40 min.
https://youtu.be/H2yQwrl1EF4
PHYS 1101: Lecture One
Welcome to Lecture 1. This is the Physics 1101 online class.
Let’s start the lecture with an overview of the things you need to have set up in order to take this class. The first one is that the lecture movies that you will watch are QuickTime movies, so you need to have installed on your computer the latest version of QuickTime. You can Google that and go to the website and download that latest version and install it.
The second major thing you’ll need is access to WebAssign. This is the environment that we’ll use for you to do your lecture quizzes and your homework. This information and access to WebAssign is explained in more detail in the syllabus. In essence, when you go to WebAssign you’ll have a login page and you will first log in to that as your 49er Express user name, the institution is UNCC, and then the password is initially set to “physics,” lower case “physics”.
Once you log in and you’ve purchased access to WebAssign, on a day-to-day basis this is the type of window that you see. Your assignments to work on will show up here, that you can click on, enter your answers, etc.
In WebAssign you have to opportunity to purchase an online version of the textbook. This is really all you need in terms of the textbook support for the class. At the top here you will see a link that will give you an option to purchasing both WebAssign and this electronic access to the textbook, which is Cutnell and Johnson, sixth edition. Alternatively, you certainly can go to the bookstore and buy a hardcopy of the textbook, or I believe the price is something like $30. You can in combination purchase your semester access to WebAssign and access to this electronic version of the textbook.
In this section let me briefly go over what’s expected of you in the class. This is spelled out in detail in the syllabus that you have a copy of. You were sent an electronic copy of this syllabus at the beginning of the semester. In essence, your grade is made up of the parts highlighted here in red. There is a collection of lectures quizzes, these are online movies that you’re expected to watch. Embedded in these movies are concept questions along the way to help you understand the material.
As you watch these movies you need to write down your answers to these concept questions and then you will be entering those answers into WebAssign for this lecture, for every lecture quiz after you’re done watching the quiz. The due dates for the movies are spelled out on the schedule page. That’s the main link that you were given as access to the electronic material for this class. Lecture quizzes have an equal weight towards your grade, as do every mid-term exam. It’s 15% of your grade. I’ll drop the four lowest lecture quizzes at the end of the semester.
Homework makes up 20% of your grade. Homework, like your lecture quizzes, are done through WebAssign. Work together as much as possible. Take advantage of the Physics Resource Center, which is in the Burson Building, Room 135. Seek help as much as possible.
There are three mid-term exams that cover the material for this class. Each is worth a total of 15% of your grade. One of these scores, the lowest score, will be replaced with your final exam score if the final exam score, of course, is higher than the lowest mid-term exam score. This is the option that accounts for situations where people have to miss a mid-term exam for one reason or another. There are no makeup exams in this class. This ability to replace one mid-term exam grade with the final exam grade is the only option for cases where a mid-term exam is missed.
Homework, like lecture quizzes, are to account for cases where homework assignments are missed. Like lecture quizzes, we drop the two lowest homework scores at the end of the semester before calculating this fraction of your grade. Again, for lecture quizzes we drop the four lowest lecture quiz scores at the end of the semester before calculating this grade.
Okay, the rest of the lecture I want to focus on three main parts. I want to describe for you a bit about the philosophy of a course like this and what you need to be thinking about in terms of the general approach to getting through the material and understanding it. Then we’ll go through the detailed mechanics, a lot of which I’ve already pointed out, but this is a little more detailed for you. Then the initial topic here I’m going to cover is an idea about change. It’ll really be a first topic that I want to teach you or introduce to you.
Okay, let me start out saying a few words about the philosophy of a physics class. The first point to make is having to do with the role of math. I’m sure you’ve heard that math is an important part of a class like this. That’s because, believe it or not, Mother Nature appears to speak math fluently. Scientists have come to appreciate that mathematics appears to be the natural language in which to go about solving the problems about nature and being able to predict things in nature, so in that way you think of it as a language.
This, I’m sure, is new to all of you. You’ve taken math classes, but it’s been strictly, either just numbers, or variables, and mathematical manipulations. You’ve never, unless you’ve done a lot of word problems, you’ve never had the opportunity to really exercise this idea of math describing real life.
