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# Normal force in an elevator

## 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 two and a half year old son is obsessed with elevators I thought I would 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 in this first picture right over here I'm going to assume that the velocity is equal to zero 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 zero meters per second zero meters per second 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 maybe is somewhat obvious to you but it's acceleration is also zero 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 and so the except the the elevator begins to accelerate upwards so in this video right over here or let this screen right over here let's say that the acceleration the acceleration is two 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 in this one dimension right here I could write two meters per second x times the J unit vector because that tells us that we are now moving let me just leave it like that that tells us that we're moving in the upward in the upward direction and let's say we do that for one second and then we get to this screen right over here so we were we had no velocity we move we accelerate let me oh this is two meters per second squared let me make sure it's two meters per second per second this is acceleration here so we do that for one second and then at the end of one second we stop accelerating so here and this once we get to this little screen over here our acceleration goes back to zero meters per second squared in the J direction although you don't have to write that because it's really just zero but now we have some now we have some velocity we did that for just for the sake of simplicity let's say we this screen lasted for one second so now our velocity is going to be two meters per second in the J direction in the J direction or in the upwards direction and then let's say we do that for 10 seconds so we traveled 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 the elevator needs to decelerate so it decelerates so that it decelerates the acceleration here is negative 2 meters per second squared times times in the j direction so it's actually accelerating downwards 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 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 the 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 the math simple let's say that I'm some type of a toddler and I'm 10 kilograms 10 kilograms so maybe this is my son although I he's I think he's 12 kilograms but we'll keep it simple so this is it's 10 this person has a let me be clear it doesn't weigh 10 kilograms that's wrong he has a mass of 10 kilograms weight is the force due to gravity mass is the amount of stuff the amount of matter there is although I have the Senate 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 in this vignette right over here and this picture right over here its mass times the gravitational field near the surface of the earth 9.8 meters per second squared let me write that over here the gravitational field near near the surface of the earth is 9.8 meters per second squared and the negative tells you it is going downward so you multiply this times 10 kilogram the force the downward force the force of gravity 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 in the J direction well what's going to be the downward force of gravity here what'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 you'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 person's mass this Toddlers 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 is 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 is and eat this that force is would be the equal would be an equal force but in the opposite direction in this case that would be the normal force so in this case the normal force is 98 98 Newtons in 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 zero 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 there's going to be 10 kilograms 10 kilograms times the acceleration of this toddler times two meters per second squared which is equal to 20 kilogram meters per second squared which is the same thing as 20 Newton's 20 Newton's upwards 20 Newton's upwards is the net force is the net force so if we already have the force due to gravity at at 98 Newton's downwards that's the same thing here that's that one right over there 98 Newton's downwards we need a force that not only balances off that 98 Newton's downwards to not only keep it stationary but it's also doing another 20 Newton's in the upwards direction so here we need a force in order for this toddler to or the excel or this in order for the the elevator to accelerate the toddler upwards at 2 meters per second you have a net force of positive 20 Newtons or 20 Newtons in the upward direction or another way to think about it if you have 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 you're going to need 118 Newton's now in the J direction so here where the elevator is accelerating upward the normal force the normal force is now 20 Newton's 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 our velocity is but our but we do have velocity so here we were stationary here we do have velocity and you might be tempted to think oh there must be maybe you know 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 zero 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 at all you would not be able to tell that difference because you there's no 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 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 that kind of compression on its body and that's what it's it's nerves or sensitive to or it's perception is sensitive to but here it's identical to the first situation of Newton's first law tells us 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 shoes is going to be identical to the downward force due to gravity so the normal force here is going to be 98 Newton's completely Nets out the downward the negative 98 Newtons so once again this is in the J direction in the positive data J direction and then when we're about to get our floor when we are about to get to our floor what is happening well once again we have a net acceleration 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 negative 2 meters and this is in the this was right here 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 Newton's in the J direction so we're not fully compensating for that because we're still going to have a net negative force while this this child is decelerating and that negative net force is a as the negative net force of keep repeating it negative 20 so we're only going to have 78 we're only going to have a 78 nu in normal force here that counteracts all but 20 Newton's of the force due to gravity so this right over here is going to be 78 Newton's 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 what'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 stationary you feel like you're just sitting you know on the on the surface of the planet someplace