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 weighmore 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 noweight.
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.