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So far in these lectures

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we've talked about mass, about
acceleration and about forces,

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but we never used the word
"weight," and weight is

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a very nonintuitive
and a very tricky thing

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which is the entire subject
of today's lecture.

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What is weight?

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Here you stand
on a bathroom scale.

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Gravity is acting upon you,
the force is mg, your mass is m.

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The bathroom scale is pushing
on you with a force F scale

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and that F scale--
which in this case

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if the system
is not being accelerated

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is the same as mg--

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that force from
the bathroom scale on you

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we define as weight.

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When I stand
on the bathroom scale

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I could see
my weight is about 165 pounds.

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Now, it may be
calibrated in newtons

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but that's, of course,
very unusual.

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If I weigh myself on the moon

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where the gravitational
acceleration is six times less

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then I would weigh six times
less-- so far, so good.

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Now I'm going to put you
in an elevator

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and I'm going
to accelerate you upwards

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and you're standing
on your bathroom scale.

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Acceleration is
in this direction

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and I will call this "plus"
and I will call this "minus."

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Gravity is acting upon you, mg

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and the bathroom scale is
pushing on you with a force F.

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That force,
by definition, is weight.

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Before I write down some
equations, I want you to realize

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that whenever, whenever you see
in any of my equations "g"

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g is always plus 9.8.

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And my signs, my minus signs
take care of the directions

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but g isalways plus 9.8
or plus 10, if you prefer that.

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Okay, it's clear that
if this is accelerated upwards

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that F of s must be
larger than mg; 

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otherwise I
cannot be accelerated.

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And so we get
Newton's Second Law:

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F of s is in plus direction...

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minus mg-- it's in this
direction-- equals m times a

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and so the bathroom scale
indicates m times a plus g.

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And I have gained weight.

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If this acceleration is

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five meters per second squared
in this direction

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I am one and a half times
my normal weight.

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If I look on the bathroom scale,
that's what I see.

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Seeing is believing--
that is my weight.

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If I accelerate upwards, with 30
meters per second squared

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30 plus 10 is 40-- I am
four times my normal weight.

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Instead of my 165 pounds, I
would weigh close to 700 pounds.

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I see that--
seeing is believing.

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That is my weight.

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Now I am going to put you
in the elevator-- here you are--

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and I'm going to accelerate
you down.

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This is now a.

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And just for my convenience

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I call this now
the plus direction

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just for my convenience--
it doesn't really matter.

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So now we have here mg--
that is gravity acting upon you.

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And now you have the force
from the bathroom scale.

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Clearly, mg must be
larger than F of s;

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otherwise you couldn't go
being accelerated downwards.

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So if now we write down
Newton's Second Law

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then we get mg minus F of s
must be m times a.

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This holds for acceleration down

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and so I get F of s
equals m times g minus a.

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This is one way of doing it

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and you put
in positive values for a.

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If a is five meters
per second squared

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you get ten minus five is five--
your weight is half.

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You've lost weight.

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Being accelerated down,
you've lost weight.

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You could also
have used this equation

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and not go through this trouble

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of setting up
Newton's Law again.

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You could simply have said

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"Okay, this a is minus
in this coordinate system"

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and so you put in
a minus five and a plus ten--

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you get the same answer.

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So you have lost weight
when you accelerate downwards.

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Suppose now I cut the cable...
cut it.

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Then this a is ten meters
per second squared

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if we round it off.

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You go down with ten meters
per second squared

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so g minus a is zero.

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You are now weightless,
you are free-falling.

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You have no longer any weight.

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You look at the bathroom scale

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and the bathroom scale
will indicate zero.

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You're floating, everything
in the elevator is floating.

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If you had a glass with water

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you could turn it over and
the water would not fall out.

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It's like having
the shuttle in orbit

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with the astronauts
being weightless.

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There is a great similarity

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between the astronauts
in the shuttle

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and a free-falling elevator.

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The only difference is

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that the elevator
will crash, will kill you.

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In the case of the shuttle

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it never hits the earth
because of its high speed.

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We'll talk about this much later

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when we deal with orbits
and with Kepler's Law.

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What exactly is free fall?

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Free fall is

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when the forces acting upon you
are exclusively gravitational.

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Nothing is pushing on you; 

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no seat is pushing on you,
no string is pushing on you.

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Nothing is pulling on you,
only gravity.

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I will return
to this weightlessness

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very shortly in great detail

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but before I do that, I would
like to address the issue--

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how could I determine
your weight

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if I hang you from a string?

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So now, instead of standing
on a bathroom scale

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you are here.

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Here is a string.

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You might even have
in the string a tension meter

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as we have seen earlier
in lectures.

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And you are holding desperately
onto that string.

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Just like that.

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The system is not being
accelerated, gravity is mg

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and so there must be tension
in the string, T

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which is pulling you up

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which, if there is no
acceleration, must be mg.

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I read the scale
and I read my weight.

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This scale indicates,
in my case, 165 pounds.

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While I'm hanging,
I can see my weight.

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So you see,
it makes very little difference

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whether I am standing
on a bathroom scale

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and read the force

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with which the bathroom scale
pushes up on me

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or whether I hang from a scale

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extend a spring
and read that value.

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It makes no difference.

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The tension here
would indicate my weight.

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There is a complete similarity
with the bathroom scale

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except in one case,
something is pulling on me;

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in the other case, something is
pushing on me from below.

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Now let's accelerate this system
upwards with an acceleration a--

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and I call this plus.

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Then, of course,
this T must grow; 

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otherwise you
cannot be accelerated.

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Newton's Second Law,
T minus mg must be ma.

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The tension in the string
equals m times a plus g.

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Ah! We've seen that before.

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No difference with the elevator.

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You accelerate the system,
the tension will increase

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and you will see that,
you will read that on the scale.

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Your weight has increased,
you weigh more.

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Needless to say, of course, if
you accelerate the system down

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that you will weigh less-- we
just went through that argument.

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And if I cut
the cable completely

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you go into free fall.

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T will go to zero, a become
minus ten plus ten is zero.

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You're in free fall.

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The scale reads zero,
you are completely weightless.

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If we accept the idea

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of weight being indicated
by the tension in a string

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then there is a very
interesting consequence of that.

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I have here a pin which
is completely frictionless

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and I have on both sides
a string

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and this string has
negligibly small mass.

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Now, just assume
that it is massless.

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And there is here an object m1
and there is here an object m2

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and I am telling you
that m2 is larger than m1.

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So we all know
what's going to happen.

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The system is going
to accelerate in this direction.

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M2 will be accelerated down
and m1 will be accelerated up.

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What comes now is important,
that you grasp that.

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I claim that the tension on
the left side must be the same

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as the tension in this string
on the right side.

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T Left must be T Right.

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Why is that?

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It is because the pin
is frictionless

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and it is because
the string is massless.

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Take a little section
of the string here

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a teeny-weeny little section.

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If there is a tension on it--

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that is, a force
in this direction

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and there is a force
in this direction--

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these two could
never be different

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because then
this massless string

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would get
an infinite acceleration.

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So there can never be
a change in tension

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from this side of the string
to the other.

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If you take a little section
of the string here--

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there it is,
teeny-weeny little section

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so there is tension
on the string

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and there is tension
on the string--

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this one could
never be larger than that

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because this little piece
of string

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would get
an infinite acceleration.