So, as I say, math is just a collection of numbers and variables, say, in your algebra classes. Now, those numbers in real life are, for science, going to have units, which give them physical meaning and they’re always going to represent some physical quantity.
There’s a certain flow to applying this notion of mathematics to carry out science. Let me walk you through how the flow of that and the process of that in the context of this example. So don’t worry about the details of this. This is a type of problem that we’re going to learn later in the class. You’re going to learn how to solve this problem. Try to focus on the flow and just the general steps that we go through.
So, you may have a problem, for example, something like a person that has a certain mass. This is actually in S.I. units, kilograms, so this is probably a, maybe a 100-pound person, or so. Actually it’s a 140-pound person, now that I remember. But this lightweight person is riding in an elevator, but that elevator it’s speeding up. It’s accelerating upward with a certain specific value. The question is, what’s the person’s apparent weight?
Now, we’re going to learn in the class, specifically, what you have to focus on when you are asked about a person’s apparent weight, but probably intuitively you can just now picture, imagine when you’re in an elevator and you’re wanting to go from the first floor up to a higher floor, when that elevator first takes off you’ll have a sensation of feeling heavier ever so briefly, just during that initial time when the elevator’s accelerating upward.
Okay, to do the science and to solve a problem like this we will come to recognize a relevant physical phenomena or principal that governs a problem like this. In this case, the physics behind it is that for all objects, an object will accelerate as a consequence of some net force or a consequence of the sum of all of the forces that are on that object. So this is a very general statement that would apply to any object, any scenario of different forces. In order to solve this problem we have to apply these general ideas, this more broad principal of physics to this specific problem, and that’s the devil in the details that’s at the heart of solving problems like this.
Okay, here’s what you have to do. The first thing you have to realize is that we’re going to have to work with the mathematical equivalent of this statement. Fortunately in our class, we’re not deriving these fundamental principles, but that’s already been done for us. In this case it was Newton back in the 1600’s that worked out what actually governs the acceleration that an object has as a consequence of forces. He already translated for us into mathematics what that means. Right here, what this equation I’ve written out here is the translation to math. This is called Newton’s Second Law.
So, we’re going to learn a lot more about Newton’s Second Law, but in essence let me show or read this equation to you. It says that the acceleration this object feels is caused by, this Greek symbol here means sum, it’s the addition of all the forces, the net force on this object. This specific number that you get for this acceleration, it turns out it doesn’t just depend on the number that you get when you add up these forces, but there’s also an important factor having to do with the inertia, the massiveness of that object, and you have to take that into account, and mathematically the proper way to do that is to divide the forces by this mass.
Okay, so this is our general equation — let’s see if this highlights well for you — that we could apply to any object of a certain mass experiencing forces to figure out its acceleration. The name of the game now is to apply this or customize this general physical principle to our particular problem. That is a step that many students find to be the most difficult. It’s to take the specific problem and to start translating it into math and to start translating it or customizing our general equation and apply it to this problem. The first step to doing this is always reading this very carefully and often what helps tremendously is to start sketching out your picture of the scenario to try to just clarify in your mind what’s going on.
Here’s my generic elevator, but I always draw the object I need to focus on, I always draw it in red. When you read this problem carefully you soon realize that it’s the person that you’re focused on. It’s the person’s apparent weight that you’re trying to learn about, so, here’s our object. That’s the object that this equation is going to apply to.
Okay, we will soon learn that to mathematically make sense of things we need to pick a convention, and we’re going to use signs to do that, plus or minus, to indicate what’s a positive direction for a force or an acceleration versus negative. So I’m going to pick positive as up. Then on this I’m going to sketch a little up arrow, because this problem tells me that this person is accelerating up.
Then I’m going to go in and draw the forces on this object. I know that the person has a force due to gravity. In this class we’re going to call that w the weight, the true weight of the person. But, the person also feels the sensation of touching the floor. Any contact results in another force, I’m just going to call it f here, the force of the floor.
