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What I want to do in this video is

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think about how the normal force might be different in different scenarios

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Since my 2.5-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 4 scenarios

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We can imagine them almost happening in some type of the sequence

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So in this first picture right over here

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I am going to assume that the velocity is equal to zero

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or another way to think about this is, the elevator is stationary

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And everything we're gonna be talking about in this video is the vertical direction

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

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So 0 m/s in the vertical dimension

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Another way to think about it, this thing is not moving

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Now it is also--this may be somewhat obvious to you, but its acceleration is also 0 m/s^2

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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 and I press the button

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So the elevator begins to accelerate upwards

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So in this screen right over here, let's say the acceleration is 2 m/s^2

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I'll use a convention that positive means upwards or negative means downward

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So we're only going to be operating in this one dimension right here

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I could write 2 m/s times the j unit vector

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because that tells us where we're moving. I'll just live it like that

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That tells us we're moving in the upward direction

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Let's say we do that for one second and then we get to this screen right over here

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So we have no velocity; we accelerate--

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oh, this is 2 m/s squared. This is acceleration here

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So we do that for one second and at the end of one second, we stop accelerating

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So here in this screen over here, our acceleration goes back to 0 m/s^2

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in the j direction. That's really just zero

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But now we have some velocity

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Just for the sake of simplicity, let's say this screen lasted for 1 second

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So now our velocity's going to be to 2 m/s in the j direction or in the upward direction

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

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So with that constant velocity, we travel for 20 meters

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We traveled a little bit when we were accelerating too

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When we're getting close to our floor

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the elevator needs to decelerate

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So it decelerates. The acceleration here is -2 m/s^2 times--in the j direction

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It's actually accelerating downward now. 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 would be the normal force

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the force that the floor of the elevator is exerting on me

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in each of these situations

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We're going to assume that we're operating near the surface of the earth

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So in every one of these situations, if we're operating near the surface of the earth

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I have some type of gravitational attraction to the earth and

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the earth has some type of gravitational attraction to me

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I'll just make the math simple--let's say that I am some type of a toddler and I'm 10 kg

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So maybe this is my son, although he's 12 kg, but we'll keep it simple

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So let me make it clear. He doesn't weigh 10 kg. That's wrong

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He has the mass of 10 kg; weight is the force due to the gravity

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mass is the amount of matter there is

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Although I haven't found the rigorous definition

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So the mass of the individual, of this toddler sitting at the elevator is 10 kg

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So what is the force of gravity, or another way to think about it, what is this person's weight?

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Well, in this picture right over here, it's

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mass times the gravitational field near the surface of the earth 9.8 m/s squared

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And the negative tells you it's going downwards

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So you multiply this times 10 kg

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The downward force, the force of gravity is going to be 10 kg times -9.8 m/s squared

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So -98 newtons. That's in the j direction

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

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It's going to be the same thing. We're still near the surface of the earth

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We're going to assume that the gravitational field is roughly constant although we know

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it slightly changes with the distance from the center of the earth but

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when we're dealing on the surface, we assume that it's roughly constant

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And so we'll assume we have the exact same force of gravity there and of course

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this toddler's mass 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 in every one of these situations

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In this first situation right here

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the 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 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, there must be some force that's counteracting this force

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because if there was nothing else, there would be a net force of gravity and this

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poor toddler would be plummeting to the center of the earth

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So that net force in this situation is the force of the floor of

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the elevator supporting the toddler

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So that force would be an equal force, but in the opposite direction and in this case

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that would be the normal force. So in this case the normal force is 98 N in the j direction

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So just completely balances off. There's no net force on this person

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they get to hold their constant velocity of zero; they don't plummet to the center of the earth

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Now what is the net force on this individual right over here?

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Well, this individual is accelerating; there is acceleration going on over here

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So there must be some type of net force

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Let's think about what the net force must be on this person, on this toddler I should say

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The net force is going to be the mass of this toddler, 10 kg

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times acceleration of this toddler, times 2 m/s squared which is equal to

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20 kg m / s squared, which is the same thing as 20 N, 20 N upwards

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20 N upwards is the net force

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So if we already have the force due to gravity at 98 N downwards

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That is the same thing here

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90 N downwards

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We need a force that not only balances off that 90 N downwards

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not only keep stationary, but also doing another 20 N in the upward direction

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Here we need a force in order for the elevator to accelerate this toddler upwards at 2 m/s

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You have a net force of positive 20 N, or 20 N in the upward direction

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Or another way to think about it

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if you have -98 N here

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you're going to need 20 more than that in the positive direction

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So you're going to need 118 N, now in the j direction

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So here where the elevator is accelerating upward

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the normal force the is now 20 N higher than it was there

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and that's what's allowing this toddler to accelerate

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Now think about this situation

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No acceleration, but we do have velocity

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So here we were stationary; here we do have velocity

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And you might be tempted to think, oh, maybe I still have some higher force here

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because I'm moving upwards. I have some upwards velocity

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But remember Newton's first law of motion. If you had a constant velocity

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including a constant velocity of zero, you have no net force on you

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So this toddler right over here, the net forces is gonna 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

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assuming it's not being bumped around at all

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you would not be able to tell the difference because there's no--

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your body is sensitive to acceleration

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your body cannot sense velocity that has no frame of reference or nothing to see passing by

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So the toddler there doesn't know whether it is stationary or there's constant velocity

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It would be able tell this; it would feel that kind of compression on its body

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and that's what its nerves or sensitive perception is sensitive to

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But here it's identical to the 1st situation

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and Newton's first law tells us that 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 shoes

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is going to be identical to the downward force due to gravity

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So the normal force here is going to be 98 N; completely nets out the downward the -98 N

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It's in the j direction, in the positive direction

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And then when we're about to get our floor, what is happening?

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Well, once again we have a net acceleration

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We have a net acceleration of -2 m/s^2

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So once again what is the net force here?

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The net force over here is going to be the mass of the toddler 10 kg times -2 m/s^2

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This is in the j direction, the vertical direction

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Remember j is just the unit vector in the vertical direction facing upwards

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So -2 m/s^2 in the j direction

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And this is equal to -20 kg m / s^2 in the j direction

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or -20 N in the j direction

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So the net force on this is -20 N

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So we have the force of gravity -98 N in the j direction

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So we we're not fully compensating for that

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because we're still gonna have a net negative force while this child is decelerating

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And that negative net force is -20

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

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that counteracts all but 20 N of the force due to the gravity

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This right over here is going to be 78 N in the j direction

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I really want you to think about this next time you're sitting in the elevator

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The only time that you realize that something is going on

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is one that elevator's really just accelerating or when it's just decelerating

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When it's just accelerating, you feel a little bit heavier

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When it's just decelerating, you feel a little bit lighter

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I want you to think a little bit about why that is

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While it's moving at a constant velocity or stationary

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you feel like you're just sitting on the surface of the planet someplace