 is larger than m1 this must have
a larger weight than that." Well, they are confusing
weight with mass. It is true that m2 is
a larger mass than m1 but it is equally true that the weight of these
two objects is now the same according to
my definition of weight. Let us calculate
the acceleration of this system and let's calculate the tension
and let's see what comes out. I first isolate here
object number one. This is my object number one. I have gravity, m1 g,
and I have a tension T. Nonnegotiable. T better be larger than m1 g. Otherwise it would
never be accelerated up and we know
it will be accelerated up. So what do we get? We get T-- I will call this plus direction,
by the way-- minus m1 g equals m times a. So the tension equals
m1 times a plus g. Hey! We've seen that one before. This one is being
accelerated upwards. Notice it gains weight. That's the tension
and this is the acceleration. I have one equation
with two unknowns so I can't solve it yet. But there is another one,
there is number two here. For number two,
we have a force, m2 g and we have the tension up. This one better be larger
than that one; otherwise it
wouldn't be accelerated down. Let me call this direction plus. The reason why I now switch
directions and call this plus-- as well as this--
is a good reason for it. It's not so arbitrary anymore. I know that this acceleration is going to be
a positive number. Because it's going
in this direction, it's a given. If I called this negative, I would get here
a negative acceleration for the same thing
for which I get here a positive. That's a pain in the neck. I don't want to have a plus
and a minus sign there, have to think about that
it means the same thing. So the moment that I decide to
define this the plus direction I know that this acceleration will also come out to be
the same sign as this one. So I flip the signs there. So now I apply Newton's Law. I get m2 g minus T equals m2 a. And so I get T--
I'll write it here-- equals m2 times g minus a. Two equations with two unknowns. Well, that shouldn't be so hard
to solve these two equations. You can immediately eliminate T,
by the way. If you add this one
with this one, you really-- I call this equation one,
you call this equation two-- you immediately lose your T and
you get that the acceleration, a equals m2 minus m1
divided by m1 plus m2 times g. And you substitute that "a"
in that equation and you'll find that the tension equals 2mg
divided by m1 plus m2. This is very easy for you
to verify. Let us look. This is m1, m2... 2m1, m2--
I lost one m-- 2m1, m2. Let's look at these equations,
let's scrutinize them a little. Let's get some feeling for it rather than accepting them
as being dumb equations. Let's first take the case that m2 equals m1,
and I'll call that "m." Notice that a becomes zero and notice, if you substitute
for m1 and m2 "m" here that you get 2m, you get mg. So T becomes mg. That isutterly obvious. If m1 and m2 are the same,
nothing is going to happen. They're going to sit there,
acceleration will be zero and the tension on both sides-- which is always the same,
we argued that-- is going to be mg. Clear. Now we're going to make
it more interesting. Suppose we make m2
much, much larger than m1 and in a limiting case
we even go with m1 to zero. Let's do that. What you see now,
if m1 goes to zero this goes away, this goes away,
a goes to g and T goes to zero. If m1 is zero, T goes to zero. That is obvious! Because if I make m1 zero,
m2 goes into free fall. And if m2 goes into free fall its weight is zero
and so the tension is zero-- that's exactly what you see-- and you see that
the acceleration of that object is g, which it better be,
because it's in free fall. So you see, this makes sense. This is exactly consistent
with your intuition. And if you wanted to make m1
much, much larger than m2 and you take the limiting case
for m2 goes to zero you'll find again that a goes
to g and that T goes to zero except that now the acceleration
is not this way... (makes whooshing sound) but now the acceleration
is this way and now this object will go
into free fall. And therefore there is no
tension in the string anymore. M1, if I return to the case
which we have there-- that m2 is larger than m1-- m1 is being
accelerated upwards. That's nonnegotiable,
so it must have gained weight. M2 is being accelerated down,
so it must have lost weight. Just like being in an elevator,
there's no difference. They each weigh the same-- one loses weight,
the other gains weight. They each weigh the same,
and so I can make the prediction that if this is m2 g,
which was its original weight and this now
is the new weight, T that m2 g must be larger than T. M1 gains weight,
so T must be larger than m1 g. M2 loses weight,
so T must be smaller than m2 g. That's my prediction--
it has to be. And we can... I can show you
that with some easy numbers. Let m1 be 1.1 kilograms
and let m2 be 1.25 kilograms. Frictionless system, and the
string has a negligible mass. What is the acceleration "a"
of the system? I get m2 minus m1-- that is 0.15 divided
by the sum, which is 2.35 and that is approximately
0.064 g, approximately 0.064 g. It's about 1/16th of
the gravitational acceleration. It's a very modest acceleration. What is the tension? Well, I substitute my numbers
for m1 and m2 in there. You can take, for g,
10, if you like that and you will find
that the tension equals 1.17 g. And now look
at what I predicted. They both weigh 1.17 g,
that's nonnegotiable. That is my definition
of weight-- the tension in both sides
is the same. That's my definition of weight. This is their weight. This one had a weight 1.25 g
without being accelerated. You see, it has lost weight,
because it accelerated down. This one had a weight of 1.1 g. You see, it has gained weight,
because it has accelerated up. So you see, the whole picture
ties together very neatly and it's important
that you look at it that way. I now want to return to the idea
of complete weightlessness and I want to remind you,
a few lectures ago how I was swinging you at the
end of a string in the vertical. I was swinging you like this. And I was swinging
a bucket of water like this. And I want to return to that. I want to look at you when you
are at the bottom of your circle and when you are
at the very top of that circle. You go around a circle
which has radius R. Here is that circle. There's a string here,
you're here. And there's a string here and at some point in time,
you're there. And you're going around...