So being able to draw this picture is one of the first steps in solving the problem. I further would then go in and write down some specific values that I have, numbers, and what the proper variable is that I need to assign to those. That’s going to help me when I go to put that information into my starting equation. So, what do I have? I know that the mass, and I would use the symbol m for that we’ll learn, the 65 kilograms. I know that the acceleration is positive up and it’s 1.8 meters per second squared. That’s all the numbered information that I have.
The other thing I would ask myself is, what is it I’m trying to solve for? Obviously, it just says here in words that it’s the apparent weight, but I have to figure out what the mathematical equivalent of that is or what’s the mathematical variable that we’re going to want to focus on that’s going to represent this person’s apparent weight. We will learn, I will teach you that that mathematical symbol that you want is going to be the variable f. It’s going to be the size of this force that the floor is providing. It turns out that all of us have our sensation of weight effectively based on how hard the floor or our chair is pushing up on us. It’s kind of a strange way of looking at it, but that’s the case.
So what we have done to do all of this is we’ve taken our first steps to translate this word problem, this real life scenario, into math. Okay, and this, my friends, is often one of the hardest parts to this class.
Okay, once we’ve done that initial translation of our problem into mathematics we need to now start with our main equation. In essence we need to start customizing this equation to our problem. That means we need to say to our self, “For our objects, this person’s acceleration, what are the forces on that object?” Then, “What’s the mass of this person?” Those are the physical numbers and quantities that are going to determine this person’s acceleration. That’s the constraint that defines how all this has to fit together.
In order to do that let me go back up here and copy this, just so we have it here and we can see it again. As we do that, I’ll make it a little bit smaller for us.
Okay, so we have to just directly substitute in to this equation. For our problem the person’s acceleration is equal to the sum of all the forces. In this case I’ve got two forces. The force from the floor is positive, because it’s up. Then I need to add to that the force of gravity, which is down, and that has a value of m times g, we’ll learn this later in the class. So, for everything in the parentheses here that’s the equivalent to this numerator, the sum of the forces. Now to complete the mathematics I have to divide by m, that’s the denominator here.
Okay, once we’ve done this direct substitution, now we need to do some algebra because our goal is to focus on this variable that we want. We were trying to determine how large this force is from the floor. Here’s how this works. You may remember in algebra, if I’ve got any algebraic equation, that as long as I carry out legitimate mathematical operations, meaning if I add 20 to the left and I add 20 to the right the equality holds. I’ve done the same thing to both sides. As long as I do that, I maintain the integrity of the equation.
When you map that into an equation that represents a physical scenario, what that means is the algebra that I do, the legitimate mathematical steps, will maintain the integrity of the relationship between these physical quantities. What I want — I’ll write it off here to the side here — our goal is to do algebra until we end up with an equation that looks like f, the thing that we want, equals blah, blah, blah, an expression on the right-hand side, so we need to do our algebra to do that.
Let me rewrite this equation a little bit neater. a now is equal to f minus mg divided by m.
I’m trying to isolate f, so my algebra would say here, well, let’s move that denominator to the other side by multiplying both sides by m. Now my equation becomes m times a equals f minus mg.
Now if I add mg to both sides the mg‘s cancel on the right, and now I’m left with my isolated f and my equation becomes ma plus mg is equal to f. Or, let me just flip each to the other side of equation. I have f equals mg plus ma.
Okay, that effectively is the bulk of our work. We, in essence, are done aside from plugging in numbers to get a real value for f. We were given the mass of the person, g you’ll learn is 9.8 meters per second squared, so that’s a known quantity, and we were given the value of a. So, we have numbers for all of these, we could plug them in to solve for f.
Okay, this equation I would refer to as the specific solution to this problem. In other words, if you had a problem that was almost exactly like this problem, perhaps the value of the acceleration was different and the mass of the person was different, but it was the same scenario, you wanted to know the apparent weight given a certain acceleration, you could use this equation and just plug in the different numbers. But this equation only applies to this specific scenario of an elevator and the apparent weight of the person just standing in the elevator.