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So because there is
no friction on the pin

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and because the strings
are massless--

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only because of that must the
tension be everywhere the same.

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If there is friction in the
pin-- which we will do later--

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then that's not the case.

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Given the fact
that the tension left

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and the tension right
are the same

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I must now conclude that these
two objects have the same weight

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because didn't we agree

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that tension is an indication
of weight?

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So these objects have now
the same weight.

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And some people may say

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"Oh, that's a lot of nonsense,
you must be kidding.

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"If m2 is larger than m1

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this must have
a larger weight than that."

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Well, they are confusing
weight with mass.

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It is true that m2 is
a larger mass than m1

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but it is equally true

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that the weight of these
two objects is now the same

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according to
my definition of weight.

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Let us calculate
the acceleration of this system

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and let's calculate the tension
and let's see what comes out.

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I first isolate here
object number one.

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This is my object number one.

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I have gravity, m1 g,
and I have a tension T.

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Nonnegotiable.

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T better be larger than m1 g.

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Otherwise it would
never be accelerated up

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and we know
it will be accelerated up.

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So what do we get? We get T--

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I will call this plus direction,
by the way--

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minus m1 g equals m times a.

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So the tension equals
m1 times a plus g.

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Hey! We've seen that one before.

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This one is being
accelerated upwards.

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Notice it gains weight.

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That's the tension
and this is the acceleration.

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I have one equation
with two unknowns

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so I can't solve it yet.

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But there is another one,
there is number two here.

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For number two,
we have a force, m2 g

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and we have the tension up.

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This one better be larger
than that one; 

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otherwise it
wouldn't be accelerated down.

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Let me call this direction plus.

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The reason why I now switch
directions and call this plus--

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as well as this--
is a good reason for it.

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It's not so arbitrary anymore.

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I know that this acceleration

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is going to be
a positive number.

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Because it's going
in this direction, it's a given.

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If I called this negative,

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I would get here
a negative acceleration

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for the same thing
for which I get here a positive.

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That's a pain in the neck.

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I don't want to have a plus
and a minus sign there,

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have to think about that
it means the same thing.

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So the moment that I decide to
define this the plus direction

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I know that this acceleration

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00:14:02 --> 00:14:08
will also come out to be
the same sign as this one.

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So I flip the signs there.

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So now I apply Newton's Law.

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I get m2 g minus T equals m2 a.

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And so I get T--
I'll write it here--

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equals m2 times g minus a.

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Two equations with two unknowns.

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Well, that shouldn't be so hard
to solve these two equations.

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You can immediately eliminate T,
by the way.

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If you add this one
with this one, you really--

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I call this equation one,
you call this equation two--

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you immediately lose your T and
you get that the acceleration, a

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equals m2 minus m1
divided by m1 plus m2 times g.

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And you substitute that "a"
in that equation and you'll find

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that the tension equals 2mg
divided by m1 plus m2.

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This is very easy for you
to verify.

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00:15:20 --> 00:15:26
Let us look.

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This is m1, m2...

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2m1, m2--
I lost one m-- 2m1, m2.

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00:15:32 --> 00:15:38
Let's look at these equations,
let's scrutinize them a little.

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Let's get some feeling for it

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00:15:36 --> 00:15:42
rather than accepting them
as being dumb equations.

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Let's first take the case

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that m2 equals m1,
and I'll call that "m."

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Notice that a becomes zero

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00:15:52 --> 00:15:58
and notice, if you substitute
for m1 and m2 "m" here

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that you get 2m, you get mg.

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So T becomes mg.

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00:16:02 --> 00:16:08
That isutterly obvious.

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If m1 and m2 are the same,
nothing is going to happen.

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They're going to sit there,
acceleration will be zero

286
00:16:11 --> 00:16:17
and the tension on both sides--

287
00:16:13 --> 00:16:19
which is always the same,
we argued that--

288
00:16:15 --> 00:16:21
is going to be mg.

289
00:16:16 --> 00:16:22
Clear.

290
00:16:18 --> 00:16:24
Now we're going to make
it more interesting.

291
00:16:21 --> 00:16:27
Suppose we make m2
much, much larger than m1

292
00:16:26 --> 00:16:32
and in a limiting case
we even go with m1 to zero.

293
00:16:30 --> 00:16:36
Let's do that.

294
00:16:33 --> 00:16:39
What you see now,
if m1 goes to zero

295
00:16:37 --> 00:16:43
this goes away, this goes away,
a goes to g and T goes to zero.

296
00:16:47 --> 00:16:53
If m1 is zero, T goes to zero.

297
00:16:50 --> 00:16:56
That is obvious!

298
00:16:54 --> 00:17:00
Because if I make m1 zero,
m2 goes into free fall.

299
00:17:00 --> 00:17:06
And if m2 goes into free fall

300
00:17:02 --> 00:17:08
its weight is zero
and so the tension is zero--

301
00:17:05 --> 00:17:11
that's exactly what you see--

302
00:17:07 --> 00:17:13
and you see that
the acceleration of that object

303
00:17:09 --> 00:17:15
is g, which it better be,
because it's in free fall.

304
00:17:12 --> 00:17:18
So you see, this makes sense.

305
00:17:15 --> 00:17:21
This is exactly consistent
with your intuition.

306
00:17:18 --> 00:17:24
And if you wanted to make m1
much, much larger than m2

307
00:17:22 --> 00:17:28
and you take the limiting case
for m2 goes to zero

308
00:17:26 --> 00:17:32
you'll find again that a goes
to g and that T goes to zero

309
00:17:31 --> 00:17:37
except that now the acceleration
is not this way...

310
00:17:35 --> 00:17:41
(makes whooshing sound )

311
00:17:37 --> 00:17:43
but now the acceleration
is this way

312
00:17:39 --> 00:17:45
and now this object will go
into free fall.

313
00:17:43 --> 00:17:49
And therefore there is no
tension in the string anymore.

314
00:17:48 --> 00:17:54

315
00:17:51 --> 00:17:57
M1, if I return to the case
which we have there--

316
00:17:55 --> 00:18:01
that m2 is larger than m1--

317
00:17:58 --> 00:18:04
m1 is being
accelerated upwards.

318
00:18:00 --> 00:18:06
That's nonnegotiable,
so it must have gained weight.

319
00:18:03 --> 00:18:09
M2 is being accelerated down,
so it must have lost weight.

320
00:18:08 --> 00:18:14
Just like being in an elevator,
there's no difference.

321
00:18:12 --> 00:18:18
They each weigh the same--

322
00:18:14 --> 00:18:20
one loses weight,
the other gains weight.

323
00:18:17 --> 00:18:23
They each weigh the same,
and so I can make the prediction

324
00:18:21 --> 00:18:27
that if this is m2 g,
which was its original weight

325
00:18:27 --> 00:18:33
and this now
is the new weight, T

326
00:18:29 --> 00:18:35
that m2 g must be larger than T.

327
00:18:32 --> 00:18:38
M1 gains weight,
so T must be larger than m1 g.

328
00:18:35 --> 00:18:41
M2 loses weight,
so T must be smaller than m2 g.

329
00:18:40 --> 00:18:46
That's my prediction--
it has to be.

330
00:18:43 --> 00:18:49
And we can... I can show you
that with some easy numbers.

