Physics 11 Final Exam Review Part 2 (Relativity, Forces Part 1)

So, we'll hope for the best. So, we're going to be doing some formula manipulation. Your final exam is about 60 questions, maybe 61, maybe 59 depending on which version that you write, but around 60ish questions. They're all multiple choice. So, you want to be thinking, how can I assess stuff multiple choice? That means probably half of it is going to be conceptual things that you can do either without writing anything down or writing down one line. And then the other half is going to be, okay, you got to apply some of the stuff we've learned. And about five questions have some teeth. And I'll drop hints about them. I dropped hints about one of them in the last section of the review of the kinematics review. So those of you that were away might want to watch that on YouTube. One of the things that I did, I've got three or four versions of the final. And so I'll give you some hints. Uh I had made some multiplechoice formula manipulation questions. We had four kinematics equations. It says get each variable by itself. You know what I'm going to do? I'm going to just draw a line down the middle of the page like this. And I'm going to draw a line kind of in the middle of the page like this. And these are my equations. Here we go. Because there's four equations. You'll notice I was nitpicky. I put the delta t. We said time was always a change in what's change in anything? Final minus initial. Anytime you're using a stopwatch, what the stopwatch is doing is it's measuring the initial time. It's measuring the final time. It's subtracting those and that's what it displays. So time you you'll find next year if you take physics 12 voltage is also always a change in it's like height. You have to to measure a height you have to measure a top and a bottom. You can't just measure one location. You have to have a ground. So you could ignore the deltas though. I didn't bother handwriting them. I just put it in there because I was nitpicky. So here's our first equation. VF= VI plus AT. You want to be having looking at that at your formula sheet in front of you. And uh hey Brendan, let's get the uh vi by itself. What's going to drop down like a domino? Good. And then how would you move the AT over? We would treat that as one term. Yeah. All right. Hey, let's same equation this time. Dallas, let's get the A by itself. So what side is the A on? It's on the right side. What's going to drop down like a domino? Good. And then we said it's formula manipulation car. It's reverse bed mass. So what's right next to the A? The T. What's the T doing to the A? So how will I move it over later? What's the VI doing? So and I do that first because it's reverse bed mass. So it's going to be minus VI / E. If this was multiple choice, one of them would be VI minus VF. That would be an easy way to mix it up. One of them would be VF plus VI. And one of them would probably be if you divided by T first and then minus. There's your three wrong answers if you didn't do reverse badmath. Okay. Ooh, Cara, we can also get the T by itself. So, I've scrolled down. You'll have to look at the one on your green sheet because I've scrolled down or you have it on the top of your page as well. Uh, look at the T. What side is the T on? The left side or the right side? So, what's going to drop down like a domino? The left side. The VF. What's right next to the T? What's the A doing to the T? Multiplying. What will I divide later? What else is on the same side? The VI. How will I move the VI over? What's the VI doing to the T? Yep. So, how move it over? Because it's reverse. So, the VF drops down and then you would minus the VI. you would divide the a and then it was equals t, but we usually put the t on this side. In fact, I already wrote the t equals. Those are the four ways I can write that equation. Uh, hey, there's three different ones here. I'll bet you I got one version of your final where I asked them to get the vi by itself. I got one where I asked them to get the a by itself. I got one where I asked them to get the t by itself. Or you might see more than one of these on one final. I can't remember. I typed these a while ago. The trickiest question because it had brackets was this one here. Okay, I can deal with it. So, first of all, let's get the T by itself. That's probably the easiest. I treat the bracket like one thing. So, Charlie, what side is the T on? The left side or the right side? What's going to drop down like a domino? Good. How well what's that bracket doing to the T? How move the whole bracket over? And when we divided, you could leave it in brackets, but technically there's implied brackets there, so you didn't need to. What about that two? And I'll just tuck it on top. That's fine. Okay. It was a little trickier getting something that was inside the brackets by itself, but we can handle it. Nolan, let's get the VF by itself. Brackets. The bed mass for the B for bed mass says do brackets first. We're going to do brackets last then because it's reverse bed mass. What's going to drop down the D? We're going to do inside the brackets last. What's the T doing to the VF bracket? How move it over? Good. What about the two? So good. And then in our imagination, we'll imagine there's an equals and a vi plus vf. And now the bracket has vanished because we took everything outside. If I want to get the vf by itself, how will I move the vi over? And it's outside the fraction like that. That equals vf. Oh, spoiler alert. Vi would work the same way because they're inside the