>> Hello class, Professor Anderson here. Let's talk about something called terminal velocity. This is most relevant for skydivers. Any of you been skydiving before out there? No? Okay. It's one of those great experiences of your life, where you scream your head off for a minute, and then you land back on earth hopefully. What does skydiving look like? Skydiving looks like this. We got an airplane. Here's our airplane. Okay, and you jump out of the airplane and you fall. Now, when you start falling out of that airplane, what is your acceleration? I'm asking you guys, what's your acceleration when you initially jump out of the airplane? Connor, yeah, you have a thought? >> Negative G. >> Negative G. Good. Jump out the airplane, you're falling towards the earth at negative G. And in fact, you don't have to jump out of an airplane to do that, right? If you jump off of the table, you're falling at negative G. If you jump off of a chair, you're falling at negative G. So what about as you continue? As you continue to fall, are you still accelerating the whole time? Christian, what you think? Am I still accelerating later on? >> No, because of air resistance, like it will be pushing back up against you? >> Okay, that's exactly right. Much later, acceleration is in fact zero because of air resistance. So does that mean that I come to a stop? What does it mean? >> It means that it's just slowing you down, in a sense, and what is it? Depends on your surface area also, how much of it is going to affect you? >> Okay, but if I have an acceleration of zero, does that mean that I'm slowing down? >> It means that you're staying constant. >> That's right. It means I'm moving at the same speed and that's exactly what we call this, right? This is terminal velocity or terminal speed, okay? You're not increasing your speed anymore. And skydivers will tell you that terminal speed is around 130 miles per hour, depending on how spread eagle you are. But it's somewhere around 130 miles per hour. Now, we know there's something else that changes at the end of this trip, right? As I keep going, let's do that. Here I am falling, right? I jumped out of an airplane. And now, as I continue towards the ground, something else happens. What happens, hopefully, before we get to the ground? What do you guys do? Open your parachute, right? If I open my parachute -- parachute looks like this, there's some strings coming down. You are, hanging on for dear life. What does that parachute do? Yeah, Thomas, what does that parachute do? >> It increases your surface area so it will like slow you down because there's more air built up underneath it. >> That's eexactly right. We're going to catch more air, right? We're trying to push more air out of the way, which increases our drag. Which direction is the acceleration when I open the parachute? >> Initially, it will be up. >> Correct. Acceleration is, in fact, up, since we are moving down. And acceleration upward is a deceleration, right? It's trying to slow us down. And then later on before I hit the ground, am I still accelerating upwards? What do you think, Thomas? >> No, because if you eventually kept accelerating upward, you'd leave the Earth's atmosphere and just go into space. So eventually it will reach zero so you can get a constant speed and land safely on the ground. >> Exactly right. You're going to accelerate upward for a little while, while your parachute opens, and that's to slow down your speed. And once that speed reaches a new terminal velocity, then the acceleration goes back to zero. So terminal velocity depends on some parameters. It depends on your cross-sectional area. It depends on the density of the air. It depends on things like drag coefficients. But it also depends on all these forces and how they interact. And when you have a big wide open parachute, initially it's is going to provide an acceleration upwards. But eventually, you'll get back to a new terminal speed, okay? So this is all due to air resistance. Let's talk about air resistance. Let's talk about air drag, because we just mentioned that air drag was responsible for this idea of terminal velocity. So when you're falling, what forces are acting on you? Yeah, Austin? What do you think? >> The force of gravity? >> Okay, force of gravity. Which way is gravity? >> Down? >> Down. Make sure you always draw gravity down. If you're drawing it some other angle, it's not right, okay? If you have MG, it better be pointing down. What else, Austin? >> The drag force? >> The drag force. Which way does that go? >> Pushing you up? >> Okay, and how big should I draw that arrow? >> Smaller than gravity? >> Smaller? Okay. If this is the drag force due to that air resistance, then if those were my forces, would I be accelerating? >> Yes. >> Yes, right? I would be accelerating downward. So this means I am still accelerating downward because the downward force is bigger than the upward force. But later, when I reach terminal speed, we know that I'm no longer accelerating. So this is sort of initial picture right there. And now we're going to do when we've reached terminal speed. So here we are falling. We know that at terminal speed, acceleration is zero. So when I draw the forces, I should draw F drag the same length as MG, but pointing up. And now, those exactly cancel out and we get zero acceleration. All right, what is F drag? F drag for the linear model -- >> Has a magnitude equal to B times V. What does this mean? This is your speed. This is a drag coefficient. Later on, we're going to look at the nonlinear model, where it goes like V squared, and we'll have some other parameters in there. But this is a fine place to start, the linear model. Drag increases with your speed. Okay, let's go over here. Sum of the forces is what? Well, we've got drag going up. MG going down. If we're at terminal speed, acceleration is equal to zero and I get F drag is equal to MG. So at terminal velocity, the air resistance force is exactly equal to MG, which is what a lot of people call weight. I like to call it the force due to gravity. All right, but F drag we know is this. So in fact, I can write the following: B times V terminal is equal to MG, and so I can solve this for the terminal speed. It's just MG divided by B. We don't know exactly what this B coefficient is, but that depends on a lot of things, like the cross-sectional area, the density of the air, whether you are wearing floppy clothing or tight clothing, okay? All sorts of things like that. And if you increase your gravitational force, you can increase the terminal speed if you don't change B. And you guys kind of know this already. For instance, if I take a bowling ball and I take a balloon that's the exact same size as the bowling ball, and I drop the two of them, which one hits the ground first? The bowling ball, right? Of course it does. And it's because B is the same for those two things. If they have the same size, same cross-sectional area, they're going through the same density of air, this coefficient is exactly the same. But obviously, the force due to gravity is much bigger on a bowling ball then it is on a balloon, and so you'll have a bigger terminal speed for the bowling ball. All right? Questions about that one? Okay, let's move on to something else. If it's not clear, definitely come see me in office hours.