331
00:18:46 --> 00:18:52
Let m1 be 1.1 kilograms
and let m2 be 1.25 kilograms.

332
00:18:56 --> 00:19:02
Frictionless system, and the
string has a negligible mass.

333
00:19:02 --> 00:19:08
What is the acceleration "a"
of the system?

334
00:19:05 --> 00:19:11
I get m2 minus m1--

335
00:19:07 --> 00:19:13
that is 0.15 divided
by the sum, which is 2.35

336
00:19:14 --> 00:19:20
and that is approximately
0.064 g, approximately 0.064 g.

337
00:19:22 --> 00:19:28
It's about 1/16th of
the gravitational acceleration.

338
00:19:25 --> 00:19:31
It's a very modest acceleration.

339
00:19:29 --> 00:19:35
What is the tension?

340
00:19:31 --> 00:19:37
Well, I substitute my numbers
for m1 and m2 in there.

341
00:19:35 --> 00:19:41
You can take, for g,
10, if you like that

342
00:19:37 --> 00:19:43
and you will find
that the tension equals 1.17 g.

343
00:19:44 --> 00:19:50
And now look
at what I predicted.

344
00:19:48 --> 00:19:54
They both weigh 1.17 g,
that's nonnegotiable.

345
00:19:53 --> 00:19:59
That is my definition
of weight--

346
00:19:54 --> 00:20:00
the tension in both sides
is the same.

347
00:19:56 --> 00:20:02
That's my definition of weight.

348
00:19:58 --> 00:20:04
This is their weight.

349
00:20:00 --> 00:20:06
This one had a weight 1.25 g
without being accelerated.

350
00:20:08 --> 00:20:14
You see, it has lost weight,
because it accelerated down.

351
00:20:12 --> 00:20:18
This one had a weight of 1.1 g.

352
00:20:16 --> 00:20:22
You see, it has gained weight,
because it has accelerated up.

353
00:20:20 --> 00:20:26
So you see, the whole picture
ties together very neatly

354
00:20:23 --> 00:20:29
and it's important
that you look at it that way.

355
00:20:27 --> 00:20:33
I now want to return to the idea
of complete weightlessness

356
00:20:34 --> 00:20:40
and I want to remind you,
a few lectures ago

357
00:20:37 --> 00:20:43
how I was swinging you at the
end of a string in the vertical.

358
00:20:41 --> 00:20:47
I was swinging you like this.

359
00:20:43 --> 00:20:49
And I was swinging
a bucket of water like this.

360
00:20:47 --> 00:20:53
And I want to return to that.

361
00:20:50 --> 00:20:56
I want to look at you when you
are at the bottom of your circle

362
00:20:57 --> 00:21:03
and when you are
at the very top of that circle.

363
00:21:01 --> 00:21:07

364
00:21:04 --> 00:21:10
You go around a circle
which has radius R.

365
00:21:09 --> 00:21:15
Here is that circle.

366
00:21:10 --> 00:21:16

367
00:21:15 --> 00:21:21
There's a string here,
you're here.

368
00:21:18 --> 00:21:24
And there's a string here

369
00:21:20 --> 00:21:26
and at some point in time,
you're there.

370
00:21:22 --> 00:21:28
And you're going around...
let's assume

371
00:21:24 --> 00:21:30
that you're going around
with an angular velocity omega

372
00:21:28 --> 00:21:34
and for simplicity,
we keep omega constant.

373
00:21:30 --> 00:21:36
But that's really
not that important.

374
00:21:34 --> 00:21:40
Okay, this is point P
and this is point S.

375
00:21:39 --> 00:21:45
Let's first look
at the situation at point P.

376
00:21:43 --> 00:21:49
You have a mass and so
gravity acts upon you, mg.

377
00:21:49 --> 00:21:55
There is tension
in the string, T.

378
00:21:53 --> 00:21:59
There must be--
this is nonnegotiable--

379
00:21:55 --> 00:22:01
a centripetal acceleration
upwards.

380
00:21:58 --> 00:22:04
Otherwise,
you could never do this.

381
00:22:01 --> 00:22:07
Remember, from the uniform
circular motion.

382
00:22:03 --> 00:22:09
So there must be here
centripetal acceleration

383
00:22:08 --> 00:22:14
which is omega squared R

384
00:22:10 --> 00:22:16
or, if you prefer,
v squared divided by R

385
00:22:14 --> 00:22:20
if v is the speed,
tangential speed at that point.

386
00:22:18 --> 00:22:24
It must be there.

387
00:22:22 --> 00:22:28
Let's look here.

388
00:22:24 --> 00:22:30
Right there,
gravity is acting upon you, mg.

389
00:22:31 --> 00:22:37
Let's assume this string
is pulling on you.

390
00:22:33 --> 00:22:39
Let's assume that for now,
so there is a tension.

391
00:22:38 --> 00:22:44
The string is pulling on you.

392
00:22:41 --> 00:22:47
Therefore, nonnegotiable, when
you make this curvature here

393
00:22:46 --> 00:22:52
there must be
a centripetal acceleration

394
00:22:49 --> 00:22:55
and that centripetal
acceleration

395
00:22:51 --> 00:22:57
must be omega squared R.

396
00:22:53 --> 00:22:59
That is nonnegotiable,
it has to be there.

397
00:22:57 --> 00:23:03
Let's now evaluate
first the situation at P

398
00:23:01 --> 00:23:07
and I will call this plus

399
00:23:04 --> 00:23:10
and I will call this minus.

400
00:23:07 --> 00:23:13
So what I get now is

401
00:23:09 --> 00:23:15
that T minus mg

402
00:23:13 --> 00:23:19
must be m times
the centripetal acceleration

403
00:23:18 --> 00:23:24
so T must be m times the
centripetal acceleration plus g.

404
00:23:24 --> 00:23:30
Hey! That looks very familiar.

405
00:23:27 --> 00:23:33
It looks like someone is being
accelerated in an elevator--

406
00:23:31 --> 00:23:37
almost the same equation.

407
00:23:35 --> 00:23:41
If the centripetal acceleration
at this point

408
00:23:40 --> 00:23:46
for instance, were 10 meters
per second squared

409
00:23:44 --> 00:23:50
then you would weigh twice
your normal weight.

410
00:23:47 --> 00:23:53
The tension here
would be twice mg.

411
00:23:53 --> 00:23:59
If this were five meters
per second squared

412
00:23:56 --> 00:24:02
then you would be
1½ times your weight.

413
00:24:01 --> 00:24:07
Let's now look
at the situation at S.

414
00:24:05 --> 00:24:11

415
00:24:07 --> 00:24:13
At point S, I'm going to call
this plus and that minus.

416
00:24:16 --> 00:24:22
I'm going to find that T plus mg

417
00:24:22 --> 00:24:28
must be m times
the centripetal acceleration--

418
00:24:25 --> 00:24:31
Newton's Second Law.

419
00:24:27 --> 00:24:33
So I find that the tension there
equals m times a of c minus g.

420
00:24:35 --> 00:24:41
Hey! Very similar
to what I've seen before.

421
00:24:39 --> 00:24:45
This object is losing weight.

422
00:24:44 --> 00:24:50
Let us take the situation

423
00:24:47 --> 00:24:53
that a of c is exactly
10 meters per second squared

424
00:24:50 --> 00:24:56
and we discussed that last time

425
00:24:52 --> 00:24:58
when we had the bucket of water
in our hands.