let's assume that you're going around
with an angular velocity omega and for simplicity,
we keep omega constant. But that's really
not that important. Okay, this is point P
and this is point S. Let's first look
at the situation at point P. You have a mass and so
gravity acts upon you, mg. There is tension
in the string, T. There must be--
this is nonnegotiable-- a centripetal acceleration
upwards. Otherwise,
you could never do this. Remember, from the uniform
circular motion. So there must be here
centripetal acceleration which is omega squared R or, if you prefer,
v squared divided by R if v is the speed,
tangential speed at that point. It must be there. Let's look here. Right there,
gravity is acting upon you, mg. Let's assume this string
is pulling on you. Let's assume that for now,
so there is a tension. The string is pulling on you. Therefore, nonnegotiable, when
you make this curvature here there must be
a centripetal acceleration and that centripetal
acceleration must be omega squared R. That is nonnegotiable,
it has to be there. Let's now evaluate
first the situation at P and I will call this plus and I will call this minus. So what I get now is that T minus mg must be m times
the centripetal acceleration so T must be m times the
centripetal acceleration plus g. Hey! That looks very familiar. It looks like someone is being
accelerated in an elevator-- almost the same equation. If the centripetal acceleration
at this point for instance, were 10 meters
per second squared then you would weigh twice
your normal weight. The tension here
would be twice mg. If this were five meters
per second squared then you would be
1½ times your weight. Let's now look
at the situation at S. At point S, I'm going to call
this plus and that minus. I'm going to find that T plus mg must be m times
the centripetal acceleration-- Newton's Second Law. So I find that the tension there
equals m times a of c minus g. Hey! Very similar
to what I've seen before. This object is losing weight. Let us take the situation that a of c is exactly
10 meters per second squared and we discussed that last time when we had the bucket of water
in our hands. If a of c... if the centripetal acceleration
when it goes through the top is 10, then this is zero. So the string has no tension,
the string goes limp and the bucket of water
and you are weightless. If the centripetal acceleration
is larger than 10 then, of course,
the string will be tight. There will be a force on you and whatever comes out of here
will indicate your weight. If a of c is smaller than 10,
that's meaningless. The tension can
never be negative. A string with negative tension
has no physical meaning. What it means is
that the bucket of water would never have made it
to this point. If you try to swing it up-- as someone tried
in the second lecture-- but didn't make it to that point the bucket of water
will just fall. You end up with a mess,
but that's a detail. So the bucket of water,
when it is here... If the acceleration there,
the centripetal acceleration were exactly 10 meters
per second squared then that bucket of water
would be weightless. So I said earlier
that when you're in free fall all objects in free fall
are weightless. It's like a spacecraft in orbit
or an elevator with a cut cable. It also means
that if I jump off the table that I'm weightless while
I am in mid-air, so to speak. It means this tennis ball... while it is in free fall,
it has no weight. Now it has weight. Now the weight is even higher
because I am accelerating it and now it has no weight. The tennis ball is weightless and I assume, for now,
that the air drag plays no role. If I jump off the table I will be weightless
for about half a second. This is about one meter. If I jump from a tower
which is 100 meters high I will be weightless
for 4½ seconds ignoring air drag. I prefer today
the half a second. I am going to jump
off this table with this water in my hand. And I'm going to tell you
how I can convince you that as I jump, that I will,
indeed, be weightless. Here is the bottle. There is a gravitational force
on the bottle. My hands are pushing up
on this bottle. My hands are being
a bathroom scale. I feel, in my muscles,
the need to push up. In fact, I might even be able
to estimate the weight playing the role
of a bathroom scale. It's a gallon of water,
it's about nine pounds. Now my own body...
