welcome to our first example Video Will investigating normal forces. In this video, we'll consider one of the most common problems in introductory physics, which involves you riding in an elevator with a scale beneath your feet. Okay, so we did this before in a previous video. So let's review really quickly when we draw our free body diagram for you. There are two forces on you. There's the force due to gravity. And then there's the force due to the scale, which is actually a normal force due to the scale. Okay. And that is the force essentially, that the scale is reading. Now this is going to be influenced by the motion of the elevator in particular. If it is accelerating up or accelerating down, then we will need to take that into account. Because when we rate this, we say okay, have to forces fn minus F G. Because F G is going down. Ethan's going up. That's going to be equal to the mass of you times your acceleration, which will match the acceleration of the elevator. Hopefully. So, looking at this, then if I wanted to solve for the force of the scale, the normal force here that would be equal to F G plus mass times acceleration. If we're accelerating up notice, that means the force of the scale will actually be greater than your normal weight than your normal F G here. But if we're accelerating down than the normal force of the scale on you or the force of the scale, that is, reading is going to be less than because we'll have a negative second term instead of a positive second term. So the right hand side will be smaller than your normal weight. So we could also rewrite this because F G is equal to M G, we could write. This is equal to mass times acceleration plus gravity, where acceleration may be positive or negative notice. One thing, though, if the elevator is moving at a constant velocity, remember, constant velocity means acceleration is zero. If acceleration is zero, then we just get a zero over here, and the reading of the scale is going to be exactly your weight. So let's give ourselves an example here. Let's say a person is writing in an elevator, standing on a scale that person normally has a mass equal to 70 kg and we'll round g to be approximately 10 m per second squared so we can do the math you quickly. So when we look at this and we say What does the scale read? If acceleration is equal to 1 m per second squared, we say All right, well, I know that I have FN up. As I said before, we have FN and then we have mg down. So we have FN minus m g is equal to mass times acceleration. F n is equal to mass times G plus a and now when we put it in, we have 10 plus one is 11 and so we have 11 times 70 kg. That means FN would be equal to 700 and 70 Newton's if, on the other hand, they were negative one and so this is for a equals positive, 1 m per second squared. If a is negative 1 m per second squared, then we would have 70 times nine. So when we have 70 times nine, we'd have 630 Newton's. So that's a huge swing there. Especially because generally speaking, mass Times G is going to be 700 Nunes so it changed by an amount of 70 Newton's because we went from positive 1 m per second, squared to negative 1 m per second squared between the two examples. If we were traveling at a constant speed of 1 m per second, constant speed means a A zero. So normal force of this force of the scale would just read as 700 Newtons like normal. So it's important to keep track of these things here and again. Notice the acceleration does not show up in the free body diagram. It shows up on the right hand side of the equation, and it's equal to the sum of your forces. It is not one of the forces, which is a problem. I see a lot of students may

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## Video Transcript

welcome to our first example Video Will investigating normal forces. In this video, we'll consider one of the most common problems in introductory physics, which involves you riding in an elevator with a scale beneath your feet. Okay, so we did this before in a previous video. So let's review really quickly when we draw our free body diagram for you. There are two forces on you. There's the force due to gravity. And then there's the force due to the scale, which is actually a normal force due to the scale. Okay. And that is the force essentially, that the scale is reading. Now this is going to be influenced by the motion of the elevator in particular. If it is accelerating up or accelerating down, then we will need to take that into account. Because when we rate this, we say okay, have to forces fn minus F G. Because F G is going down. Ethan's going up. That's going to be equal to the mass of you times your acceleration, which will match the acceleration of the elevator. Hopefully. So, looking at this, then if I wanted to solve for the force of the scale, the normal force here that would be equal to F G plus mass times acceleration. If we're accelerating up notice, that means the force of the scale will actually be greater than your normal weight than your normal F G here. But if we're accelerating down than the normal force of the scale on you or the force of the scale, that is, reading is going to be less than because we'll have a negative second term instead of a positive second term. So the right hand side will be smaller than your normal weight. So we could also rewrite this because F G is equal to M G, we could write. This is equal to mass times acceleration plus gravity, where acceleration may be positive or negative notice. One thing, though, if the elevator is moving at a constant velocity, remember, constant velocity means acceleration is zero. If acceleration is zero, then we just get a zero over here, and the reading of the scale is going to be exactly your weight. So let's give ourselves an example here. Let's say a person is writing in an elevator, standing on a scale that person normally has a mass equal to 70 kg and we'll round g to be approximately 10 m per second squared so we can do the math you quickly. So when we look at this and we say What does the scale read? If acceleration is equal to 1 m per second squared, we say All right, well, I know that I have FN up. As I said before, we have FN and then we have mg down. So we have FN minus m g is equal to mass times acceleration. F n is equal to mass times G plus a and now when we put it in, we have 10 plus one is 11 and so we have 11 times 70 kg. That means FN would be equal to 700 and 70 Newton's if, on the other hand, they were negative one and so this is for a equals positive, 1 m per second squared. If a is negative 1 m per second squared, then we would have 70 times nine. So when we have 70 times nine, we'd have 630 Newton's. So that's a huge swing there. Especially because generally speaking, mass Times G is going to be 700 Nunes so it changed by an amount of 70 Newton's because we went from positive 1 m per second, squared to negative 1 m per second squared between the two examples. If we were traveling at a constant speed of 1 m per second, constant speed means a A zero. So normal force of this force of the scale would just read as 700 Newtons like normal. So it's important to keep track of these things here and again. Notice the acceleration does not show up in the free body diagram. It shows up on the right hand side of the equation, and it's equal to the sum of your forces. It is not one of the forces, which is a problem. I see a lot of students may

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