Main content

## Physics library

# Normal force in an elevator

How the normal force changes when an elevator accelerates. Created by Sal Khan.

## Want to join the conversation?

- At1:22, Sal mentions the j unit vector. What is that?(32 votes)
- The j unit vector is a unit vector (a vector of magnitude/length 1) that points in the positive "y" direction on an x-y graph. Two dimensional vectors are often written in terms of their x-y components, expressed as a number multiplied by the i unit vector (the x component) and a number multiplied by the j unit vector (the y component).(13 votes)

- In the second case, isn't it the external force that pulls the elevator in the upper direction? As I see it, the toddler is at rest relative to the elevator, which means that it was accelerated by the external upper force along with the elevator rather than by a normal force?(27 votes)
- Yes, you are correct. The external force is the wire that pulls the elevator. The "actual" normal force comes from the floor of the elevator exerting the same force as the baby's weight (force) which follows Newton's third law. Therefore the baby does not plummet down the earth. And it goes same for the fourth case.

Hope this helped and +1 vote for you for your good observation :D(22 votes)

- I don't understand it. In example 2 (second elevator) if we have gravity force which is - 98N and force which is F= m *a F = 10*2 = 20 therefore positive force will suggest that it's direction is up, therefore this 20N will balance out partially this 98N down and natural force will have to balance out only 78 N left. Similarly in elevator 4 we get F = -20 therefore it will add up to -98N and natural force will have to balance out 118N! Is there mistake in my logic or is there a mistake in video?(18 votes)
- Everybody's explanation in here is wrong because their answer disobeys Newton's third law. The normal force does not lift the elevator instead, it would accelerate the baby to space. The force that accelerates the elevator comes from the cable of the elevator. And yes, Normal force is present but comes from the floor of the elevator which always exerts the same force of 98 N to balance the baby and prevent it from plummeting to the center of the earth; and this follows the Newton's third law. The video only gave you simple explanation but your question is required to be answered in depth.(17 votes)

- I'm very confused with this topic in particular. Since the elevator is also accelerating with the toddler, isn't it an outside force that is causing them to accelerate and not the normal force? From what I've learned, normal force on a horizontal surface must be equal and opposite to the applied force, so I don't think it is the normal force which is accelerating the toddler.(6 votes)
- It's important that you understand the concept of a diagram of forces. In order to understand the physics of a situation, you must understand how the forces act on the object(s).

In the 1st and 3rd scenarios, the forces on the toddler are identical, i.e. a 98N downward-acting force due to gravity, and a 98N upward-acting force due to the normal force of the elevator floor pushing up on the toddler's feet.

Here's where it gets tricky: in the 2nd and 4th scenarios,**the gravity force and the normal force are identical**to the 1st and 3rd scenarios, except that in the 2nd and 4th scenarios, there is an additional force in the normal direction which must be accounted for. In the 2nd scenario, there is a 10kg*2m/s^2=20N upward force added to the normal force of 98N for a total upward force of 118N. In the 4th scenario, the direction of the 20N force is in the opposite direction, yielding a total of 78N upward.

To summarize, from a diagram of forces perspective, in scenario 1, there are two force arrows at 98N, equally opposed and balanced. In scenario 2, there are the same two arrows, but a third unbalanced 20N arrow points up. In scenario 3, there are the same two opposing arrows as scenario 1. In scenario 4, the same two opposing arrows, with a third, unbalanced 20N force pointing downward.(19 votes)

- Can someone please explain to me the concept of INERTIAL and NON-INERTIAL frames?(6 votes)
- Inertial frames are frames that have a uniform speed relative to the outside world. This means that speed must be constant, and therefore acceleration must be 0 m/s². However, non-inertial frame do not have a uniform speed: this is where it differs from inertial frames. Non-inertial frames have an acceleration that is usually constant, but not equal to 0 m/s².