same bracket. So to get the VI by itself, run out of room. I'll do it right here. I would say drop the D down like a domino. I would say, hey, we're going to divide the T over. We're going to times the two over. We're going to minus the VF. That gives me the VI. I'm trying to remember, Michaela. I know on version one of the final, I had people get these by itself. I had to shorten the final. This equation might have got axed. I can't. Part of my brain is saying it did. Part of my brain is saying maybe I found a workaround because your the first final was 75 questions and it was too long. So they're about 60 basically in two hours. It works out to about 2 minutes a question. Some will take you longer but some will be like 15 seconds. Okay. Probably the toughest one to work with is d= vit plus a half a t^2. So Jordan, I saved that one for you. Let's get the a by itself. So stare at it. What side is the A on the left side or the right side? So the D is going to drop down like a domino. What? Right. What's right next to the A? There are two things. A.5, a half, and a T squ. What are they doing to the A? How move them over later. What else is on the same side as the A? A vit. I treat that as one term. How will I move it over? How do you know? Because it's adding. So the D would drop down, Cara. I would minus the vit and I would divide by the 0.5 t^2. Yeah. Oh, if I was making up wrong answers, uh, a plus sign here, uh, d over.5t ^2 plus vi I I can mix and match this quite a bit. Michaela, the other one I can get by itself is the vi. Let's see if we can do that. What's going to drop down like a domino? giving you. By the way, I'm going to give you less hints as we go, so don't feel bad. I'm not trying to make fun of you. We're brushing cobwebs off. I get it. Uh, let's Oh, what's right next to the VI? Oh, that. Okay. What's that? Okay, good. So, got a minus a.5 at squ. I agree. Then what? Yes. Tyson, why can't I ask you to get the t by itself here? It's a quadratic. Now, if vi is zero, the equation becomes d = a t^2 / 2 or it becomes d =.5 a t ^2. That one I did put on. I think I said assuming vi is zero, get the t by itself. And then you know what? I'm pretty sure I use this format here. So, get the T by itself. What's going to drop down like a domino? Then what? How? Good. What about the two? Good. What's that equal? T ^2. And I'll put the t on this side. Or if you rewrote it this way, it would be the ds down / 5a inside the square root that equals t. Um, hey, I'll even tell you the possible wrong answers. One of the wrong answers would have a 0.5 on the top instead of on the bottom. Um, one of them would have the A on the top, D on the bottom. One of them would be forgetting the square root. There's your three wrong answers. Oh, here your multiple choice test. There's four answers to pick from. ABC, BC, D. I didn't go like ABCDE E FG or anything like that. Last one is the squared squared one. First of all, I got to be nitpicky. The VF isn't by itself. How would I get the VF by itself? Yeah, I have to square. No matter what, I'm gonna be square rooting if I just want to get the VF by itself. And this was the weird one where we sometimes had to overrule our calculator and I want the negative answer because I know I'm going down. Okay. Oo, Destiny, how would I get the V VI by itself? What's going to drop down like a domino? The VF squared. And then good. That gives me vi 2. So yeah. Hey, you want to know the wrong answers? One would have a plus sign there. One would forget to square root and one would be vf squ / 2 a. I just told you a question. If if you get that version, those are the wrong answers I would have put on there because those are the most likely mistakes. Tyler, how would I get the a by itself? I know it's been a while. Go meticulously. So imagine a little dot above the a. What's going to drop down like a domino? Good. Then what? Good. Then what? Yep. Getting by the getting the D by itself was really similar because the A and the D are kind of in the same location of the equation. The VF 2 would drop down like a domino. It would be minus VI^ 2. It would divide by 2 A all over D. If I was giving you one of those, what would the wrong answers be? forgetting to divide by two, forgetting the squares. For some reason, I see kids tell me, "Oh, VF minus VI over 2A is an equation." No, it's not. So, that's our review of kinematics and a little bit of formula manipulation. Let's go to special relativity. You probably want to flip your page over to the back of your formula sheet. your formula sheet. All the special relativity stuff was on the back page except for one thing, but you've probably out of laziness memorized it, so we'll be okay. So, one of the key concepts, if we have two objects moving at different speeds, we used VR, relative speed. We said rather than deal with two objects moving at different speeds, pretend one is at rest and just compare the other's speed if it was at rest. Oh, what did we say in special relativity? What did we say the acceleration was for every question? What? Loud and proud. Yeah. Einstein couldn't figure out how to work acceleration into his thinking. General relativity worked it in. In fact, the mathematics of special relativity really wasn't bad. It was square rooting. Complicated, but it was square rooting. Uh general relativity, it's 10-dimensional tensor field calculus. It's crazy, but cool. So, we started out before we started going near light speed, we just had objects moving at different speeds at normal speeds. If two objects are coming towards each