426
00:24:54 --> 00:25:00
If a of c...

427
00:24:56 --> 00:25:02
if the centripetal acceleration
when it goes through the top

428
00:24:59 --> 00:25:05
is 10, then this is zero.

429
00:25:02 --> 00:25:08
So the string has no tension,
the string goes limp

430
00:25:06 --> 00:25:12
and the bucket of water
and you are weightless.
 

431
00:25:11 --> 00:25:17
If the centripetal acceleration
is larger than 10

432
00:25:16 --> 00:25:22
then, of course,
the string will be tight.

433
00:25:19 --> 00:25:25
There will be a force on you

434
00:25:21 --> 00:25:27
and whatever comes out of here
will indicate your weight.

435
00:25:26 --> 00:25:32
If a of c is smaller than 10,
that's meaningless.

436
00:25:33 --> 00:25:39
The tension can
never be negative.

437
00:25:36 --> 00:25:42
A string with negative tension
has no physical meaning.

438
00:25:39 --> 00:25:45
What it means is
that the bucket of water

439
00:25:41 --> 00:25:47
would never have made it
to this point.

440
00:25:43 --> 00:25:49
If you try to swing it up--

441
00:25:45 --> 00:25:51
as someone tried
in the second lecture--

442
00:25:47 --> 00:25:53
but didn't make it to that point

443
00:25:48 --> 00:25:54
the bucket of water
will just fall.

444
00:25:51 --> 00:25:57
You end up with a mess,
but that's a detail.

445
00:25:55 --> 00:26:01
So the bucket of water,
when it is here...

446
00:26:00 --> 00:26:06
If the acceleration there,
the centripetal acceleration

447
00:26:03 --> 00:26:09
were exactly 10 meters
per second squared

448
00:26:05 --> 00:26:11
then that bucket of water
would be weightless.

449
00:26:11 --> 00:26:17
So I said earlier
that when you're in free fall

450
00:26:14 --> 00:26:20
all objects in free fall
are weightless.

451
00:26:17 --> 00:26:23
It's like a spacecraft in orbit
or an elevator with a cut cable.

452
00:26:23 --> 00:26:29
It also means
that if I jump off the table

453
00:26:28 --> 00:26:34
that I'm weightless while
I am in mid-air, so to speak.

454
00:26:33 --> 00:26:39
It means this tennis ball...

455
00:26:35 --> 00:26:41
while it is in free fall,
it has no weight.

456
00:26:38 --> 00:26:44
Now it has weight.

457
00:26:41 --> 00:26:47
Now the weight is even higher
because I am accelerating it

458
00:26:44 --> 00:26:50
and now it has no weight.

459
00:26:46 --> 00:26:52
The tennis ball is weightless

460
00:26:48 --> 00:26:54
and I assume, for now,
that the air drag plays no role.

461
00:26:55 --> 00:27:01
If I jump off the table

462
00:26:58 --> 00:27:04
I will be weightless
for about half a second.

463
00:27:01 --> 00:27:07
This is about one meter.

464
00:27:03 --> 00:27:09
If I jump from a tower
which is 100 meters high

465
00:27:06 --> 00:27:12
I will be weightless
for 4½ seconds

466
00:27:09 --> 00:27:15
ignoring air drag.

467
00:27:11 --> 00:27:17
I prefer today
the half a second.

468
00:27:17 --> 00:27:23
I am going to jump
off this table

469
00:27:20 --> 00:27:26
with this water in my hand.

470
00:27:25 --> 00:27:31
And I'm going to tell you
how I can convince you

471
00:27:28 --> 00:27:34
that as I jump, that I will,
indeed, be weightless.

472
00:27:33 --> 00:27:39
Here is the bottle.

473
00:27:35 --> 00:27:41
There is a gravitational force
on the bottle.

474
00:27:39 --> 00:27:45
My hands are pushing up
on this bottle.

475
00:27:43 --> 00:27:49
My hands are being
a bathroom scale.

476
00:27:46 --> 00:27:52
I feel, in my muscles,
the need to push up.

477
00:27:50 --> 00:27:56
In fact, I might even be able
to estimate the weight

478
00:27:53 --> 00:27:59
playing the role
of a bathroom scale.

479
00:27:56 --> 00:28:02
It's a gallon of water,
it's about nine pounds.

480
00:28:00 --> 00:28:06

481
00:28:04 --> 00:28:10
Now my own body...
gravity is acting upon me

482
00:28:07 --> 00:28:13
but I am being pushed up,
right there.

483
00:28:13 --> 00:28:19
Suppose we jumped.

484
00:28:17 --> 00:28:23
There would be no pushing
from me on the bottle anymore

485
00:28:21 --> 00:28:27
no pushing there on me,
the table.

486
00:28:25 --> 00:28:31
Only gravitation would act upon
us and we would be weightless.

487
00:28:30 --> 00:28:36
How can I show you
that we are weightless?

488
00:28:32 --> 00:28:38
Well, if I don't have to use

489
00:28:34 --> 00:28:40
my muscles to push
on this bottle upwards

490
00:28:37 --> 00:28:43
I might as well
lower my hands a little bit

491
00:28:39 --> 00:28:45
during this free fall.

492
00:28:41 --> 00:28:47
And you will see that the bottle
will just stay above my hands

493
00:28:45 --> 00:28:51
without my having to push up.

494
00:28:47 --> 00:28:53
Therefore,
being the bathroom scale

495
00:28:50 --> 00:28:56
I no longer have to push on it.

496
00:28:52 --> 00:28:58
I no longer... my muscles
don't feel anything

497
00:28:55 --> 00:29:01
and the bottle is
therefore weightless.

498
00:28:58 --> 00:29:04
The bottle is weightless
when we jump; 

499
00:29:00 --> 00:29:06
I am weightless and even
this bagel is weightless.

500
00:29:03 --> 00:29:09
We're all weightless
during half a second.

501
00:29:07 --> 00:29:13
There is no such thing
in physics as a free lunch.

502
00:29:12 --> 00:29:18
You have to pay a price for this
half a second of weightlessness.

503
00:29:17 --> 00:29:23
What happens
when I hit the floor?

504
00:29:19 --> 00:29:25
I hit the floor with a velocity
in this direction

505
00:29:22 --> 00:29:28
which is about
five meters per second.

506
00:29:24 --> 00:29:30
You can calculate that.

507
00:29:26 --> 00:29:32
But a little later,
I've come to a stop.

508
00:29:29 --> 00:29:35
That means during the impact

509
00:29:30 --> 00:29:36
there must be
an acceleration upwards.

510
00:29:33 --> 00:29:39
Otherwise my velocity
in this direction

511
00:29:35 --> 00:29:41
could never become zero.

512
00:29:38 --> 00:29:44
Therefore, I will weighmore
during this impact--

513
00:29:42 --> 00:29:48
there is an acceleration
in this direction.

514
00:29:44 --> 00:29:50
The five meters
per second goes to zero.

515
00:29:49 --> 00:29:55
If I make the assumption

516
00:29:50 --> 00:29:56
that it takes
two-tenths of a second--

517
00:29:52 --> 00:29:58
that's a very rough guess,
this impact time--

518
00:29:53 --> 00:29:59
then the average acceleration

519
00:29:55 --> 00:30:01
will be five meters per second
divided by 0.2;

520
00:29:58 --> 00:30:04
that is 25 meters
per second squared.

