 Because you get a great explanation. Everybody there? Read along with me, boys and girls. A force with which you have had some experience is the force of gravity between you and the Earth. This force is also known as weight. How much do you weigh? The answer should not be in kilograms. The answer should be in newtons. Weight is mg. It's measured in newtons. Or in the imperial system, it's measured in pounds. Found where we are? OK. Because it's not like I haven't had it up there for about 15 minutes or so. Let's just keep going. We'll ignore that on the internet. I think we're on the front page still, aren't we? Like the first page? We're there now? OK. So as I was saying, force of gravity is also called weight. Force of gravity is not the same thing as mass, although they are related. Mass is the amount of matter in an object, which we measure in kilograms. Or on the imperial system that was measured in slugs, believe it or not. To relate mass to force, we need to know the number of newtons of force per kilogram of matter. This quantity is known as, here's the term I want you to highlight or underline. This is the new term, gravitational field strength. Gravitational field strength. Find it? Ze? Find it? Hunt. I think you're here. So let me say this again. The number of newtons of force per kilogram is gravitational field strength. Near the Earth's surface, the gravity field strength is 9.8 newtons per kilogram. Now we've seen that 9.8 before, but what were the units that we attached to 9.8 previously? When I said to you 9.8, what was that number last year all the time? It's meters per second squared. It's the acceleration due to gravity. As it turns out, it's also the Earth's gravitational field strength measured in newtons per kilogram. And newtons per kilogram, if you muck around with the units, and we will in a second, is meters per second squared. Usually, if I'm dropping an object and I'm calculating its velocity, I'll say 9.8 meters per second squared. Usually, if I'm calculating a force on an object, I'll often say 9.8 newtons per kilogram, because it's the gravitational field strength. Moon's gravitational field is about 1.6 newtons per kilogram, which means if you dropped an object on the moon, it would fall at an acceleration of 1.6 meter per second squared. Here's the equation. Assuming the pen decides to write, let's try that again. Here's the equation. Fg equals mg, where g is 9.8 newtons per kilogram or meters per second squared. Basic example, example two. Find the weight of a 10-kilogram object on Earth and on the moon. So both of these are asking you to find the weight, which is fg. And in both of these, it's going to be mg. It's going to be mg. Only on the moon, I'll make sure I use g on the moon. And on the Earth, I'll make sure I use g, the gravitational field strength, on the Earth. The mass is 10, g is 9.8. A 10-kilogram mass exerts a force of 98 newtons. That's why when I had the two people pushing on the scale, I said, you know what? If you look at kilograms and multiply by 10, that's roughly the force in newtons. How much force would a 10-kilogram mass on the moon exert? Well, right here it says the moon's gravitational field is 1.6, so that's where the 1.6 came from, 16 newtons. You'd feel about 1.6 to your weight on the moon, which would take some getting used to. Your timing would be way off if you tried to play catch on the moon. Even your jumping would feel weird. Now in a space suit, you can't jump very well. But suppose we built a dome on the moon that had oxygen and a regular atmosphere in it, and so you didn't need to wear a space suit. I suspect the tricky part would be timing your landings because everything would be happening so much slower, you'd overreact and probably trip because you overreacted the land. Now turn the page. Emily, that means you can turn the page now. Example three says, example three says, select the best answer. Here's another one of those using principles of physics right to explain questions. If the force of gravity acts on an object, then the object A remains at rest, B moves at a constant speed, C accelerates in the direction of the force, D, all of the above. Once again, we're going to vote. Once again, how high you hold your hand is how certain you are of the answer. I'm positive. I'm pretty sure I'm only voting because Mr. Dewick is going to remember which people I haven't voted and he'll make fun of me, okay? So if the force of gravity acts on an object, then the object A remains at rest, B moves at a constant speed, C accelerates in the direction of the force, one, two, three, four, five, six, D, all of the above. All right, if you voted C convince me that D is wrong or if you voted D convince me that C is wrong. Can you remain at rest? Can A be true? Well, are all of you being pulled down by gravity right now? Yes, are all of you at rest right