other, how do we find the relative speed? If they're coming towards each other, did we add their speeds together or did we go bigger minus smaller? Why? How can I remember? What's worse, a head-on collision or getting rear ended? Why? Bigger answer. So, we add the two speeds. This also works if they're heading in opposite directions. If they're moving in the same direction, [clears throat] we found the relative speed by going bigger minus smaller. In fact, we started out, Nathan, initially finding the relative velocity where I talked about one being positive, one being negative. And then partway through I said, hey, let's forget about relative velocity direction. We're just going to get relative speed bigger minus smaller. Our equation for the first lesson was d= vit plus a half a t^2 except what did we say a was. So what's going to happen to that half a t ^2? And so it modified to d equals and I wrote vl* t instead of vi I said that's where the relative speed goes because we're not accelerating. That's where that's what's going to go there. So if I have that Roberto, I could solve for T. Get the T by itself, please. D / V R. I could also solve for the V. Valentin, how would I get the No, you joined us afterwards. Never mind. Sorry, Nolan. How would I get the V by itself? How to move the Okay. Once we started going near the speed of light, we had to use special relativity. This is what your Q was a spaceship or some percentage of C. You need to know the difference between T and T0. Which one is the time on board the spaceship? T or T0. What's a dumb way to remember? to on board. So T0 is going to be time on board spaceship or if it's not a spaceship, the time the moving object experiences relative to the objects that we're saying is at rest. What about L and L0? Which of those was the original length at rest? Okay. So, you ready? Everyone listen. Which of those was the original length at rest speed zero? There's two ways to remember. L0 is the O original length at rest. What we noticed was that for a moving object, time moves slower. We called it time dilation. But when objects are moving, their lengths contract. Or if you're moving through space, space gets shorter in the direction of travel. Oh, mass and m0. Which one of those was the original mass at rest? That was how I remembered it. O original mass at rest. You want your calculators handy. I'm going to show some work, but not all of my work cuz I want to try and see how far I can get in class. And we'll treat it like we writing an exam. So, example one. Ooh, Violet. How fast is the rabbit going? How fast is the wolf going? Now, we do have two objects moving at different speeds. Are they moving or the speed of light? I'm not using special relativity. I'm going to be using for all of this d= v real * t. So what is the oh what is the relative speed? Are they going in the same direction or are they running towards each other? Bigger minus smaller. It's going to be 34 take away 24 in your head please. Violet. Thank you. B. If the rabbit has a head start, what's B asking me to find? Violet. What's it asking me to find as a physics concept? Time. Okay, A is zero because I got two objects moving at different speeds. We're going to start with D equals V RL * T. We're going to get the T by itself. It's going to be D / V R. What's the distance? 16 m. What's V re 10? I don't need a calculator for that, Roberto. I can divide by 10 in my head. It's 1.6. Really, dude? Wow. Okay. Vienna, what's C asking me to find? And and by the way, I should change that to speed. But you know what? We're asked to find We're going to find VL first. So I'm going to make a little note here. VL equals question mark. That must mean they gave me a distance. Yep. How do I know? I memorized units cuz even though I hate memorizing, that was worth it. That must mean they gave me a time. What's that? 160. That's how fast the bad guys are actually going. But I start out by pretending they're at rest. I'm going to figure out how much faster the police need to go. Then I'll add it to the bad guys. Uh D. You know what? I can go with uh d= v real * t. Get the v by itself. So again, this is all a consequence. Dallas of d= vit plus a/ a t² a is zero. D= vit. You know what? It's the relative speed. D equals v*. How would I get the v by itself? It's going to be 175 / 6.4. I can go to my calculator for that because I'm not dividing by 10. Kayla, I get I'm going to write 27.3, but you know, I'm storing this on my calculator. That's meters/s. Oh, what do they want the speed to be in? I need to convert this. How do I convert meters/s to kilometers/ hour? Is it times by 3.6? I know it has something to do with 3.6 times by 3.6. The answer is not 98.4. That's their relative speed. I'll write that down. 98.4 km hour. That's how much faster they need to go than the bad guys. That's their relative. How fast are the bad guys going? So, if I actually want to figure out how fast the police are going to go, it's going to be 98.4 plus 160. And I'll let you use a calculator for that if you really want to. Yeah, which is really fast. I made up okay numbers, but barely. That's about the limit of probably what a police car can do. 258 kilometers per hour. What did I ask you to find in part B of number one? Violet, what did I ask you to find in number two? Hey, I'll bet you I got multiple versions. In some of them, I ask you to find Vrel. And some of them I ask you to find time, but there'll be two objects moving at different speeds. I also put a train question on each exam. So, this says, "How long until the