What I want to do in this video is
think about how the normal force might be different in different scenarios
Since my 2.5-year-old son is obsessed with elevators
I thought I would focus on those
So here I've drawn 4 scenarios
We can imagine them almost happening in some type of the sequence
So in this first picture right over here
I am going to assume that the velocity is equal to zero
or another way to think about this is, the elevator is stationary
And everything we're gonna be talking about in this video is the vertical direction
That's the only dimension we're going to be dealing with
So 0 m/s in the vertical dimension
Another way to think about it, this thing is not moving
Now it is also--this may be somewhat obvious to you, but its acceleration is also 0 m/s^2
in this picture right over here
Then let's say that I'm sitting in this transparent elevator and I press the button
So the elevator begins to accelerate upwards
So in this screen right over here, let's say the acceleration is 2 m/s^2
I'll use a convention that positive means upwards or negative means downward
So we're only going to be operating in this one dimension right here
I could write 2 m/s times the j unit vector
because that tells us where we're moving. I'll just live it like that
That tells us we're moving in the upward direction
Let's say we do that for one second and then we get to this screen right over here
So we have no velocity; we accelerate--
oh, this is 2 m/s squared. This is acceleration here
So we do that for one second and at the end of one second, we stop accelerating
So here in this screen over here, our acceleration goes back to 0 m/s^2
in the j direction. That's really just zero
But now we have some velocity
Just for the sake of simplicity, let's say this screen lasted for 1 second
So now our velocity's going to be to 2 m/s in the j direction or in the upward direction
And then let's say we do that for 10 seconds
So with that constant velocity, we travel for 20 meters
We traveled a little bit when we were accelerating too
When we're getting close to our floor
the elevator needs to decelerate
So it decelerates. The acceleration here is -2 m/s^2 times--in the j direction
It's actually accelerating downward now. Has to slow it down to get it back to stationary
So what I want to do is think about what would be the normal force
the force that the floor of the elevator is exerting on me
in each of these situations
We're going to assume that we're operating near the surface of the earth
So in every one of these situations, if we're operating near the surface of the earth
I have some type of gravitational attraction to the earth and
the earth has some type of gravitational attraction to me
I'll just make the math simple--let's say that I am some type of a toddler and I'm 10 kg
So maybe this is my son, although he's 12 kg, but we'll keep it simple
So let me make it clear. He doesn't weigh 10 kg. That's wrong
He has the mass of 10 kg; weight is the force due to the gravity
mass is the amount of matter there is
Although I haven't found the rigorous definition
So the mass of the individual, of this toddler sitting at the elevator is 10 kg
So what is the force of gravity, or another way to think about it, what is this person's weight?
Well, in this picture right over here, it's
mass times the gravitational field near the surface of the earth 9.8 m/s squared
And the negative tells you it's going downwards
So you multiply this times 10 kg
The downward force, the force of gravity is going to be 10 kg times -9.8 m/s squared
So -98 newtons. That's in the j direction
Well, what's going to be the downward force of gravity here?
It's going to be the same thing. We're still near the surface of the earth
We're going to assume that the gravitational field is roughly constant although we know
it slightly changes with the distance from the center of the earth but
when we're dealing on the surface, we assume that it's roughly constant
And so we'll assume we have the exact same force of gravity there and of course
this toddler's mass does not change depending on going up a few floors
So it's going to have the same force of gravity downwards in every one of these situations
In this first situation right here
the person has no acceleration
If they have no acceleration in any direction
and we're only concerning ourselves with the vertical direction right here
that means that there must be no net force on them
This is from Newton's first law of motion
But if there's no net force on them, there must be some force that's counteracting this force
because if there was nothing else, there would be a net force of gravity and this
poor toddler would be plummeting to the center of the earth
So that net force in this situation is the force of the floor of
the elevator supporting the toddler
So that force would be an equal force, but in the opposite direction and in this case
that would be the normal force. So in this case the normal force is 98 N in the j direction
So just completely balances off. There's no net force on this person
they get to hold their constant velocity of zero; they don't plummet to the center of the earth
Now what is the net force on this individual right over here?
Well, this individual is accelerating; there is acceleration going on over here
So there must be some type of net force
Let's think about what the net force must be on this person, on this toddler I should say
The net force is going to be the mass of this toddler, 10 kg
times acceleration of this toddler, times 2 m/s squared which is equal to
20 kg m / s squared, which is the same thing as 20 N, 20 N upwards
20 N upwards is the net force
So if we already have the force due to gravity at 98 N downwards
That is the same thing here
90 N downwards
We need a force that not only balances off that 90 N downwards
not only keep stationary, but also doing another 20 N in the upward direction
Here we need a force in order for the elevator to accelerate this toddler upwards at 2 m/s
You have a net force of positive 20 N, or 20 N in the upward direction
Or another way to think about it
if you have -98 N here
you're going to need 20 more than that in the positive direction
So you're going to need 118 N, now in the j direction
So here where the elevator is accelerating upward
the normal force the is now 20 N higher than it was there
and that's what's allowing this toddler to accelerate
Now think about this situation
No acceleration, but we do have velocity
So here we were stationary; here we do have velocity
And you might be tempted to think, oh, maybe I still have some higher force here
because I'm moving upwards. I have some upwards velocity
But remember Newton's first law of motion. If you had a constant velocity
including a constant velocity of zero, you have no net force on you
So this toddler right over here, the net forces is gonna look identical over here
And actually if you're sitting in either this elevator
or this elevator
assuming it's not being bumped around at all
you would not be able to tell the difference because there's no--
your body is sensitive to acceleration
your body cannot sense velocity that has no frame of reference or nothing to see passing by
So the toddler there doesn't know whether it is stationary or there's constant velocity
It would be able tell this; it would feel that kind of compression on its body
and that's what its nerves or sensitive perception is sensitive to
But here it's identical to the 1st situation
and Newton's first law tells us that there's no net force on this
So it's just like the first situation
the normal force, the force of the elevator on this toddler's shoes
is going to be identical to the downward force due to gravity
So the normal force here is going to be 98 N; completely nets out the downward the -98 N
It's in the j direction, in the positive direction
And then when we're about to get our floor, what is happening?
Well, once again we have a net acceleration
We have a net acceleration of -2 m/s^2
So once again what is the net force here?
The net force over here is going to be the mass of the toddler 10 kg times -2 m/s^2
This is in the j direction, the vertical direction
Remember j is just the unit vector in the vertical direction facing upwards
So -2 m/s^2 in the j direction
And this is equal to -20 kg m / s^2 in the j direction
or -20 N in the j direction
So the net force on this is -20 N
So we have the force of gravity -98 N in the j direction
So we we're not fully compensating for that
because we're still gonna have a net negative force while this child is decelerating
And that negative net force is -20
So we're only going to have a 78 N normal force here
that counteracts all but 20 N of the force due to the gravity
This right over here is going to be 78 N in the j direction
I really want you to think about this next time you're sitting in the elevator
The only time that you realize that something is going on
is one that elevator's really just accelerating or when it's just decelerating
When it's just accelerating, you feel a little bit heavier
When it's just decelerating, you feel a little bit lighter
I want you to think a little bit about why that is
While it's moving at a constant velocity or stationary
you feel like you're just sitting on the surface of the planet someplace