gravity is acting upon me but I am being pushed up,
right there. Suppose we jumped. There would be no pushing
from me on the bottle anymore no pushing there on me,
the table. Only gravitation would act upon
us and we would be weightless. How can I show you
that we are weightless? Well, if I don't have to use my muscles to push
on this bottle upwards I might as well
lower my hands a little bit during this free fall. And you will see that the bottle
will just stay above my hands without my having to push up. Therefore,
being the bathroom scale I no longer have to push on it. I no longer... my muscles
don't feel anything and the bottle is
therefore weightless. The bottle is weightless
when we jump; I am weightless and even
this bagel is weightless. We're all weightless
during half a second. There is no such thing
in physics as a free lunch. You have to pay a price for this
half a second of weightlessness. What happens
when I hit the floor? I hit the floor with a velocity
in this direction which is about
five meters per second. You can calculate that. But a little later,
I've come to a stop. That means during the impact there must be
an acceleration upwards. Otherwise my velocity
in this direction could never become zero. Therefore, I will weigh more
during this impact-- there is an acceleration
in this direction. The five meters
per second goes to zero. If I make the assumption that it takes
two-tenths of a second-- that's a very rough guess,
this impact time-- then the average acceleration will be five meters per second
divided by 0.2; that is 25 meters
per second squared. That means the acceleration
upwards is 2½ g. That means I will weigh
3½ times more. Remember it is a plus g, so a is 2½ g up
plus the g that we already have; that makes it 3½ g. So instead
of weighing 165 pounds I weigh close to 600 pounds
for two-tenths of a second. So we get four phases. Right now, I'm my normal weight if I stand
on a bathroom scale. I jump for half a second,
weightless hit the floor for about
two-tenths of a second maybe close to 600 pounds. And then after that I will have
my normal weight again. Now, you're going to have
only half a second to see that this bottle, as I jump,
is floating above my hands. I will pull my hands off so you will see that
I no longer have to push it. That means it's weightless. Are you ready? I'm ready. Three, two, one, zero. Did you see it floating
above my hands? We were both weightless. Now, I have been thinking
about this for a long, long time. I have been thinking whether perhaps this could not be shown
in a more dramatic way perhaps even
a more convincing way. And so I thought of the idea of putting a bathroom scale
under my feet tying it very loosely so that it
wouldn't fall off when I jump and then show you that while I
am half a second in free fall that the bathroom scale
indeed indicates zero. And don't think
that I haven't tried it. I've tried it many times
with many bathroom scales. I made many jumps. There is a problem,
and the problem is the bathroom scales
that you buy-- that you normally
get commercially-- they indeed want to go to zero. It takes them a long time. They have a lot of inertia,
their response time is slow. But even if they make it to zero
by the time you hit the floor then immediately
the weight increases because you hit the floor and your weight comes up
by 3½ times. So it begins to swing
back and forth and it becomes
completely chaotic and you can no longer see
what's happening. And it just so happened that
about six months ago, Dave... I had dinner
with Professor Dave Trumper and I explained it to him
that it is just unfortunate that you can
never really show it that you jump off the table,
have a bathroom scale under you and see that weight go down to
zero when you are in free fall. And he said, "Duck soup--
I can do that." He says, "I can make you a scale "which has a response time
of maybe 10 milliseconds "so when you jump off the table in 10 milliseconds you will see
that thing go down to zero." And he delivered,
he came through. He built this wonderful device which he and I are going
to demonstrate to you. Let me first give you
some reasonable light for this. And I would like to show you
on the scale there what this scale that he built
is indicating. Here is the scale,
I have it in my hands. And on top of this scale
is a little platform just like on your scale. This platform weighs
4½ pounds. And you can see that,
it says about 4½. Now, you will say "Hmm! I wouldn't want
that kind of a bathroom scale. "I mean, if I want to see
my bathroom scale "I want to see a zero
before I want to go up. "I'm heavy enough all by myself. I don't want to get
another 4½ pounds." The manufacturer has simply
zeroed that scale for you but obviously also your bathroom
scale has a cover on it. Once you have seen
these demonstrations you will be able to answer for
yourself why we don't zero this why we really leave this
to be 4½. That's the actual mass which is
on top of the spring. But it's not really a spring-- it is a pressure gauge,
but think of it as a spring. 4½ pounds. Here we have a weight which is a barbell weight,
which is 10 pounds. Is this from one
of your children, Dave or were you doing it yourself? 10 pounds...
we put it on top here. What do you see?