two trains completely pass each other?" And example four also says, "How long until the two trains completely pass each other?" Oh, uh, Cara, when I say how long, what are they asking me to find in terms of physics language? You're right. Loud and proud time. I'm going to go t equals question mark. In fact, I'm going to use because I see two objects moving at different speeds. Cara, I'm going to use D equals the relative speed times time. I want to get the T by itself. What's the V doing to the T? Adding, subtracting, multip What's the V doing to the T? Adding, subtracting, multiplying, or dividing. Do you see a plus sign there? Say no. Do you see a minus sign there? Say no. So if there's nothing between them, what mathematical operation is that? So how I move the V over? Time is going to be Terra, which distance? I'm going to argue that for the trains to pass each other, the back of that has to get past the back of that. It's going to be this whole distance here. So, it's going to be, and I could crunch it, but I'm just going to do straight in my equation. It's going to be 120, the first train, plus 510, the gap between them, plus 80. That's what's going to be in the distance. Whatever it works out to, I don't care. Cara, are they heading towards each other or are they heading in the same direction? Am I is Vil add them together or bigger minus smaller? Add them together because head-on collisions are worse because it's a bigger relative speed. So, it's going to be I'll write 12 + 10. If you did the 22 in your head, I'm writing it out because this is for my studying. Once you've written that down, you want to go to your calculators. Brackets around the top, brackets around the bottom, or use your fancy fancy fraction button. Did you get is it 15.9 or did I type that in wrong? 510. You know what? I got the five and the one mixed up. There we go. Hey, is it 32 and then the two sevens repeat? 32.3 seconds. Okay, don't clear your calculator. Hang on a second. Pause the YouTube lesson. Emily, I think example four is really similar in that I think it's still going to be t equals the distance divided by the relative speed. I think it's going to be again to pass each other. I'm gonna argue the back of the first train has to get past the front of the second train. So I think the total distance is going to be 150 plus 250 plus 100. Ooh, what's the relative speed? Are they going in the same direction this time? Then do I add them together? No, it's going to be bigger minus smaller. I'm going to write 18 takeway 11. I know you probably got the seven in your head, but in my notes so that when we're studying, I know what the heck we did. Hey, you're all going to get a train question. I bet you in some of them the trains are going to be going towards each other and some of them are going to be going in the same direction. See what we get. Bracket 150 + 250 + 100 close bracket divided by bracket 18 - 11. And I could have done the seven in my head there. What'd you get? Yes. Anyone else? 71.4 seconds. Did I put the right units on the previous one? I did. I can barely see, but they're there. All righty. Caleb, what's the second word of example five? Starts the letter S. I'm probably now going to be looking at my special relativity stuff. Okay. for.99 C. What percent of the speed of light is that? 99%. Okay. So, I'll mix and match between percentages and decimals. And I hope you're comfortable doing that. Uh, how much time will pass on Earth? What's this asking me to find? T or T0? So, I think my equation, correct me if I'm wrong, I'm going from memory. Is it T= T 0 / the square root of that gamma thingy? So t0 time on board is 12 / the square of 1 minus and then it's going to be.99 c over c all squared. And then I'm sure I did the terribly stupid pun where I would have said, "Caleb, do you see? Do you see? Do you see? What do you see?" And what would your response be? Uhoh. Help them out, folks. What would the response be? Yeah, the C's cancel, right? All of you want to try typing these into your calculator because one of the most common mistakes on this test was not know how to type it in 12 / of 1 -.99 squared. I know on my TI it assumes there's a bracket in the bottom so I can get away without it. If you're not sure, put the square root in brackets. What'd you get? I don't think that's right. Okay, don't clear your calculator. Now, some things I know. I know time slows down on the non-moving object, so I have to figure out how to use your calculator. Uh, the rest of us 85.1. Yes, the technical abbreviation for years is A for annually, but if you put a Y, I'm fine. On your test, it's going to be multiple choice on the final. So, just pick the answer that's rounded off properly and closest to the whatever on your calculator. Example six. Ooh, Haley, what are they asking me to find in example six? How much time has passed on the is that t or t0? Oh, how will I get the t0 by itself? What's the square root thing doing to the t0? So, and I don't need to memorize that. I can just derive it. Hopefully, you're comfortable with that level of formula, all of you. So it's going to be t 0 = t * that. It's going to be 46 * the of 1us 975 c over c all squared. Haley, do you see? Do you see? Do you see? What do you see? It's a stupid joke, but it helps you remember, right? Doesn't help me to remember, Mr. Dick. It's just a stupid joke. Shut up. Okay. 1 minus 97.5% of the speed of light.975 C. Oh, we did some examples where I gave you the speeds in meters per second. I didn't put those on your final. I put them on your test. It's so much typing, Tyson, and I wanted to cut corners for time. So, all the speeds that I gave you, I gave them to you as percentages of feet. Less typing. Otherwise, you have to divide it by 3 * 10 8 to really make it a percentage. I got 10.22. Haley, am I right? 