That’s a very limited set of problems. This main basic equation, this main starting equation, this applies to any object in any scenario, what its acceleration will be given the particular forces on it. This is really the strong equation behind the physics that applies to many, many, all scenarios, many different scenarios.
Okay. So let me, real quick, translate this equation back to real life for you. We have here that f is equal to mg plus ma, so how does that read? What is that in real words? This is, the person’s apparent weight is caused by or equivalent to m times g is the person’s true weight. So this is the weight of the person if they’re just standing on the ground, you’re sitting in your chair, you’re not accelerating–but the person’s apparent weight is not just equal to the true weight, but that force that the floor is supplying, your sense of weight is larger. It’s actually large by an amount that causes this upward acceleration, the part here that — let me put a little arrow here for the “and” as well. Let me highlight this section. Both of those terms represent the part that provides this upwards acceleration.
Okay, so that, in essence, is the answer. If you want to, for our particular problem, if you need a number at the end of the day, you would plug those numbers in. Meaning, m is 65 kilograms, g is 9.8, multiply those together add to it 65 times the 1.8 meters per second squared. In fact I think I have that done for you.
Well, I’ll do it for you right here. You would plug in f equals 65 kilograms times 9.8, and then I’ve got to add to it the 65 kilograms times 1.8 meters per second squared, and when you multiply all that out with your calculator you end up with 754 Newtons. So that translates to, as I’ve shown you here below, that the person’s sensation, their weight sensation, their apparent weight is 754 Newtons. That’s about 170 pounds and it’s just interesting to compare that to what their true weight is. If they’re just standing on the ground it’s 637 Newtons or 143 pounds.
Okay, that gives you an idea of the flow of the problem. Let’s start at the very beginning here. We’ve gone from a problem needing to know a certain value. We had to realize what the physical principle is behind it and what the general expression or general equation is for that physical principle, so this is the conversion of the principle into mathematics. We then had to convert our problem into mathematics and that meant defining some variables to represent physical things, identify forces, etc.
Then this is always the flow and always the thing to focus on. We’re always going to start with this very powerful general equation that applies to any objects and then we’re going to customize that to our specific problem. Then we carry out our algebra, being careful not to make any algebra mistakes, until we get to our specific solution for this problem.
Then I walked you through here translating it back into real life. When you plug in numbers it’s always a good thing to just check to be sure that it physically makes sense, the answer that you’re coming to. Once thing to watch for is, and you’ll see more of this, is that the units work out and simplify. If they don’t, it can be a flag that you’ve had an algebra mistake somewhere. If the number turns out being something that doesn’t make any sense then you may have made a sign error or something. It’s an indication that something might be wrong with your math or you need to go back.
Okay, so here I’ll just highlight for you a couple of statements here that you’re going to do this translation between the physical problem, a real life scenario, and mathematical variables and the mathematical representation of that problem. Lots of times in this class you’re going to go back and forth. This is the skill most people coming in to the class don’t have at all. You’re learning it for the first time and you’ll get very good at it. You’ll be impressed with your skills by the time the class is done.
I have one more bullet here to point out, just to emphasize to you again that because this will be very new to you, it may sound strange, but in a lot of ways math is acting as a foreign language to us and we have to learn how to speak that language.
Okay, that’s my scenario to describe the role of Math and here would be your first quiz question for this lecture. For this first lecture I have a lecture quiz made up for you in WebAssign. There’s no right or wrong to any of these answers. I’ve just filled it with some interesting, kind of, survey questions just to see where the class stands and where you are. So, read through this question, pause the video if you’d like, take your time, and just give me your opinion on how strong, what do you think your math skills are?
Now I want to say just a few more things about this flow of the class, the philosophy of the class. I’m going to use this analogy of a tree to try to keep emphasizing to you what you need to focus on. So, my picture that I have here, it’s a beautiful oak tree and think of it like this. In this class we’re going to learn only a few, really a few very basic principles, like Newton’s Second Law that governs how an object accelerates given forces and a mass. But that general principle allows us to solve for a whole range of specific problems.