I hope that clarifies a little bit about the concept of (non-)inertial frames.(15 votes)

- I would have thought that the negative acceleration (in the last example) creating the 20 N of force would be added to the force pointing downwards, and not reduce the normal force exerted by the floor. Is that assumption wrong or is it another way of thinking about the problem?(3 votes)
- The better way to think about it is that the normal force normally acts as a buffer. In this case, 98 Newtons down, 20 Newtons, up, and the elevator 's force needs to balance out, so let's add 78 N of normal force in the upward direction to the elevator. In this case 20N is canceling out with the normal force, but rather that since there are 20 N of force upward already, only 78 N of normal force is needed.(5 votes)

- When Sal mentions 'in the J direction' such as in "acceleration is 2 meters per second square in the j direction', what does he mean by j direction(3 votes)
- j is a unit vector along the Y axis, or in the upward direction.(4 votes)

- awhat if a helium balloon is placed in an elevator and there is vacuum in the elevator.suddenly the elevator cable snaps, sending the elevator into free fall.what will happen to the balloon will it go up, down or remain stationary?(3 votes)
- The balloon stays in place because Buoyancy is a direct consequence of gravity. In free fall, the effective gravity within the elevator is zero (assuming perfect free fall of the elevator, with no air drag) and thus the balloon stays where it is.(4 votes)

- I have a bit of a random question. If you were in an object that was accelerating at a constant rate, but not at a rate of zero, would you be able to tell that you were moving, assuming you cannot tell from any other external factors (turbulence, windows, etc.)?

I'm trying to figure out whether you can feel acceleration or if what you're feeling when the elevator accelerates is really just the jerk.(3 votes)- Constant acceleration feels like gravity. In fact, that is Einstein's equivalency principle.(4 votes)

- Can somebody tell me what happens if the lift is accelerating downwards with an acceleration of 10m/s^2. I know that if the acceleration of the lift in downward direction is 9.8m/s^2 then we will feel weightless. And if we exceed 9.8 and go up to 10 then we will bump on the ceiling of the elevator and it will be pushing us downwards. But if the acceleration is 10m/s^2 then we get the normal force to be -2N. Is that the normal force exerted by the ceiling of the elevator??(3 votes)
- Yes, in that case the elevator is accelerating down faster than you fall, so the ceiling of the elevator hits you on the head and causes you to accelerate faster.(3 votes)