10.2. Yes. And this is where it was around for something like this. We did that astronaut question where an astronaut returned home younger than her own child and all of you were this is what space travel is really going to be like. Example seven. Matthew, what's example seven want me to find? Do you have the review here? Yeah. Sorry. Read before that. What physics concept is it asking me to find? So, what physics concept is it asking me to find? Speed V. Okay, we're going to get the V by So, all of you at the bottom of your green sheet on the back page, there are three V equals equations. One if they give you the times. One if they give you the lengths. One if they give you the masses. Which one am I going to use here, Matthew? Did they give me times or lengths or masses? Okay. So, it's going to look like this. C. Sorry, not C, Mr. Dick. It's going to It's going to look like this. V equals the uh Gez, Dick, you're botching this. There's a C in front. Yes. I'm just going to leave that there. square of 1 minus is it t 0 over t all squ? Okay, you want the cheap hack. If you can't remember or you're too lazy to look it up, it's always going to be the smaller number on top and the bigger number on the bottom when you're squaring it. Otherwise, you get a negative square root. You get an error. So, it's going to be C square root of 1 minus and it's a 15 on top and 150 on the bottom. Don't forget the squared. And you're just going to leave your answer as a percentage of C, which just means you keep the C tracking along the way. And the decimal you get from the square root is the percentage. Um, I've memorized this one because this is a 10:1 time dilation ratio. I think you're going to get 99.5%. But let me double check that. That's just because I've done so many of these, I noticed that pattern. One minus. Now to type that in bracket 15 / 150 close bracket x^2 outside the bracket and I have to close off my square root and I get yeah 99.9949 99.5%. So I would take.995 or 99.5% of C. Depending on which version of the test that you write, I might have left it as a decimal, like the top one, or Cara, I might have put it as a percentage, but I'm going to assume you're comfortable flipping back and forth and finding the correct answer. I won't put both of those to try and trick you. And oh, I said a percentage. I'm not going to do that. I'm not cheap that way. Okay, Mia, what does example eight want me to find? L or L0. Oh, this 625 was measured when the spaceship is stationary. If the spaceship is stationary, how fast was it traveling when we measured that length? Zero. That's L. This has got to be L0. They're asking me to find L. And I think the equation you have has the L by itself already, does it not? It's going to be L equals L0. And I think it's times the square root, not divided by. Is that correct? Yeah. Yeah. Yeah. So, it's going to be 625 times the square of 1us 98 C over C all squared. Mia, do you see? Do you see? What do you see? C's cancel. Here's what I know to check my answer. I know that as objects move, their lengths shrink. the fancy word. Their lengths contract. So, you're going to get an answer less than 625. I hope Dallas, you type this in already. If you haven't, put your headphones down and type it in. Got to get practice typing these in. Right. Right. By the way, the other reason I'm pushing you to get practice, the faster you get at typing, that saves you time on the final, it's it's a win-win. uh 625 times the square of 1 minus bracket.98^ squar close Oh, I don't even need to technically put it in brackets because it cancels out. Hey, do you get 124? I'll call it 124. Yes, 124 uh meters. Oo, Destiny example nine. What's it asking me to find? M or M0. So I think that equation is m = m0 / the square root thingy. Yes, it's going to be 63 / the square. Thank you. 1 -.94 C over C all squared. Do you see? Shut up. Okay. Sorry. I think it's a funny joke. Do you see? Do you see? Do you see? / the square of 1 -.94. Don't forget the squared. I know masses get heavier, so I know I'm going to get an answer bigger than 63, 185 if I round off properly. Uh, what I would feel maybe comfortable doing only once is having 184 as an answer to pick from cuz you know how much it drives me crazy when you round off sloppy. I wouldn't do that on every question, but I would feel comfortable somewhere on your exam when I especially if I notice like a five or a point 6 after the decimal. Anyways, this is going to be 185 kilogram. Destiny, what if we went faster? What would happen to the relativistic mass? This is why objects with mass can't get to the speed of light because to get to the speed of light, the mass would have to be infinite. And K equals a K equals a half MV². You know how much energy you need to get an infinite mass to the speed? Infinite amount of energy more than there is in the universe. Oh, by the way, a corollary that means photons have no mass because they can travel at the speed of light. Oh yeah, [clears throat] but yeah. Yeah. Just saying they do. Okay. Dallas, what's example 10 asking me to find? Is that going to be L or L0? How do you know? Yes. So, let's look at the equation. Get the L0 by itself. I think I divide by the square root. Yes. I think L0 is going to be L / that. It's going to when it's at rest be longer. It's going to be L 125 / the square of 1 - 985 C over C all squared. Do you see? Do you see? Do you see? What do you see? Oh, C's cancelled. 