521
00:30:01 --> 00:30:07
That means the acceleration
upwards is 2½ g.

522
00:30:06 --> 00:30:12
That means I will weigh
3½ times more.

523
00:30:09 --> 00:30:15
Remember it is a plus g,

524
00:30:11 --> 00:30:17
so a is 2½ g up
plus the g that we already have;

525
00:30:14 --> 00:30:20
that makes it 3½ g.

526
00:30:17 --> 00:30:23
So instead
of weighing 165 pounds

527
00:30:19 --> 00:30:25
I weigh close to 600 pounds
for two-tenths of a second.

528
00:30:23 --> 00:30:29
So we get four phases.

529
00:30:25 --> 00:30:31
Right now, I'm my normal weight

530
00:30:27 --> 00:30:33
if I stand
on a bathroom scale.

531
00:30:29 --> 00:30:35
I jump for half a second,
weightless

532
00:30:31 --> 00:30:37
hit the floor for about
two-tenths of a second

533
00:30:34 --> 00:30:40
maybe close to 600 pounds.

534
00:30:37 --> 00:30:43
And then after that I will have
my normal weight again.

535
00:30:40 --> 00:30:46
Now, you're going to have
only half a second to see

536
00:30:44 --> 00:30:50
that this bottle, as I jump,
is floating above my hands.

537
00:30:48 --> 00:30:54
I will pull my hands off

538
00:30:50 --> 00:30:56
so you will see that
I no longer have to push it.

539
00:30:54 --> 00:31:00
That means it's weightless.

540
00:30:57 --> 00:31:03
Are you ready? I'm ready.

541
00:31:01 --> 00:31:07
Three, two, one, zero.

542
00:31:03 --> 00:31:09
Did you see it floating
above my hands?

543
00:31:07 --> 00:31:13
We were both weightless.

544
00:31:09 --> 00:31:15
Now, I have been thinking
about this

545
00:31:14 --> 00:31:20
for a long, long time.

546
00:31:16 --> 00:31:22
I have been thinking whether

547
00:31:18 --> 00:31:24
perhaps this could not be shown
in a more dramatic way

548
00:31:23 --> 00:31:29
perhaps even
a more convincing way.

549
00:31:27 --> 00:31:33
And so I thought of the idea

550
00:31:28 --> 00:31:34
of putting a bathroom scale
under my feet

551
00:31:31 --> 00:31:37
tying it very loosely so that it
wouldn't fall off when I jump

552
00:31:35 --> 00:31:41
and then show you that while I
am half a second in free fall

553
00:31:39 --> 00:31:45
that the bathroom scale
indeed indicates zero.

554
00:31:43 --> 00:31:49
And don't think
that I haven't tried it.

555
00:31:45 --> 00:31:51
I've tried it many times
with many bathroom scales.

556
00:31:47 --> 00:31:53
I made many jumps.

557
00:31:49 --> 00:31:55
There is a problem,
and the problem is

558
00:31:51 --> 00:31:57
the bathroom scales
that you buy--

559
00:31:54 --> 00:32:00
that you normally
get commercially--

560
00:31:56 --> 00:32:02
they indeed want to go to zero.

561
00:31:58 --> 00:32:04
It takes them a long time.

562
00:32:00 --> 00:32:06
They have a lot of inertia,
their response time is slow.

563
00:32:04 --> 00:32:10
But even if they make it to zero
by the time you hit the floor

564
00:32:08 --> 00:32:14
then immediately
the weight increases

565
00:32:12 --> 00:32:18
because you hit the floor

566
00:32:13 --> 00:32:19
and your weight comes up
by 3½ times.

567
00:32:14 --> 00:32:20
So it begins to swing
back and forth

568
00:32:17 --> 00:32:23
and it becomes
completely chaotic

569
00:32:18 --> 00:32:24
and you can no longer see
what's happening.

570
00:32:21 --> 00:32:27
And it just so happened that
about six months ago, Dave...

571
00:32:24 --> 00:32:30
I had dinner
with Professor Dave Trumper

572
00:32:27 --> 00:32:33
and I explained it to him
that it is just unfortunate

573
00:32:30 --> 00:32:36
that you can
never really show it

574
00:32:32 --> 00:32:38
that you jump off the table,
have a bathroom scale under you

575
00:32:35 --> 00:32:41
and see that weight go down to
zero when you are in free fall.

576
00:32:38 --> 00:32:44
And he said, "Duck soup--
I can do that."

577
00:32:41 --> 00:32:47
He says, "I can make you a scale

578
00:32:44 --> 00:32:50
"which has a response time
of maybe 10 milliseconds

579
00:32:48 --> 00:32:54
"so when you jump off the table

580
00:32:50 --> 00:32:56
in 10 milliseconds you will see
that thing go down to zero."

581
00:32:54 --> 00:33:00
And he delivered,
he came through.

582
00:32:59 --> 00:33:05
He built this wonderful device

583
00:33:01 --> 00:33:07
which he and I are going
to demonstrate to you.

584
00:33:05 --> 00:33:11
Let me first give you
some reasonable light for this.

585
00:33:13 --> 00:33:19
And I would like to show you
on the scale there

586
00:33:18 --> 00:33:24
what this scale that he built
is indicating.

587
00:33:21 --> 00:33:27
Here is the scale,
I have it in my hands.

588
00:33:26 --> 00:33:32
And on top of this scale
is a little platform

589
00:33:28 --> 00:33:34
just like on your scale.

590
00:33:30 --> 00:33:36
This platform weighs
4½ pounds.

591
00:33:33 --> 00:33:39
And you can see that,
it says about 4½.

592
00:33:38 --> 00:33:44
Now, you will say

593
00:33:39 --> 00:33:45
"Hmm! I wouldn't want
that kind of a bathroom scale.

594
00:33:42 --> 00:33:48
"I mean, if I want to see
my bathroom scale

595
00:33:44 --> 00:33:50
"I want to see a zero
before I want to go up.

596
00:33:46 --> 00:33:52
"I'm heavy enough all by myself.

597
00:33:48 --> 00:33:54
I don't want to get
another 4½ pounds."

598
00:33:50 --> 00:33:56
The manufacturer has simply
zeroed that scale for you

599
00:33:54 --> 00:34:00
but obviously also your bathroom
scale has a cover on it.

600
00:33:58 --> 00:34:04
Once you have seen
these demonstrations

601
00:34:01 --> 00:34:07
you will be able to answer for
yourself why we don't zero this

602
00:34:05 --> 00:34:11
why we really leave this
to be 4½.

603
00:34:08 --> 00:34:14
That's the actual mass which is
on top of the spring.

604
00:34:12 --> 00:34:18
But it's not really a spring--

605
00:34:14 --> 00:34:20
it is a pressure gauge,
but think of it as a spring.

606
00:34:17 --> 00:34:23
4½ pounds.

607
00:34:19 --> 00:34:25
Here we have a weight

608
00:34:23 --> 00:34:29
which is a barbell weight,
which is 10 pounds.

609
00:34:29 --> 00:34:35
Is this from one
of your children, Dave

610
00:34:33 --> 00:34:39
or were you doing it yourself?

611
00:34:35 --> 00:34:41
10 pounds...
we put it on top here.