Roughly 14½ pounds. All right, we are going
to tape it down. There we go. And we're going to drop it from about 1½, two meters and we drop it in here,
well-cushioned because we don't want to break
this beautiful device. When we drop it,
the response is so fast that you will see, indeed,
that pointer go to zero. Now, keep in mind,
when it hits the cushion that the weight will go up. For now, I want you
to concentrate only on the thing going to zero
and not what comes later. We will deal with that
within a minute. Okay... 14½ pounds. You know why the thing
is actually jiggling back and forth? I can't hold it exactly still and so I slightly accelerate it
upwards and downwards and when I accelerate it
slightly upwards it weighs a little more and when I accelerate it
downwards, it weighs less. It's interesting. You can see I'm nervous. That's my nervous
tension meter there. Okay, we're ready? Look and... don't look at me,
now, look at that pointer. Three, two, one, zero. Did you see it go to zero?
All the way to zero. Now comes something
even more remarkable. He said to me, "I can also make
the students see the response on a time scale of about
a fraction of a second." By the way, this is the hero
who made all this stuff. He's fantastic. (class applauds) LEWIN:
He can show you the weight
on an electronic scale and this weight you will see
as a function of time. I will put the ten pounds
back on again... tape it a little tighter and so the level that you see
now is 14½ pounds. This is 14½ pounds and this is
zero, this mark is zero. I'm going to hold it in my hand. And notice,
if I can hold it still you're back
to your 14½ pounds. Now I'm going to drop it. You will see it go down to zero. It will hit the floor,
the cushion. It will get
an acceleration upwards. It will become way heavier
than it was before and then it will even be
bounced back up in the air and it goes again
into free fall. We will freeze that for you,
and you will be able... we will be able to analyze it,
then, after it all happens. So, 14½ pounds...
three, two, one, zero. And now Professor Trumper
is freezing it for you. Now look at this, look
at this incredible picture. This is truly an eye-opener
for me, when I saw it. The physics in here
is unbelievable. Here is your 14½ pounds. Tick marks from here to here
are half a second. It was half a second
in free fall and it goes to zero,
that's no weight. Now it hits the floor,
the cushion and its weight goes up in something
like a tenth of a second. Look, this is
about one, two, three... It's about 3½ times
its weight now. So the 14½
has to be multiplied by 3½ or four which is exactly
what we predicted-- that it would be much higher. But now it's being... it bounces off, because
it's a very nice cushion. It throws it back up. So it goes back into the air so it goes immediately
to weightlessness again and then it oscillates
back and forth. And then here you would expect that this level, 14½ pounds,
would be the same as this. And the only reason
why that's not the case is there's a little cable
that fell with it which is pushing a little bit up on the upper... on the upper
disc that is there so it's making it
a little lighter. Isn't it incredible? You see here in front of you
the weightlessness and you see the extra weight
when it hits and again followed
by weightlessness. Dave, A-plus,
you passed the course. There is a great interest in doing experiments
under weightless conditions. NASA was very interested in it. And if you would jump
100 meters up in the sky you would only be
nine seconds up. You wouldn't even be weightless
because of air drag. However, if you could jump up way near the top
of the atmosphere-- where the air drag
is negligible-- then you would be weightless
for quite some time. And that is
what people have been doing for the past few decades. Professor Young
and Professor Oman here at the Aeronautics Department have done what they call
"zero gravity experiments" from airplanes-- and I will
explain that in detail-- but first I want you
to appreciate that "zero gravity"
is a complete misnomer. "Zero weight," yes--
"zero gravity," no. If you have an airplane
anywhere near Earth, flying whether the engines are on
or whether the engines are off or whether it is free-falling
doesn't matter. There is never zero gravity. There is always gravity--
thank goodness. But if you are in free fall,
indeed, there is no weight. Apart from that, they call them
"zero gravity experiments" and why not? Maybe it sells better. They fly an airplane,
which is the KC-135 and they do these experiments at an altitude
of about 30,000 feet. If I could clean this
as best as I can... The plane comes in
at one point in time at an angle of about 45 degrees. There's nothing special
about that 45 degrees. It's just...