125 / the of 1us.985. Don't forget the squared. Dallas, I got 724.4. Anybody else? This is the nods. More nods. So, I'll go 724 kilograms. Mr. Do it. No, no, no, no, no, no, no, no. Meters. Yeah. Yeah. Yeah. Okay. Jordan, what's example 11 asking me to find which equation am I going to use and how do I know the mass one? So I think the mass one says v= c square of 1 minus I think the m0 is on the top and the m is on the bottom. Is that right? Yeah. The L1 is the one that's flipped, which is why also why its equation looks different from the mass and the time one as well. Um, keep the C as a C. It's going to be 1 - 3 / 9 all squared square of 1us and then in brackets 3 / 9 close bracket square outside the bracket. Close off the square root and I get 942. I'll go 943 C. Is that right? 0.943. Yes. Or 94.3% of C. This question didn't say it wanted as a percentage. The test will or you'll look at the answers and figure it out. Matias, I saved this one for you. Example 11. What's it asking me to find? Do we have a length? Now, we did this. This was the actual space travel question. I put one of these on your test. I put a couple of these in your lesson. When we did it the first time, I kind of used it as a way to prove the length contraction equation where we did uh here we found the time back home. We found the time on board and then we found the length. There's a much quicker way, a much better way to do it, and that's just tackle it as a length equation. What we can do is we can pretend the spaceship isn't moving. Space is moving past it and contracting. Anybody you see the movie Project Hail Mary when it came out over spring break? Maybe you read the book. So they allude to it in the movie. He goes into more detail in the book. The reason Rocky the aliens ship has so much extra astrophase because they don't see light. They never discovered special relativity because they don't see photons. And so Rocky talks to Grace, the the astronaut, and says, "It was really weird. We were heading towards the planet, and the faster we went, it got closer, so we would slow down, thinking we were going to get there too soon. Suddenly would get further away, and so we would speed up and it would get closer, and then we would slow it further away." Very strange because they didn't know what was happening. The faster you go, the more space contracts. They would slow down thinking they were almost there. Nope. Not get further away. So, it was a really nice, very subtle nod to special relativity. I had to give Andy Weir, the author, credit. It's the quickest way to do this is to say, you know what? They want me to find L. The length we measured when Earth was at rest was 45. Now, it's light years, but I don't know if you remember, I said Einstein's equations are unit agnostic. You can put whatever units in you want, and you'll get the same units out. You don't have to convert everything to meters. Uh, so I can go like this. L= L0 * the square thing. It's going to be 45 times the square of 1 minus oh 97.8%. Can you convert that please? I hope you're all okay with doing that preferably in your head otherwise it's divide by 100. I know that it's going to be shorter. So that's my error check to make sure I've done this correctly. Earth measures that the star to be 45 light years away. The astronauts as soon as they start to travel, as soon as they hit their 97.8% of the speed of light, they're going to find it much closer. 45 square of 1us bracket.978. Do you see? Do you see? Shut up. Uh 9.39 light years. 9 39 light years. That's the quickest way if all I'm interested in is the distance. And I think I stuck one of those. I hope your generation Emily becomes the space traveling generation. I don't know. The physics is really tough. The engineering, the technology, it's really tough. But I hope I'd like us to become a Star Trek warp drive exploring the galaxy species. That brings us to the end of special relativity. Now we're going to pivot to probably the toughest unit of the year, forces. If you found it tough, congratulations. You're normal. What were some of the key concepts? I will not care be asking you which of the following is Newton's first or which of the following is Newton's third. I told you you didn't have to memorize which one is which, but you need to know what they are. Newton's first law said this. Um, if a equ= 0, forces must be I'm looking for a word that starts with letter B, balanced, balanced. And it also worked in reverse. So if a is zero, forces are balanced. If forces are not balanced, we must be accelerating in the direction of the unbalanced force. So if a does not equal zero, forces are not balanced. In fact, there should be an unbalanced force in the direction that we're accelerating. We used this one to draw our free body diagrams. Newton's second was really our only equation technically of the whole unit. F equals what? What? Now, we started out by saying fnet equals m a but then we modified it. We're actually going to scroll down here. We said if we're going to do this properly, it's winner minus lozar equals ma. That was really Newton's second in disguise, but Vienna way more flexible because it allowed us to deal with multiple forces. What was Newton's third law? I phrased it as forces come in. And I'll be nitpicky. I'm going to say forces come in I never bothered saying opposite, but I will in our notes pairs, which is also why impulses came in opposite