612
00:34:40 --> 00:34:46
What do you see?
Roughly 14½ pounds.

613
00:34:44 --> 00:34:50
All right, we are going
to tape it down.

614
00:34:47 --> 00:34:53

615
00:34:52 --> 00:34:58
There we go.

616
00:34:53 --> 00:34:59
And we're going to drop it

617
00:34:56 --> 00:35:02
from about 1½, two meters

618
00:34:59 --> 00:35:05
and we drop it in here,
well-cushioned

619
00:35:02 --> 00:35:08
because we don't want to break
this beautiful device.

620
00:35:04 --> 00:35:10

621
00:35:07 --> 00:35:13
When we drop it,
the response is so fast

622
00:35:11 --> 00:35:17
that you will see, indeed,
that pointer go to zero.

623
00:35:14 --> 00:35:20
Now, keep in mind,
when it hits the cushion

624
00:35:18 --> 00:35:24
that the weight will go up.

625
00:35:20 --> 00:35:26
For now, I want you
to concentrate

626
00:35:22 --> 00:35:28
only on the thing going to zero
and not what comes later.

627
00:35:26 --> 00:35:32
We will deal with that
within a minute.

628
00:35:28 --> 00:35:34

629
00:35:32 --> 00:35:38
Okay... 14½ pounds.

630
00:35:39 --> 00:35:45
You know why the thing
is actually jiggling

631
00:35:41 --> 00:35:47
back and forth?

632
00:35:43 --> 00:35:49
I can't hold it exactly still

633
00:35:45 --> 00:35:51
and so I slightly accelerate it
upwards and downwards

634
00:35:48 --> 00:35:54
and when I accelerate it
slightly upwards

635
00:35:50 --> 00:35:56
it weighs a little more

636
00:35:51 --> 00:35:57
and when I accelerate it
downwards, it weighs less.

637
00:35:54 --> 00:36:00
It's interesting.

638
00:35:55 --> 00:36:01
You can see I'm nervous.

639
00:35:56 --> 00:36:02
That's my nervous
tension meter there.

640
00:36:00 --> 00:36:06
Okay, we're ready?

641
00:36:02 --> 00:36:08
Look and... don't look at me,
now, look at that pointer.

642
00:36:06 --> 00:36:12
Three, two, one, zero.

643
00:36:09 --> 00:36:15
Did you see it go to zero?
All the way to zero.

644
00:36:14 --> 00:36:20
Now comes something
even more remarkable.

645
00:36:18 --> 00:36:24
He said to me, "I can also make
the students see the response

646
00:36:26 --> 00:36:32
on a time scale of about
a fraction of a second."
 

647
00:36:30 --> 00:36:36
By the way, this is the hero
who made all this stuff.

648
00:36:33 --> 00:36:39
He's fantastic.

649
00:36:34 --> 00:36:40
(class applauds )

650
00:36:41 --> 00:36:47
LEWIN:
He can show you the weight
on an electronic scale

651
00:36:48 --> 00:36:54
and this weight you will see
as a function of time.

652
00:36:54 --> 00:37:00
I will put the ten pounds
back on again...

653
00:36:58 --> 00:37:04
tape it a little tighter

654
00:37:04 --> 00:37:10
and so the level that you see
now is 14½ pounds.

655
00:37:10 --> 00:37:16
This is 14½ pounds and this is
zero, this mark is zero.

656
00:37:15 --> 00:37:21
I'm going to hold it in my hand.

657
00:37:24 --> 00:37:30
And notice,
if I can hold it still

658
00:37:25 --> 00:37:31
you're back
to your 14½ pounds.

659
00:37:27 --> 00:37:33

660
00:37:28 --> 00:37:34
Now I'm going to drop it.

661
00:37:31 --> 00:37:37
You will see it go down to zero.

662
00:37:34 --> 00:37:40
It will hit the floor,
the cushion.

663
00:37:37 --> 00:37:43
It will get
an acceleration upwards.

664
00:37:39 --> 00:37:45
It will become way heavier
than it was before

665
00:37:41 --> 00:37:47
and then it will even be
bounced back up in the air

666
00:37:45 --> 00:37:51
and it goes again
into free fall.

667
00:37:47 --> 00:37:53
We will freeze that for you,
and you will be able...

668
00:37:50 --> 00:37:56
we will be able to analyze it,
then, after it all happens.

669
00:37:56 --> 00:38:02
So, 14½ pounds...
three, two, one, zero.

670
00:38:02 --> 00:38:08

671
00:38:05 --> 00:38:11
And now Professor Trumper
is freezing it for you.

672
00:38:07 --> 00:38:13
Now look at this, look
at this incredible picture.

673
00:38:11 --> 00:38:17
This is truly an eye-opener
for me, when I saw it.

674
00:38:14 --> 00:38:20
The physics in here
is unbelievable.

675
00:38:17 --> 00:38:23
Here is your 14½ pounds.

676
00:38:20 --> 00:38:26
Tick marks from here to here
are half a second.

677
00:38:23 --> 00:38:29
It was half a second
in free fall

678
00:38:25 --> 00:38:31
and it goes to zero,
that's no weight.

679
00:38:28 --> 00:38:34
Now it hits the floor,
the cushion

680
00:38:30 --> 00:38:36
and its weight goes up

681
00:38:32 --> 00:38:38
in something
like a tenth of a second.

682
00:38:34 --> 00:38:40
Look, this is
about one, two, three...

683
00:38:36 --> 00:38:42
It's about 3½ times
its weight now.

684
00:38:39 --> 00:38:45
So the 14½
has to be multiplied

685
00:38:42 --> 00:38:48
by 3½ or four

686
00:38:43 --> 00:38:49
which is exactly
what we predicted--

687
00:38:45 --> 00:38:51
that it would be much higher.

688
00:38:46 --> 00:38:52
But now it's being...

689
00:38:48 --> 00:38:54
it bounces off, because
it's a very nice cushion.

690
00:38:50 --> 00:38:56
It throws it back up.

691
00:38:51 --> 00:38:57
So it goes back into the air

692
00:38:53 --> 00:38:59
so it goes immediately
to weightlessness again

693
00:38:55 --> 00:39:01
and then it oscillates
back and forth.

694
00:38:57 --> 00:39:03
And then here you would expect

695
00:38:59 --> 00:39:05
that this level, 14½ pounds,
would be the same as this.

696
00:39:03 --> 00:39:09
And the only reason
why that's not the case is

697
00:39:05 --> 00:39:11
there's a little cable
that fell with it

698
00:39:07 --> 00:39:13
which is pushing a little bit up

699
00:39:09 --> 00:39:15
on the upper... on the upper
disc that is there

700
00:39:13 --> 00:39:19
so it's making it
a little lighter.

701
00:39:14 --> 00:39:20
Isn't it incredible?

702
00:39:16 --> 00:39:22
You see here in front of you
the weightlessness

703
00:39:19 --> 00:39:25
and you see the extra weight
when it hits

704
00:39:21 --> 00:39:27
and again followed
by weightlessness.

705
00:39:25 --> 00:39:31
Dave, A-plus,
you passed the course.

706
00:39:27 --> 00:39:33

707
00:39:31 --> 00:39:37
There is a great interest

708
00:39:33 --> 00:39:39
in doing experiments
under weightless conditions.