now? Yes, some of you more than others apparently Mitchell. B, can you move at a constant speed while under the force of gravity? Yeah, I did that when I jumped out of an airplane in free fall. Have I showed the free fall video yet? I haven't, have I? I'll just show that in a bit then. When I jumped out of my airplane, eventually I hit terminal velocity, which meant that air resistance up and gravity down were equal. So my net acceleration was zero even though gravity was pulling me down, I was moving at a constant speed. Certainly when I opened the parachute, I was moving at a constant speed. C, can you accelerate in the direction of the force? Well, yeah, that's true whenever you drop an object. So the answer is D, all of the above. And where it says explain your answer, I would give the three examples that I just gave an object on a table is at a constant speed even though it's under gravity, we're not gonna write it out. B, constant speed, terminal velocity, C, free fall when you first start to fall. That's how I would explain that one. We're not gonna write all that one out. Instead, we're gonna move to Newton's second law. So Newton's second law says that if we have balanced forces, then objects at rest remain at rest and objects in motion remain in motion. If we have unbalanced forces, actually crossed out Newton's second law, Newton's first law says that if we have balanced forces, then objects remain at rest and objects at rest remain at rest and objects in motion remain in motion. If we have unbalanced forces and the object accelerates in the direction of the net force. We write it this way. F net equals ma where F net is the total sum of all the forces, except writing out total sum is too much work. Does anybody know what's the symbol that we use in chemistry and in physics for the sum of or add them all up? So here's a great shorthand for you. You can reuse it often during this year. If you ever want to write the total or the sum of, it's that, a capital M on its side. It's a Greek letter sigma. It's where we get our letter S from. There's our S, there's the sigma. We just stopped doing that last little bit and curved it. And it stands for, well, here's what it looks like. That there means the total sum of the force, which is the net force in Newton's. Now, F net will never appear on our vector diagrams. It'll never appear on our free body diagrams. It's not a real force because it's not based on an interaction. It's the vector sum of all of the actual real forces. By the way, back here, I said that Newton's per kilogram were the same as meters per second squared. Here's the proof. One Newton per kilogram is the same as a meter per second squared because a Newton meter per second, sorry, kilogram meter per second squared is the same as a Newton. Why? Force is what times what, Conor? Mass, which is measured in kilograms and acceleration, which measured in. Okay, so here's what I'm gonna say. Kilogram meters per second squared. That's force, that's MA. And another way to write force is, another way to write acceleration is force divided by the mass. So if I take the force, kilogram meters per second squared, and I divide it by the mass, kilograms. Kayla, what happens to the kilograms if there's one on top and one on the bottom? So here's what I'm saying is it turns out force divided by mass is meters per second squared is acceleration, but what do I measure force in? Newton's, what do I measure mass in? What we're really saying is, Newton's per kilograms is the same as meters per second squared. There's your little proof. I shouldn't have done that big loopy thing because that's gonna be in the way. Another term for acceleration due to gravity is gravitational field strength. Measured in Newton's per kilogram. So often in a question, instead of saying, the acceleration is five meters per second squared, they'll say the acceleration is five Newton's per kilogram. That is meters per second squared, it's an acceleration. Or they'll say the gravitational field strength is five Newton's per kilogram, that's acceleration. Example four says find the unbalanced or the net force in each case, including direction. What's my net force in diagram A? How big? Two Newton's, what direction? You know what, let's go north, east, south, and west. Let's pretend we're looking down at an object. So this would be two Newton's east. My at symbol doesn't look very good. What's my net force in B? What's my net force in B? 3.7, direction, due south. What's my net force in C? What's my net force in C? One Newton, and this is why I put the at symbol in, so if otherwise there would be one N, then you wouldn't know what the heck it was going on. So one Newton at north. What's my net force in D? Brett, I heard you, thought I heard you. Oh, no, I didn't, okay, five Newton's east. And you can write out the word east so you can go at and put