that's the way it's done. You have to also think
of the convenience-- convenience for the passengers. The speed is then
about 425 miles per hour so the horizontal component
is about 300 miles per hour and the vertical component is
also 300. The air drag is very little. Let's assume, for the sake
of the argument that the engines are cut and the plane goes
into free fall. It's no different
from this tennis ball-- (makes whooshing sound) the same thing. You're going to see a parabola. And so this plane
is going to free-fall and comes back to this level. And let's analyze this arc,
this parabola. Right here at the top, clearly there will still be
300 meters per second in the absence of any air drag. You should be able to calculate with all the tools
that you have available how high this goes
from this level. In other words, what is the time that the velocity in the y
direction comes to zero? You can calculate that and then you know
how much it has traveled. Very crude number,
this is about 900 meters. And it will take about 15
seconds to reach this point so it will take about 30 seconds
to go from here to here and in those 30 seconds the horizontal displacement
is about 3½ kilometers. And all these numbers
you should be able to confirm. Right here,
the engines are restarted. During this free fall, everyone
in the airplane is weightless including the airplane itself. Now the engines start,
and the engine is sort of... The plane is going to pull up,
it goes into this phase and then the plane flies
horizontally for a while. During this phase,
as we just discussed it's like hitting the floor. You need an acceleration
in this direction. There will be weight increase so there is here
an acceleration upwards. And during this time,
very roughly people have
about twice their weight. And then here,
they have again normal weight. And then the plane
pulls up again and here it goes
and repeats the whole thing again going into free fall. So again here, people have
more than their normal weight. Zero weight,
more than normal weight normal weight, more
than normal weight, free fall. And the whole cycle takes
about 90 seconds. You can imagine
that it is very important when you are here in free fall,
when you have no weight that when your weight comes back
and your weight doubles-- and Professor Oman told me
that this change from zero to twice your weight takes
less than a second-- that you better know where your
feet are and where your head is because if your head is down and you all of a sudden
double your weight you crush your skull,
so you have to be sure that you are standing
straight up in the plane when your weight begins
to double and we will see that
very shortly, how that works. I want to show you first some
slides from these experiments. So here you see the situation
that we just described. Let us start here, that is
where I started with you. The plane turns the engines off. This is the parabola. Here the engines are restarted. This is the free-fall period. This is about 30 seconds. The engine is restarted,
and during this time there is an acceleration upwards
and they call it "2g peak." Well, they really mean 1g. What they really mean,
that my weight doubles. They call that "2g" but, of course,
they call this "0g" which is equally incorrect. It's not 0g--
you have no weight. This is weightless,
here your weight is double here your weight is normal,
here your weight roughly doubles and you go into
another free-fall period and the cycle from here to here
is about 90 seconds. Now, the irony has it that the reason
why these flights are done is to study motion sickness
under weightless conditions. Astronauts were complaining
about motion sickness. And so Professor Young
and Oman have done lots and lots of experiments
with airplanes and later, also, in the shuttle
to study this motion sickness. I find it rather ironic because if you and I were
part of these experiments we would get terribly sick
because of the experiments. Just imagine that you go
from weightlessness into twice your weight,
back to weightlessness. We would be puking all day! How can you study people
who are sick? How can you study the sickness
due to weightlessness? Well, they must
have found a way. They do this
about 50 times per day. And now I want to show you
some real data which were kindly given to me
by Professor Young where you see them actually
in the plane. I believe I have to put this
on one and start the... Can you turn off
the slide projector? So here you see them
in the plane. They are not weightless,
they are climbing up. I think this is Professor Young. The guys lying on the floor
must be a bit tired. The light will shortly go on,
and when the light goes on that's an indication that
the weightlessness is coming up. It already went on, I must have
missed it, I wasn't looking. And there they go
into weightlessness. See, this person is
upside down here. You better get straight up
before your weight doubles because you'll crash
into the floor. (class laughs) LEWIN:
And now it takes 60 seconds because the whole cycle
is 90 seconds and in these 60 seconds they get ready
for the next free fall-- for the next weightlessness. And you will see very shortly the light will go on again,
and that will tell them that the weightlessness
is coming up and then they will be weightless
for another 30 seconds. The sound that you hear is
obviously the engines of the plane. There you go-- light goes on, they get a warning, they
take their headphones off and everything
becomes weightless. They may not like that and so they put their headphones
in a secure place. You see that here
Professor Young takes his off. And there they go again...
swimming in mid-air. (class laughs) 30 seconds weightless. (class laughs) LEWIN:
And the plane
in which this happens... (class laughs) LEWIN:
Yeah, these things happen. I'd like to show you
a last slide of the plane that they do
these experiments from. This is the plane
while it is in free fall. About 45-degree angle and these people have done
a tremendous job in indeed making
a major contribution to the airsickness due
to weightlessness. All right, see you Friday.