709
00:39:37 --> 00:39:43
NASA was very interested in it.

710
00:39:41 --> 00:39:47
And if you would jump
100 meters up in the sky

711
00:39:46 --> 00:39:52
you would only be
nine seconds up.

712
00:39:48 --> 00:39:54
You wouldn't even be weightless
because of air drag.

713
00:39:51 --> 00:39:57
However, if you could jump up

714
00:39:53 --> 00:39:59
way near the top
of the atmosphere--

715
00:39:55 --> 00:40:01
where the air drag
is negligible--

716
00:39:58 --> 00:40:04
then you would be weightless
for quite some time.

717
00:40:01 --> 00:40:07
And that is
what people have been doing

718
00:40:04 --> 00:40:10
for the past few decades.

719
00:40:06 --> 00:40:12
Professor Young
and Professor Oman here

720
00:40:08 --> 00:40:14
at the Aeronautics Department

721
00:40:10 --> 00:40:16
have done what they call
"zero gravity experiments"

722
00:40:14 --> 00:40:20
from airplanes-- and I will
explain that in detail--

723
00:40:17 --> 00:40:23
but first I want you
to appreciate

724
00:40:19 --> 00:40:25
that "zero gravity"
is a complete misnomer.

725
00:40:23 --> 00:40:29
"Zero weight," yes--
"zero gravity," no.

726
00:40:28 --> 00:40:34
If you have an airplane
anywhere near Earth, flying

727
00:40:30 --> 00:40:36
whether the engines are on
or whether the engines are off

728
00:40:33 --> 00:40:39
or whether it is free-falling
doesn't matter.

729
00:40:35 --> 00:40:41
There is never zero gravity.

730
00:40:36 --> 00:40:42
There is always gravity--
thank goodness.

731
00:40:39 --> 00:40:45
But if you are in free fall,
indeed, there is no weight.

732
00:40:44 --> 00:40:50
Apart from that, they call them
"zero gravity experiments"

733
00:40:48 --> 00:40:54
and why not?

734
00:40:49 --> 00:40:55
Maybe it sells better.

735
00:40:51 --> 00:40:57

736
00:40:53 --> 00:40:59
They fly an airplane,
which is the KC-135

737
00:40:59 --> 00:41:05
and they do these experiments

738
00:41:01 --> 00:41:07
at an altitude
of about 30,000 feet.

739
00:41:07 --> 00:41:13
If I could clean this
as best as I can...

740
00:41:10 --> 00:41:16

741
00:41:12 --> 00:41:18
The plane comes in
at one point in time

742
00:41:19 --> 00:41:25
at an angle of about 45 degrees.

743
00:41:21 --> 00:41:27
There's nothing special
about that 45 degrees.

744
00:41:24 --> 00:41:30
It's just...
that's the way it's done.

745
00:41:26 --> 00:41:32
You have to also think
of the convenience--

746
00:41:29 --> 00:41:35
convenience for the passengers.

747
00:41:31 --> 00:41:37
The speed is then
about 425 miles per hour

748
00:41:40 --> 00:41:46
so the horizontal component
is about 300 miles per hour

749
00:41:43 --> 00:41:49
and the vertical component is
also 300.

750
00:41:48 --> 00:41:54
The air drag is very little.

751
00:41:50 --> 00:41:56
Let's assume, for the sake
of the argument

752
00:41:52 --> 00:41:58
that the engines are cut

753
00:41:55 --> 00:42:01
and the plane goes
into free fall.

754
00:41:57 --> 00:42:03
It's no different
from this tennis ball--

755
00:41:59 --> 00:42:05
(makes whooshing sound )

756
00:42:01 --> 00:42:07
the same thing.

757
00:42:02 --> 00:42:08
You're going to see a parabola.

758
00:42:04 --> 00:42:10
And so this plane
is going to free-fall

759
00:42:07 --> 00:42:13
and comes back to this level.

760
00:42:12 --> 00:42:18
And let's analyze this arc,
this parabola.

761
00:42:15 --> 00:42:21
Right here at the top, clearly

762
00:42:18 --> 00:42:24
there will still be
300 meters per second

763
00:42:21 --> 00:42:27
in the absence of any air drag.

764
00:42:23 --> 00:42:29
You should be able to calculate

765
00:42:24 --> 00:42:30
with all the tools
that you have available

766
00:42:26 --> 00:42:32
how high this goes
from this level.

767
00:42:30 --> 00:42:36
In other words, what is the time

768
00:42:32 --> 00:42:38
that the velocity in the y
direction comes to zero?

769
00:42:36 --> 00:42:42
You can calculate that

770
00:42:37 --> 00:42:43
and then you know
how much it has traveled.

771
00:42:39 --> 00:42:45
Very crude number,
this is about 900 meters.

772
00:42:43 --> 00:42:49
And it will take about 15
seconds to reach this point

773
00:42:47 --> 00:42:53
so it will take about 30 seconds
to go from here to here

774
00:42:50 --> 00:42:56
and in those 30 seconds

775
00:42:54 --> 00:43:00
the horizontal displacement
is about 3½ kilometers.

776
00:42:58 --> 00:43:04
And all these numbers
you should be able to confirm.

777
00:43:03 --> 00:43:09
Right here,
the engines are restarted.

778
00:43:09 --> 00:43:15
During this free fall, everyone
in the airplane is weightless

779
00:43:13 --> 00:43:19
including the airplane itself.

780
00:43:15 --> 00:43:21
Now the engines start,
and the engine is sort of...

781
00:43:17 --> 00:43:23
The plane is going to pull up,
it goes into this phase

782
00:43:21 --> 00:43:27
and then the plane flies
horizontally for a while.

783
00:43:24 --> 00:43:30
During this phase,
as we just discussed

784
00:43:26 --> 00:43:32
it's like hitting the floor.

785
00:43:28 --> 00:43:34
You need an acceleration
in this direction.

786
00:43:31 --> 00:43:37
There will be weight increase

787
00:43:34 --> 00:43:40
so there is here
an acceleration upwards.

788
00:43:37 --> 00:43:43
And during this time,
very roughly

789
00:43:40 --> 00:43:46
people have
about twice their weight.

790
00:43:43 --> 00:43:49
And then here,
they have again normal weight.

791
00:43:46 --> 00:43:52
And then the plane
pulls up again

792
00:43:49 --> 00:43:55
and here it goes
and repeats the whole thing

793
00:43:52 --> 00:43:58
again going into free fall.

794
00:43:56 --> 00:44:02
So again here, people have
more than their normal weight.

795
00:44:02 --> 00:44:08
Zero weight,
more than normal weight

796
00:44:05 --> 00:44:11
normal weight, more
than normal weight, free fall.

797
00:44:08 --> 00:44:14
And the whole cycle takes
about 90 seconds.

798
00:44:14 --> 00:44:20
You can imagine
that it is very important

799
00:44:16 --> 00:44:22
when you are here in free fall,
when you have no weight

800
00:44:19 --> 00:44:25
that when your weight comes back
and your weight doubles--

801
00:44:23 --> 00:44:29
and Professor Oman told me
that this change from zero

802
00:44:26 --> 00:44:32
to twice your weight takes
less than a second--

803
00:44:28 --> 00:44:34
that you better know where your
feet are and where your head is

804
00:44:32 --> 00:44:38
because if your head is down

805
00:44:34 --> 00:44:40
and you all of a sudden
double your weight

806
00:44:36 --> 00:44:42
you crush your skull,
so you have to be sure

807
00:44:39 --> 00:44:45
that you are standing
straight up in the plane

808
00:44:42 --> 00:44:48
when your weight begins
to double

809
00:44:44 --> 00:44:50
and we will see that
very shortly, how that works.