an E for east. E, first of all, what's my net north-south force in E? Zero, that's convenient. What's my net east-west force in E? Seven Newton's direction, west. If Y is greater than, is bigger than X, what's my net force here? Matt, louder. In fact, if I'm not mistaken, you went winter minus loser. Which is the approach that I use with my students. I turn every single force question into a great big tug of war. The reason is, in the unit we just finished, we always let down be negative and up be positive, so we always put in negative 9.8 meters second squared. In this unit, because we're often gonna have things moving up and something else moving down, we're just gonna decide the winning direction is positive, and that will take care of the negatives. We're not gonna put in negative 9.8. The math will take care of that for me. To solve force problems, first thing you're gonna hear me do is we're gonna draw a free body diagram. We draw one arrow for each force that acts on the object. We never ever, we never ever, we never ever, we never ever, we never ever put the net force on a free body diagram. It doesn't exist really. It's the mathematical combination of all of them, and we use it to solve things, but it's not an actual force per se. Label all the arrows, put the tail of the arrow at the center of each object, and if you want to, acceleration and velocity vectors can be drawn differently, for example, using wiggly lines. I usually don't put acceleration and velocity on my free body diagram, and a free body diagram, we represent all of the mass of an object with a dot, and then we label the forces. Then you're gonna use the free body diagram to write an algebraic net force equation, solve for any unknowns. Our force equation will be solved by using a tug of war analogy. We will ask ourselves, which force is winning? We can almost always figure that out just by looking at the diagram and scratching our brain. And we will then go like this, Andrew. Winner minus loser equals F net, where F net equals ma. In fact, often you'll see me just go winner minus loser equals ma. This allows us to avoid having to decide which directions are positive and which directions are negative. Do I put in a negative 9.8? Never in this unit. We will decide the positive and the negative and it'll take care of itself. Example five, turn the page, no? Nothing, guys a little tired it seems. Yeah, a long weekend, should be awake. Not, absolutely. So, example five, a 2000 Newton rock, hanging from a rope accelerates upwards at three meters per second squared. A says draw a free body diagram. I'm gonna draw the free body diagram right there. I'm gonna represent the forces on the rock with a dot. The mass of the rock I represent as a dot. So put a dot right there. Apparently I have to be really clear this morning. Okay. What are the forces acting on that rock? Get the obvious ones. Okay, gravity is always pulling down. Is the rock in free fall? No, then there must be another force in the opposite direction. What? Well, I notice it's a rope. What did we traditionally call a force exerted by a rope? Tension. Why did I draw my tension arrow so much bigger than my gravity arrow? Who's winning? You know how I know? That's why. That's how I know. And I'll always exaggerate my arrows to remind myself tension is winning and gravity in this case is losing. What's my equation? Well, we'll write this down the first few times. Write this down. Winner, take away loser is equal to the net force, which is just MA. Who's winning? Tension. So anything in the tension direction, anything pointing up is going to be positive. Winner, minus. Who's losing? Loser, that equals MA. So A said draw a free body diagram. B said compare the forces that act on the object. We actually did that in our free body diagram with our arrow lengths. C says write a net force equation. There's our answer to part C. There's our net force equation. Trevor, what does D want us to find? Get the tension by itself, huh? Turns out tension is gonna be MA plus FG. Now let's see here. Do I know the mass? I saw one person nod and one person say no. I think I do, but not blatantly. I can figure out the mass. How can I figure out the mass from this? Emily? Divided by 9.8. You know what I'm gonna do? I'm actually just gonna write in for the mass, 2000 over 9.8, and that way I don't have to worry about sig figs or decimal places or anything. I'll just do that, because I'm gonna do it no matter what. Why not do it in the equation? So there's the mass. Do I know A? Do I know my net acceleration? I do. How big, Kara? Three, minus, or sorry, not minus, plus. Do I know the force of gravity? Yeah, how big? Ooh, maybe I don't know the force of gravity. They blatantly told it to me very, very easily. What's the force of gravity on this rock? Come on, folks, what's the force of gravity on this rock? What's the weight of this rock? I just spent 10 minutes talking about how gravitational fields, we said that weight was the same as MG, that force of gravity is measured in newtons. Boys and girls, what's the force of gravity on this rock? 2,000 people. Really? 