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What I want to do
in this video is

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think about how the
normal force might

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be different in
different scenarios.

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And since my 2 and 1/2-year-old
son is obsessed with elevators,

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I thought I would
focus on those.

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So here I've drawn
four scenarios.

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And we could imagine
them almost happening

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in some type of a sequence.

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So in this first
picture right over here,

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I'm going to assume that
the velocity is equal to 0.

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Or another way to think about it
is this elevator is stationary.

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And everything we're going to
be talking about in this video,

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I'm talking about in
the vertical direction.

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That's the only dimension
we're going to be dealing with.

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So this is 0 meters per second
in the vertical direction.

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Or another way to think about
it, this thing is not moving.

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Now also it is
also-- and this may

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be somewhat obvious to
you-- but its acceleration

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is also 0 meters
per second squared

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in this picture right over here.

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Then let's say that I'm sitting
in this transparent elevator.

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And I press the button.

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So the elevator begins
to accelerate upwards.

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So in this video
right over here,

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or in this screen
right over here,

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let's say that the acceleration
is 2 meters per second.

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And I'll use the convention
that positive means

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upwards or negative
means downwards.

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We're only going to be operating
in this one dimension right

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here.

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I could write 2 meters per
second times the j unit vector

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because that tells us
that we are now moving.

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Why don't we just
leave it like that.

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That tells us that we are
moving in the upward direction.

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And let's say we do
that for 1 second.

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And then we get to this
screen right over here.

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So we had no velocity.

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We move.

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We accelerate.

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Let me-- oh, this is 2
meters per second squared.

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Let me make sure I--
It's 2 meters per second.

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This is acceleration here.

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So we do that for 1 second.

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And then at the end of 1
second, we stop accelerating.

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So here, once we get to this
little screen over here,

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our acceleration
goes back to 0 meters

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per second squared
in the j direction,

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only you don't have to write
that because it's really

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just 0.

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But now we have some velocity.

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We did that just for
the sake of simplicity.

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Let's say this screen
lasted for 1 second.

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So now our velocity is going
to be 2 meters per second

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in the j direction, or
in the upwards direction.

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And then let's say we
do that for 10 seconds.

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So at least at the
constant velocity,

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we travel for 20 meters.

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We travel a little bit while
we're accelerating, too.

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But we're getting
close to our floor.

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And so the elevator
needs to decelerate.

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So then it decelerates.

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The acceleration here
is negative 2 meters

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per second squared times--
in the j direction.

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So it's actually
accelerating downwards now.

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It has to slow it down to
get it back to stationary.

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So what I want to do
is think about what

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would be the normal
force, the force

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that the floor of the
elevator is exerting

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on me in each of
these situations.

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And we're going to assume
that we are operating

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near the surface of the Earth.

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So in every one of
these situations,

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if we're operating near
the surface of the Earth,

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I have some type of
gravitational attraction

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to the Earth and the
Earth has some type

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of gravitational
attraction to me.

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And so let's say that
I'm-- I don't know.

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Let's just make the math simple.

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Let's say that I'm
some type of a toddler.

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And I'm 10 kilograms.

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So maybe this is
my son, although I

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think he's 12 kilograms.

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But we'll keep it simple.

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Oh, let me be clear.

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He doesn't weigh 10 kilograms.

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That's wrong.

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He has a mass of 10 kilograms.

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Weight is the force
due to gravity.

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Mass of the amount of stuff,
the amount of matter there is.

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Although I that's not
a rigorous definition.

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So the mass of the individual,
of this toddler sitting

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in the elevator,
is 10 kilograms.

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So what is the force of gravity.

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Or another way to
think about it,

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what is this person's weight?

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Well, in this vignette
right over here,

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in this picture right
over here, its mass

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times the gravitational
field near the surface

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of the Earth, the 9.8
meters per second squared.

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Let me write that over here.

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The gravitational field near
the surface of the Earth

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is 9.8 meters per
second squared.

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And the negative tells
you it is going downwards.

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So you multiply this
times 10 kilograms.

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The downward force,
the force of gravity,

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is going to be 10 times negative
9.8 meters per second squared.

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So negative 98 newtons.

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And I could say that that's
going to be in the j direction.

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Well, what's going to be the
downward force of gravity here?

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Well, it's going to
be the same thing.

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We're still near the
surface of the Earth.

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We're going to assume that the
gravitational field is roughly

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constant, although
we know it slightly

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changes with the distance
from the center of the Earth.

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But when we're dealing
on the surface,

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we assume that it's
roughly constant.

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And so what we'll assume we have
the exact same force of gravity

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there.

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And of course, this person's
mass, this toddler's mass,

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does not change, depending
on going up a few floors.

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So it's going to have the same
force of gravity downwards

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in every one of
these situations.

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In this first
situation right here,

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this person has no acceleration.

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If they have no acceleration
in any direction,

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and we're only
concerning ourselves

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with the vertical
direction right here,

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that means that there must
be no net force on them.

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This is from Newton's
first law of motion.

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But if there's no
net force on them,

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there must be some force that's
counteracting this force.

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Because if there
was nothing else,

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there would be a net force of
gravity and this poor toddler

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would be plummeting to
the center of the Earth.

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So that net force
in this situation

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is the force of the floor
of the elevator supporting

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the toddler.

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So that force would
be an equal force

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but in the opposite direction.

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And in this case, that
would be the normal force.

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So in this case,
the normal force

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is 98 newtons in
the j direction.