Let me imagine that each leaf out here at the top of the tree represents a whole collection of very specific problems, like the one that we worked with here with the person in the elevator and what’s the person’s apparent weight. This specific problem, we learned, had a solution, the equation for it was this, and then the specific number for this person was the 754 Newtons.
Okay, what we want to focus on in this class, as I emphasized, is always starting with this basic equation and then as we read our problem, we’re customizing it, we’re effectively moving up this tree making logical choices, drawing the right picture, making the right identification of a value with a variable, etc., to go from the customization of this to our specific problem. The details of all that I’ve got in this red bubble here, off to the left. That’s the synopsis of all the mathematics that we did. What I want you to encourage you to think about is that it’s this flow, this process, that I want you to focus on. That’s what you really need to learn in this class.
If you are heading to med school and you’ll be taking the MCAT, you’ll find recent versions of that test. That’s what they’re testing you on is focusing on the basic principles, the meaning of it, being able to logically solve these problems.
The tendency in this class is to try to focus on just the leaves. In other words, people find themselves being drawn to trying to just memorize the equation which is the answer to a specific problem. That’s a very narrow approach because it really won’t help you solve all the different types of problems you need to be able to solve. You need to know the process so you can arrive at your own solution for a whole range of different problems.
So the quiz questions I’ll ask you throughout lectures, the exam questions, the majority of the class is going to focus on, “Do you understand this process? Can you follow and can you execute this process or carry it out?” “Execute” is probably not a very good word there, “carry it out”.
Okay, the only thing I would add to it is, as we go through the class there’s a handful of these basic principles we’re going to learn. We’re going to learn problem solving steps that teach us how to do this process, basic principle, out to our specific solution.
Let me just write here the one example I’ve been introducing you to is the basic principle of a equals the sum of the forces, divided by the mass. Every time we introduce a new basic principal in this class I’m going to give you problem solving steps to help guide you through this logical reasoning process.
I’m going to go ahead and flip the tree upside-down, because really the order in which we do things is more from, so that it’s the base of the tree out to the leaves. It’s a little more consistent to put that in a top working your way down kind of representation, so maybe this works a little bit better for you. We start here at the top, we follow these processes, these steps from our specific problem, we’re mapping it into this, until we get down to, eventually, our specific solution.
So those are my two bullets here, off to the left, that I’ve just emphasized for you. I’ll really emphasize these problem solving steps and show you how to use them in lots of examples throughout the class.
Okay, so it’s an interesting class in that there’s different components to it. A lot of the emphasis is on developing these problems steps and this reasoning ability, as I’ve mentioned. But there is some memorization that you’re going to have to do as well. You will need to memorize the definition of terms and of physical laws that we’re going to introduce along the way. You need to memorize the variables that are used in this textbook to represent the specific different physical quantities we’re going to be looking at.
You need to understand and recognize in different contexts what that quantity is and what variable has to be assigned to that. You also want to memorize the units that go along with every physical quantity and then the variable we use to represent that. That’s one component of the class.
The other main component is this understanding the meaning, the physical principles, and then being able to execute — I used that word again — carry out these problem solving steps. Those are skills that you’re going to have to practice and develop.
Okay, the lecture quizzes that I’ll give you, you’ll find a lot of them are going to focus on the reasoning, but on occasion I will sprinkle in questions asking if you’ve memorized the names of these variables and what they represent. In fact, let me point out here that this first section, the memorization, this is an excellent goal as you read the textbook. I find the textbook can be confusing to a lot of students. At the very least, if you read the textbook and make this memorization your primary goal it’s very useful. It gives you something to focus on as you do your reading.
Okay, so here I have a couple more quiz questions for you. Again, I’ll just give you 3 points just for giving me your opinion. Just let me know what your tendencies are, how well do you feel or find that you can memorize things in general, etc. Your next question here is, what kind of classes have you taken in the past? Do you have some experience with this memorization versus learning reasoning skills in a class?
Question 4 is just your attitude about reasoning and carrying that out. Do you think you’ll enjoy that? The next one here, what’s your attitude, I guess, toward that? Do you think you’ll enjoy that part of the class?