## Video transcript

What I want to do
in this video is think about how the
normal force might be different in
different scenarios. And since my 2 and 1/2-year-old
son is obsessed with elevators, I thought I would
focus on those. So here I've drawn
four scenarios. And we could imagine
them almost happening in some type of a sequence. So in this first
picture right over here, I'm going to assume that
the velocity is equal to 0. Or another way to think about it
is this elevator is stationary. And everything we're going to
be talking about in this video, I'm talking about in
the vertical direction. That's the only dimension
we're going to be dealing with. So this is 0 meters per second
in the vertical direction. Or another way to think about
it, this thing is not moving. Now also it is
also-- and this may be somewhat obvious to
you-- but its acceleration is also 0 meters
per second squared 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 video
right over here, or in this screen
right over here, let's say that the acceleration
is 2 meters per second. And I'll use the convention
that positive means upwards or negative
means downwards. We're only going to be operating
in this one dimension right here. I could write 2 meters per
second times the j unit vector because that tells us
that we are now moving. Why don't we just
leave it like that. That tells us that we are
moving in the upward direction. And let's say we do
that for 1 second. And then we get to this
screen right over here. So we had no velocity. We move. We accelerate. Let me-- oh, this is 2
meters per second squared. Let me make sure I--
It's 2 meters per second. This is acceleration here. So we do that for 1 second. And then at the end of 1
second, we stop accelerating. So here, once we get to this
little screen over here, our acceleration
goes back to 0 meters per second squared
in the j direction, only you don't have to write
that because it's really just 0. But now we have some velocity. We did that just for
the sake of simplicity. Let's say this screen
lasted for 1 second. So now our velocity is going
to be 2 meters per second in the j direction, or
in the upwards direction. And then let's say we
do that for 10 seconds. So at least at the
constant velocity, we travel for 20 meters. We travel a little bit while
we're accelerating, too. But we're getting
close to our floor. And so the elevator
needs to decelerate. So then it decelerates. The acceleration here
is negative 2 meters per second squared times--
in the j direction. So it's actually
accelerating downwards now. It 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. And we're going to assume
that we are 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. And so let's say that
I'm-- I don't know. Let's just make the math simple. Let's say that I'm
some type of a toddler. And I'm 10 kilograms. So maybe this is
my son, although I think he's 12 kilograms. But we'll keep it simple. Oh, let me be clear. He doesn't weigh 10 kilograms. That's wrong. He has a mass of 10 kilograms. Weight is the force
due to gravity. Mass of the amount of stuff,
the amount of matter there is. Although I that's not
a rigorous definition. So the mass of the individual,
of this toddler sitting in the elevator,
is 10 kilograms. So what is the force of gravity. Or another way to
think about it, what is this person's weight? Well, in this vignette
right over here, in this picture right
over here, its mass times the gravitational
field near the surface of the Earth, the 9.8
meters per second squared. Let me write that over here. The gravitational field near
the surface of the Earth is 9.8 meters per
second squared. And the negative tells
you it is going downwards. So you multiply this
times 10 kilograms. The downward force,
the force of gravity, is going to be 10 times negative
9.8 meters per second squared. So negative 98 newtons. And I could say that that's
going to be in the j direction. Well, what's going to be the
downward force of gravity here? Well, 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 what we'll assume we have
the exact same force of gravity there. And of course, this person's
mass, 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, this 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 newtons in
the j direction. So it just completely
bounces off. There's no net force
on this person. They get to hold their
constant velocity of 0. And 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. Well, let's think about
what the net force must be on this person, or on
this toddler, I should say. The net force is going to
be the mass of this toddler. It's going to be 10 kilograms
times the acceleration of this toddler, times 2 meters
per second squared, which is equal to 20 kilogram meters
per second squared, which is the same thing as
20 newtons upwards. 20 newtons upwards
is the net force. So if we already have
the force due to gravity at 98 newtons downwards--
that's the same thing here; that's that one
right over there, 98 newtons downwards-- we need a
force that not only bounces off that 98 newtons downwards to
not only keep it stationary, but is also doing
another 20 newtons in the upwards direction. So here we need a force
in order for the elevator to accelerate the toddler
upwards at 2 meters per second, you have a net force
is positive 20 newtons, or 20 newtons in the
upward direction. Or another way to think about
it, if you have negative 98 newtons here, you're going
to need 20 more than that in the positive direction. So you're going to need 118
newtons now in the j direction. So here, where the elevator
is accelerating upward, the normal force is
now 20 newtons higher than it was there. And that's what's allowing
this toddler to accelerate. Now let's 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're at a
constant velocity, including a constant
velocity of 0, you have no net force on you. So this toddler right over
here, once the toddler gets to this stage,
the net forces are going to look
identical over here. And actually, if you're
sitting in either this elevator or this elevator, assuming it's
not being bumped around it all, you would not be able
to tell the difference because your body is
sensitive to acceleration. Your body cannot sense its
velocity if it has no air, if it has no frame of reference
or nothing to see passing by. So to the toddler
there, it doesn't know whether it is
stationary or whether it has constant velocity. It would be able to
tell this-- it would feel that kind of
compression on its body. And that's what its nerves
are sensitive towards, perception is sensitive to. But here it's identical
to the first situation. And Newton's first law tells
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 newtons. Completely nets out the
downward, the negative 98 newtons. So once again, this
is in the j direction, in the positive j direction. And then when we
are about to get to our floor, what is happening? Well, once again we
have a net acceleration of negative 2 meters per second. So if you have a negative
acceleration, so once again what is the net force here? The net force over
here is going to be the mass of the
toddler, 10 kilograms, times negative 2
meters per second. And this was right here
in the j direction. That's the vertical direction. Remember j is just
the unit vector in the vertical
direction facing upwards. So negative 2 meters per second
squared in the j direction. And this is equal to negative
20 kilogram meters per second squared in the j direction, or
negative 20 newtons in the j direction. So the net force on this
is negative 20 newtons. So we have the force of
gravity at negative 98 newtons in the j direction. So we're fully
compensating for that because we're still going
to have a net negative force while this child
is decelerating. And that negative net force
is a negative net force of-- I keep repeating
it-- negative 20. So we're only going to have
a 78 newton normal force here that counteracts all but
20 newtons of the force due to gravity. So this right over
here is going to be 78 newtons in the j direction. And so I really want
you to think about this. And I actually 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 when that elevator is
really just accelerating or when it's just decelerating. When it's just accelerating,
you feel a little bit heavier. And when it's just decelerating,
you feel a little bit lighter. And I want you to think a
little bit about why that is. But while it's moving
at a constant velocity or is stationary, you
feel like you're just sitting on the surface
of the planet someplace.