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So it just completely
bounces off.

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There's no net force
on this person.

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They get to hold their
constant velocity of 0.

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And they don't plummet to
the center of the Earth.

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Now, what is the net force
on this individual right

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over here?

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Well, this individual
is accelerating.

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There is acceleration
going on over here.

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So there must be some
type of net force.

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Well, let's think about
what the net force must

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be on this person, or on
this toddler, I should say.

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The net force is going to
be the mass of this toddler.

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It's going to be 10 kilograms
times the acceleration

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of this toddler, times 2 meters
per second squared, which

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is equal to 20 kilogram meters
per second squared, which

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is the same thing as
20 newtons upwards.

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20 newtons upwards
is the net force.

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So if we already have
the force due to gravity

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at 98 newtons downwards--
that's the same thing here;

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that's that one
right over there,

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98 newtons downwards-- we need a
force that not only bounces off

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that 98 newtons downwards to
not only keep it stationary,

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but is also doing
another 20 newtons

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in the upwards direction.

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So here we need a force
in order for the elevator

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to accelerate the toddler
upwards at 2 meters per second,

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you have a net force
is positive 20 newtons,

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or 20 newtons in the
upward direction.

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Or another way to think about
it, if you have negative 98

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newtons here, you're going
to need 20 more than that

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in the positive direction.

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So you're going to need 118
newtons now in the j direction.

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So here, where the elevator
is accelerating upward,

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the normal force is
now 20 newtons higher

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than it was there.

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And that's what's allowing
this toddler to accelerate.

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Now let's think
about this situation.

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No acceleration, but
we do have velocity.

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So here we were stationary.

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Here we do have velocity.

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And you might be
tempted to think,

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oh, maybe I still
have some higher force

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here because I'm moving upwards.

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I have some upwards velocity.

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But remember Newton's
first law of motion.

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If you're at a
constant velocity,

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including a constant
velocity of 0,

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you have no net force on you.

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So this toddler right over
here, once the toddler

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gets to this stage,
the net forces

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are going to look
identical over here.

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And actually, if you're
sitting in either this elevator

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or this elevator, assuming it's
not being bumped around it all,

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you would not be able
to tell the difference

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because your body is
sensitive to acceleration.

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Your body cannot sense its
velocity if it has no air,

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if it has no frame of reference
or nothing to see passing by.

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So to the toddler
there, it doesn't

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know whether it is
stationary or whether it

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has constant velocity.

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It would be able to
tell this-- it would

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feel that kind of
compression on its body.

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And that's what its nerves
are sensitive towards,

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perception is sensitive to.

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But here it's identical
to the first situation.

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And Newton's first law tells
there's no net force on this.

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So it's just like
the first situation.

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The normal force, the force of
the elevator on this toddler's

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shoes, is going to be
identical to the downward force

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due to gravity.

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So the normal force here
is going to be 98 newtons.

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Completely nets out the
downward, the negative 98

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newtons.

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So once again, this
is in the j direction,

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in the positive j direction.

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And then when we
are about to get

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to our floor, what is happening?

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Well, once again we
have a net acceleration

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of negative 2 meters per second.

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So if you have a negative
acceleration, so once again

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what is the net force here?

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The net force over
here is going to be

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the mass of the
toddler, 10 kilograms,

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times negative 2
meters per second.

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And this was right here
in the j direction.

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That's the vertical direction.

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Remember j is just
the unit vector

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in the vertical
direction facing upwards.

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So negative 2 meters per second
squared in the j direction.

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And this is equal to negative
20 kilogram meters per second

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squared in the j direction, or
negative 20 newtons in the j

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direction.

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So the net force on this
is negative 20 newtons.

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So we have the force of
gravity at negative 98 newtons

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in the j direction.

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So we're fully
compensating for that

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because we're still going
to have a net negative force

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while this child
is decelerating.

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And that negative net force
is a negative net force

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of-- I keep repeating
it-- negative 20.

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So we're only going to have
a 78 newton normal force here

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00:11:08,240 --> 00:11:11,250
that counteracts all but
20 newtons of the force

251
00:11:11,250 --> 00:11:13,220
due to gravity.

252
00:11:13,220 --> 00:11:15,280
So this right over
here is going to be

253
00:11:15,280 --> 00:11:18,295
78 newtons in the j direction.

254
00:11:18,295 --> 00:11:20,170
And so I really want
you to think about this.

255
00:11:20,170 --> 00:11:22,700
And I actually really want you
to think about this next time

256
00:11:22,700 --> 00:11:24,180
you're sitting in the elevator.

257
00:11:24,180 --> 00:11:27,770
The only time that you realize
that something is going on

258
00:11:27,770 --> 00:11:30,380
is when that elevator is
really just accelerating

259
00:11:30,380 --> 00:11:32,090
or when it's just decelerating.

260
00:11:32,090 --> 00:11:35,220
When it's just accelerating,
you feel a little bit heavier.

261
00:11:35,220 --> 00:11:38,289
And when it's just decelerating,
you feel a little bit lighter.

262
00:11:38,289 --> 00:11:40,580
And I want you to think a
little bit about why that is.

263
00:11:40,580 --> 00:11:42,420
But while it's moving
at a constant velocity

264
00:11:42,420 --> 00:11:44,750
or is stationary, you
feel like you're just

265
00:11:44,750 --> 00:00:00,000
sitting on the surface
of the planet someplace.