pairs. What's FBD and a brief for? And I taught you to draw them systematically. One of the things I and I've heard this from my physics students that have gone to university, a lot of their peers, they don't know how to do a free body diagram because they always want to start with the mystery force. No, I always said get the obvious one. Which one did I mean? We started with gravity. Next year that will be the same unless we're in outer space. If we're in outer space, no gravity, then we won't. But otherwise, gravity, we go went systematically. Then we often said, are we sinking into the round like are we flying like Superman? And by doing that, by the time you got to the more complicated forces, I felt Tyler, they became more obvious. You you could figure out what they had to be. You need to know the difference between weight and mass. What's mass measured in kilograms? In fact, the very first video I showed you was telling why it wasn't grams. Turns out grams were too small. We talked about how they were redefining the kilogram. I showed you the smoothest object in the universe. How do I calculate weight? It's on your formula sheet. There's no excuse for freezing up. How do I calculate weight? No. Now, it's on your formula sheet. No excuse for freezing up. How do I calculate weight, Charlie? How do I calculate it? It's on your formula sheet. MG. It's on your formula sheet. Notice where it is. So, if it's a force, what must the units for weight be? What got to be? kilogram meters/s squared if you break it down. But got to be Newtons. Okay. Then I went on a big rant about what a bathroom scale measures. A bathroom scale does not measure mass. It does not measure weight. What does a bathroom measure scale? Bathroom scale measure when you're standing on it. How do I find FN? You'll notice there is no equation for normal force. Instead, we had to draw a this is a good job for a I'm going to a brief. And then I often said for the simplest ones, I said something like this. I don't know the normal force. Oh, but look look look. I don't know the force the same size as the normal force. And in the simplest case, the normal force was mg. But as soon as you had extra arrows pointing up or down, uh-uh. Physics 12, we're almost always going to be on a ramp. Normal force is not mg. It's a component of gravity, but it's not all of gravity. So, what if there was extravertical forces? Then I had to be even more general. I had to say everything up equaled everything. And then when I wrote that equation, I would get the normal force by itself. I may have made a joke. I would get an FN clue or something like that is what I would say. Remember the elevator question? and a person standing on a scale in an elevator. We're going to do some of those. I put a number of those on your exam. Some just asking whether you're feeling heavier or lighter. Some where you actually have to do the calculations. What about for a car? What force makes a car accelerate? And spoiler alert, it's the same force that makes a car come to a stop. In both cases, I told you the story of how I was at a a conference and I had a colleague next to me who didn't have a physics background. They had labeled their car with F engine pointing forward. Okay, then that means if you put that car on ice, it still has F engine. It should be able to drive just fine. Why can't you drive on ice? Which force gets smaller or near zero? That's how I know frictions makes a car go forward and stop. Then we started looking at multi-mass questions. If there is more than one mass, we said, well, first of all, this is a job for us. Want to draw a free body diagram. And then we tweaked our equation. It was still winner minus loar, but if there was more than one mass, we tweaked the right hand side. It wasn't ma. Who remembers what we wrote if there was more than one mass? Like for the Atwood machine? I heard someone say it. I think you're right. No, it was just a very if I have forces from more than one mass on the left hand side, I had to have more than one mass on the right hand side. How did I show that? Yes. And then I said actually it's always been m all a because for one mass that's also by definition m all. It's always been that. What would you mean by m all if there was two masses? M1 plus m2. If there's three masses, I'm not going to give you a three mass question on your final, but we did them in our homework. M1 plus two3. And then we said this. Well, we know to find the acceleration of everything. We wrote an equation for everything. We walked along the rope. And then I almost always did this stupid joke. What was I insinuating whenever I did the stupid stretching out? Okay. And I gave you the horrible attention deficit disorder joke. I said we can't find tension from our equation for everything cuz the T's cancel. So then I said to find an individual force. We wrote an equation for an individual mass. Which mass Haley? The one that made your life the easiest because you'd get the same tension either side of the rope. So pick the least cluttered one. That's why we stopped always saying down was negative and up was positive. We started letting the winner be whatever makes the math easier. Uh remember the Atwood machine? there is going to be an Atwood machine on your final. So, let's jump on in. Here's an elevator question. An 833 Newton person stands on a scale on the floor of an elevator. What is the scale reading if the elevator has an acceleration? Now, I although they're saying find the scale reading, what are they really asking me to find? Normal