Then a very important resource you have available to you is a resource center, a help session. It’s on a walk-in basis, it’s through the Physics Department. It’s in the Burson Building in Room 135. It’s a great resource. It’s open Monday through Thursday from 9 a.m. to 5 p.m. on a walk-in basis. You can just go in there, there’s computers, you can log in to WebAssign. There’s people there to help you with questions. I strongly encourage you to take advantage of that, and I just want to know here in this question if you think you will have the opportunity to do that.
We’re at the very last part of the lecture. Let me draw a line here. I want to walk you through this, it will probably take only five minutes, just a quick introduction to a very important topic that we’re going to come across several times throughout this class. This concept has to do with change. Let me show you what I mean.
I think it’s something that we typically aren’t accustomed to really thinking about or being aware of. Let me introduce it to you this way. So consider this scene, this picture here that I’ve pasted for you. It’s obviously a very cold, snowy day. This looks like the trash guy picking up the trash. Let’s say that the thermometer reads 28 degrees Fahrenheit, so it’s below freezing. Here’s the snapshot.
In addition to looking at this snapshot, it’s interesting to try to imagine, it’s useful to have some information about how the weather is changing. In other words, here’s the snapshot of this instant in time, what’s it going to be like in an hour? What do you think? Is it going to be colder? Is there going to be more snow coming down? Would it have warmed up, stopped snowing?
So those questions — let me just write it here — what’s the scene in one hour? How is this weather changing as time goes on? That’s very important and additional information about what’s going on here physically. Okay, so as I’ve stated here — I put a star beside it — I want to encourage to think about, not only the value of something, let’s say the temperature, but also to think about how that temperature is changing as time goes on. That’s the change in time of that quantity.
Just to give you an example, let’s say in this problem that for this weather, for this scene, that the temperature change — I’m going to underline change here for you — is -3 degrees Fahrenheit per hour. Okay, the mathematical translation of that is really just a number -3, but the units of it are critical. The units that represent degrees Fahrenheit per hour you would write as, “degree Fahrenheit per hour.” So the information that this quantity, this -3 degrees tells us how something is changing, is because we see that it’s -3 degrees Fahrenheit, but that is per hour. The presence of this time unit is critical in telling us that this is a quantity that tells us about the temperature change.
Okay, if I were to tell you that the temperature change for this scene is -3 degrees Fahrenheit per hour, what would be the temperature in one hour from now? Well, if it’s -3 degrees that negative sign, it’s very important. That would tell us the temperature’s getting colder, the temperature is lowering. So that would mean one hour later we’re looking at 25 degrees Fahrenheit. If this temperature change continues then an hour later, the next hour, so this would be two hours later, we’d be down to 22 degrees Fahrenheit.
As we all know the temperature, through storms and the environment, it fluctuates a lot, so it won’t stay this temperature change forever. Eventually it’ll start warming up again, but at any instant it makes sense or it’s useful to know what the change in this temperature is with time.
Okay, so I have a couple of bullet points here. It is important to remember that the value is a separate physical entity and quantity than the change in the value. You can see that and perhaps help to appreciate it by noting that the units are different for these two quantities, 28 has units of degrees Fahrenheit, the -3 has units of degrees Fahrenheit per hour. Every hour the temperature changes by 3 degrees.
So let me give you some examples to emphasize how the value and the change in the value are really unique independent quantities. Let me make a little table here for you where I’m going to give you some examples of a value of a temperature and then another column beside it, the change in the value.
Okay, you could have a warm sunny day where the temperature is 70 degrees. Ah, wouldn’t that be nice? And for a particular weather scenario we could have this case where the temperature is 70 degrees Fahrenheit, but maybe the change is -3 degrees Fahrenheit per hour. A storm’s coming in, a cold front’s coming in.
Alternatively we could have another scenario, like above, where the temperature is 28 degrees Fahrenheit, but maybe it has a temperature change of +1 degree Fahrenheit per hour, so there’s no correlation here. You can have different scenarios and different scenes. These are separate quantities and it’s important to keep that distinction. So we’re going to see this notion of a quantity that changes with time a lot as we work through motion and we’re understanding people’s position changing with time, their speed can be changing with time, etc.