2,000 newtons, yes? I don't need to do nine point, they did that for me. I don't need to go through all that garbage. They gave me the weight in newtons. Good, now crunch the numbers. Please, wake yourselves out of these doldrums. I hope that was tiredness and not not knowing. If it was not knowing, you in trouble. Because I just spent five minutes talking about it. Turn your brains on. Find the answer, please. I'm gonna freeze my screen and not tell you the answer because some of you right now are so out of it. John, what'd you get? John, what'd you get? 2,612? Why is that wrong? Because it is. Why is that still wrong? Because it is. Oh, you guys know you got a test on Thursday, right? What do I want every single answer to be this year? Two or three sig figs. Why is this wrong? Four sig figs. How about 2.61 times 10 to the third newtons? Example six. Boy, wake up, people. Example six. Is it correct to say that if the rock in example five is moving upwards, then the string tension must always be greater than the weight of the rock. If the rock in example five is moving upwards, if the rock in example five is moving upwards, will tension always be bigger than FG? Convince me. I hear yes, convince me. Or do I hear no, convince me? Yes or no? If the rock is moving upwards, is tension always bigger than FG? Here's my rock. Right here, see it? What can you tell me about the speed that I just moved at? Constant, so what was my net acceleration? Zero, so if that's zero, how big is this number right here? Zero, what could you tell me about tension and FG? Would tension have to be bigger? In fact, it would be the, if A equals zero, constant speed, tension minus FG equals zero, there's my winner minus loser equation that we started out with, where the zero come from. Well, if acceleration is zero, what's zero times the mass? Zero, tension equals FG. If they're equal, are they greater? No, there's a mathematical explanation with a tiny bit of English, but there's a mathematical answer using principles of physics. For a rock moving upwards, is it ever possible for the chord tension to be less than the weight of the rock? Is it ever possible for this to be smaller than that? Yes or no? Katie said yes, convince me. Katie's right, it's something to do with acceleration, but she's wrong, she doesn't know what. Watch, was the rock moving upwards for a while? Did you see slack in the chord? Would that suggest that, what? I don't even think tension existed at all. In fact, I think tension was zero, but gravity hadn't vanished, had it? So this is really, I think Katie, what you were trying to visualize is this. For a split second, give it a big tug. So my answer to here would be, is it possible? Yes, if mass is in free fall, but still traveling up. You know what, instead of traveling, let's just say still moving, let's use their word, moving up. If your initial velocity upwards is enough that it stays in free fall for a few seconds before coming to a stop, once it starts to come back down and tension yanks up, okay, then tension, but on the way up for a split second in free fall, you all saw the string went limp there, yes? So yeah, it can be an interesting equation to try and draw. A little technical comment here on force equations and vectors. If the mass, in example five, is accelerating down, say at two meters second squared, we have two choices. We could always let down be positive and always let up, sorry, down be negative and always let up be positive. So up and right could be positive, down and left are negative, and we would say that, I don't like that approach. Caitlyn, it works great for small one-dimensional problems, but for two-dimensional problems, we have a problem. For example, here, this mass is moving down negative, but this mass is moving to the right, which last unit was positive. So we are going to use our tug of war, winner minus loser approach to try and deal with these. We will decide to let winner be positive. We will decide to let loser be negative. What's your homework? Well, your homework is really study for the test on Thursday, but then I don't see you for a week. Like your test is Thursday, next Tuesday, number one, number two, three is great. So one, two, three, four is good, parachute, yay. By the way, on question four, part C is on the next page just so that you know, I don't know it's saying which of the following is true, A, B, and C. Five is good, six, seven, and nine. Nine is a nice challenging one, but it's a great combination of last unit and this unit. That would be a great example of if I was wanting to give you a B-level written question. Okay?