force. What might this be a good job for? I'm going to try and do one free body diagram for both of these. So over here I'm going to represent this person with a dot. What are the forces acting on him? Dallas, get the obvious one. Which way? And I usually just wrote mg. What force is pointing up on this person? And because I'm going to try and do a generic diagram, I'm going to make the normal force the same size as mg. And I'll just imagine it getting longer or shorter as necessary because I'm looking at the clock and I'm cutting corners. So we can handle this. Uh, you know what? I'm going to go. Here's part A. Here's part B. Cara, in part A, what direction are we accelerating? The question tells me, which way is going to be the unbalanced force? Same answer. Which way is the winner? Same answer. Look at my free body diagram. Which force is pointing up? Which is the winner? Which is the loser? Who? Oh, no. I missed my dumb joke. Normally I said, fine. Who's the loser? And then I would have gone. You looked at Haley. Oh, she looked at So, you remember the stupid joke of I made the big salmon dance and I wasn't fine. Who's the losing force? The losing force must be MG. And everybody, what does winner minus loser always equal? What? What? MA. Cara, back to you. What are they asking me to find? Read the second sentence of the question. Which of these is telling me the scale reading? What does a scale actually measure? Not mg. What does it measure? the nor we're going to get the normal force by itself. I need to move the mg over. This is not a swappy dance. The mg is negative, but the normal force isn't. How would I move the mg over if it's minusing? And so I would say the normal force is going to be m a + mg. And I have a problem. The mass. Oh, how do I know this can't be the mass? How do I know newtons? And also, if you're 833 kg, you're not fitting in an elevator. That's over 2,000 lb. In fact, I don't think you'd be able to survive at that mass. Your organs would collapse on each other. This is Newtons. You know what this is? This is mg. If I know mg, how do I get the mass in kilograms on your calculator? Everybody go 833 divided by 9.85. Okay, Cara, now I'm good. I can say the normal force is going to be 85. What's a? They told me in part a three plus. And then I could go 85 * 9.8. But Cara, that's 833. And I'm lazy. I'll just drop that number down. Once you've written that out, go to your calculator. If we accelerate up, is this person going to feel heavier or lighter? Heavier. What if we accelerate down? What if we move down at a constant velocity? What if we're at rest? What if we're in freef fall? I just gave you five questions you're going to see in your future. I turned those into multiple choice questions. Uh what do you get? 188. If I That's Newtons. What if I wanted that in kilograms? What is it? So, even though their mass is 85 kg, they feel like their mass is 111 kg. They feel heavier. Okay, good. Michaela's yawning, so I'll come at her to keep her awake. Michaela, in part B, which way are we accelerating? Yeah. Which way is the winning direction? Same answer. Who's winning? More specific from my free body diagram. Who's winning? losing equals. And here's where I gave you a clever hack. What's right in front of the normal force that I don't like? This is where I introduced that swappy dance. A student nicknamed that a few years ago. I said, you know what? You can plus that to that side while at the same time minusing that over. The mg just drops down like a domino. Cthunk. You have a minus ma here. And then Michaela, I'm going to put the normal force by itself on the left where we're used to seeing the things by itself. I already know mg, it's 833 minus m is 85 and acceleration is 2.5. What do you get? 600 something I think 620.5 if I rounded that to three sigfigs correctly would I write 620 or 621 okay just saying uh how what if I wanted that in kilograms divide by 9.8 point it and you'll see. Yeah, this person feels lighter. We're going to finish with one more example, too. This is as far as we're going to get. Thank you for your patience. I appreciate it. I see the yawns. Charlie, you walked right into that one. Charlie, I also see an elevator and a scale. Uh, what are they asking me to find though in example two? You know, this is a good job for what are the forces acting on this person? Get the obvious one. What else? Bigger, smaller, or the same size as mg? Problem. I don't know. Wait a minute. How big is the normal force? How big is mg? Get your calculators out. Crunch it. 62 * 9.8. So, I'm going to put the normal force on here, and that's 423. What was mg, Charlie? be stupid obvious. Who's winning? Which way are we accelerating? Is this person feeling heavier or lighter? Those are all tweaks I could add if I wanted to. So, yeah, it's going to be mg minus normal force equals ma. We're going to get the a by itself. I'm sure I named it after somebody. Whose theorem was this? Dallas. I named it after Dallas. Wow. Right at the bottom of the barrel. Uh anyways, it's going to be 607.6 minus 423 divided by the actual mass 62, which is what? Oh, there's a built-in error check. I know it's got to be less than 9.8 cuz if I cut the cable, then we'd be accelerating at 9.8 8 m/s squared. >> Did you all get 2.98 m/s squared? We're going to pause here on When do I see you next? Do I see you Friday? So on Monday next week, we'll finish off forces and I'll try and get some momentum in or we'll get momentum the next day. Also on Monday, I'm going to give you a practice final exam for your studying.