810
00:44:48 --> 00:44:54
I want to show you first some
slides from these experiments.

811
00:44:53 --> 00:44:59
So here you see the situation
that we just described.

812
00:44:59 --> 00:45:05
Let us start here, that is
where I started with you.

813
00:45:04 --> 00:45:10
The plane turns the engines off.

814
00:45:06 --> 00:45:12
This is the parabola.

815
00:45:07 --> 00:45:13
Here the engines are restarted.

816
00:45:10 --> 00:45:16
This is the free-fall period.

817
00:45:12 --> 00:45:18
This is about 30 seconds.

818
00:45:15 --> 00:45:21
The engine is restarted,
and during this time

819
00:45:18 --> 00:45:24
there is an acceleration upwards
and they call it "2g peak."

820
00:45:22 --> 00:45:28
Well, they really mean 1g.

821
00:45:24 --> 00:45:30
What they really mean,
that my weight doubles.

822
00:45:27 --> 00:45:33
They call that "2g"

823
00:45:28 --> 00:45:34
but, of course,
they call this "0g"

824
00:45:31 --> 00:45:37
which is equally incorrect.

825
00:45:32 --> 00:45:38
It's not 0g--
you have noweight.

826
00:45:35 --> 00:45:41
This is weightless,
here your weight is double

827
00:45:37 --> 00:45:43
here your weight is normal,
here your weight roughly doubles

828
00:45:40 --> 00:45:46
and you go into
another free-fall period

829
00:45:43 --> 00:45:49
and the cycle from here to here
is about 90 seconds.

830
00:45:48 --> 00:45:54
Now, the irony has it

831
00:45:50 --> 00:45:56
that the reason
why these flights are done

832
00:45:53 --> 00:45:59
is to study motion sickness
under weightless conditions.

833
00:45:57 --> 00:46:03
Astronauts were complaining
about motion sickness.

834
00:46:00 --> 00:46:06
And so Professor Young
and Oman have done

835
00:46:03 --> 00:46:09
lots and lots of experiments
with airplanes

836
00:46:05 --> 00:46:11
and later, also, in the shuttle
to study this motion sickness.

837
00:46:09 --> 00:46:15
I find it rather ironic

838
00:46:10 --> 00:46:16
because if you and I were
part of these experiments

839
00:46:15 --> 00:46:21
we would get terribly sick
because of the experiments.

840
00:46:18 --> 00:46:24
Just imagine that you go
from weightlessness

841
00:46:20 --> 00:46:26
into twice your weight,
back to weightlessness.

842
00:46:23 --> 00:46:29
We would be puking all day!

843
00:46:25 --> 00:46:31
How can you study people
who are sick?

844
00:46:29 --> 00:46:35
How can you study the sickness
due to weightlessness?

845
00:46:32 --> 00:46:38
Well, they must
have found a way.

846
00:46:35 --> 00:46:41
They do this
about 50 times per day.

847
00:46:38 --> 00:46:44
And now I want to show you
some real data

848
00:46:41 --> 00:46:47
which were kindly given to me
by Professor Young

849
00:46:47 --> 00:46:53
where you see them actually
in the plane.

850
00:46:51 --> 00:46:57
I believe I have to put this
on one and start the...

851
00:47:00 --> 00:47:06
Can you turn off
the slide projector?

852
00:47:02 --> 00:47:08

853
00:47:06 --> 00:47:12
So here you see them
in the plane.

854
00:47:08 --> 00:47:14
They are not weightless,
they are climbing up.

855
00:47:11 --> 00:47:17

856
00:47:20 --> 00:47:26
I think this is Professor Young.

857
00:47:22 --> 00:47:28
The guys lying on the floor
must be a bit tired.

858
00:47:25 --> 00:47:31
The light will shortly go on,
and when the light goes on

859
00:47:28 --> 00:47:34
that's an indication that
the weightlessness is coming up.

860
00:47:33 --> 00:47:39
It already went on, I must have
missed it, I wasn't looking.

861
00:47:37 --> 00:47:43
And there they go
into weightlessness.

862
00:47:42 --> 00:47:48
See, this person is
upside down here.

863
00:47:44 --> 00:47:50
You better get straight up
before your weight doubles

864
00:47:47 --> 00:47:53
because you'll crash
into the floor.

865
00:47:50 --> 00:47:56
(class laughs )

866
00:47:53 --> 00:47:59

867
00:48:03 --> 00:48:09
LEWIN:
And now it takes 60 seconds

868
00:48:06 --> 00:48:12
because the whole cycle
is 90 seconds

869
00:48:09 --> 00:48:15
and in these 60 seconds

870
00:48:13 --> 00:48:19
they get ready
for the next free fall--

871
00:48:17 --> 00:48:23
for the next weightlessness.

872
00:48:18 --> 00:48:24
And you will see very shortly

873
00:48:20 --> 00:48:26
the light will go on again,
and that will tell them

874
00:48:23 --> 00:48:29
that the weightlessness
is coming up

875
00:48:25 --> 00:48:31
and then they will be weightless
for another 30 seconds.

876
00:48:29 --> 00:48:35

877
00:48:33 --> 00:48:39
The sound that you hear is
obviously

878
00:48:35 --> 00:48:41
the engines of the plane.

879
00:48:37 --> 00:48:43

880
00:48:42 --> 00:48:48
There you go-- light goes on,

881
00:48:44 --> 00:48:50
they get a warning, they
take their headphones off

882
00:48:46 --> 00:48:52
and everything
becomes weightless.

883
00:48:48 --> 00:48:54
They may not like that

884
00:48:50 --> 00:48:56
and so they put their headphones
in a secure place.

885
00:48:53 --> 00:48:59
You see that here
Professor Young takes his off.

886
00:48:57 --> 00:49:03
And there they go again...
swimming in mid-air.

887
00:49:04 --> 00:49:10
(class laughs )

888
00:49:08 --> 00:49:14
30 seconds weightless.

889
00:49:10 --> 00:49:16

890
00:49:16 --> 00:49:22
(class laughs )

891
00:49:17 --> 00:49:23
LEWIN:
And the plane
in which this happens...

892
00:49:19 --> 00:49:25
(class laughs )

893
00:49:24 --> 00:49:30
LEWIN:
Yeah, these things happen.

894
00:49:26 --> 00:49:32
I'd like to show you
a last slide of the plane

895
00:49:30 --> 00:49:36
that they do
these experiments from.

896
00:49:33 --> 00:49:39
This is the plane
while it is in free fall.

897
00:49:37 --> 00:49:43
About 45-degree angle

898
00:49:41 --> 00:49:47
and these people have done
a tremendous job

899
00:49:44 --> 00:49:50
in indeed making
a major contribution

900
00:49:47 --> 00:49:53
to the airsickness due
to weightlessness.

901
00:49:52 --> 00:49:58
All right, see you Friday.

902
00:49:55 --> 00:50:01

903
00:50:00 --> 00:50:06.000