https://youtu.be/3BHHFSDQV6s
PHYS 1101: Lecture Ten, Part Four
So here’s what Newton would argue, if somebody asks him what’s the natural state of the book if it’s really left alone, he would say that simply that the motion doesn’t changed. He would come to this conclusion; in fact I think Galileo was the first to think this through and start heading logically in this right direction for understanding motion by considering what we call limiting cases. If Galileo had done that same experiment with the book, he would have asked himself, well what if the table were slicker and slicker? What if I did that experiment on a slick sheet of ice?
Your intuition tells you that the book would go further and further, that it would decelerate much more slowly on a sheet of ice. And so Galileo argued that if you went to a limiting case where you really eliminated all sources of friction that likely he proposed the book wouldn’t slow down that the motion would not change. And that when we did that experiment with the book we really weren’t leaving it alone or doing nothing to it, so it really was not a good test of asking about the natural state of the book. If you really left the book alone, once it had some initial velocity if nothing was touching it, it would keep going at that same speed.
So it was really Newton that put it all together. And I’m going to begin to summarize that with his laws, that we now call the Set of Newton’s Laws. There are laws 1 through 3. The first one, which is called Newton’s First Law, which often gets overlooked to some extent, but it really is fundamental and it was a milestone in people’s realization about the ideas behind this. It really starts with asking this question about what is the natural state and Newton’s first law is that if you really left something alone the motion won’t change. By that I mean the velocity won’t change.
So, behind the fundamentals of motion we are going to make this black and white distinction between leaving an object alone versus not leaving it alone. And if you leave an object alone, if it started out moving at some velocity, that velocity is going to continue. Likewise, if you leave the object alone, if it’s just sitting there, it’s going to continue to sit there. So this whole category corresponds to leaving an object alone.
So from that then we can conclude on the flip side that if it’s not left alone if something does interact with this object it is going to cause then the velocity to change. Let me add down here, by change in motion we mean that the velocity changes. We’ve come to appreciate that can mean because velocity is a vector that either the velocity vector tilts and changes its direction or stretches or compresses, changes the magnitude or the length in this delta-v is what we have defined to be or call acceleration.
So these scenarios I drew here below like the book sliding and coming to a stop, it is not left alone there is an interaction from the roughness of the table and that contact, that interaction, causes it to decelerate or slow down. There’s also a fundamental interaction that’s causing this woman to speed up: to accelerate forward. So there has to be some forward interaction that causes that forward acceleration.
And now I need to say several more things about specifically what leaving an object alone means. What qualifies as an object being left alone? Said simply if you picture an ideal scenario where you’re talking about say an object out in space, not leaving it alone means that there’s nothing touching it, no object either pushing or pulling on it. Not leaving it alone means that you’re applying what we call in physics a force to that object.
So a force in physics has a very specific definition. And I’m going to give you the criteria for that here in a minute. And you really have to guard against confusing for our class what we mean by force with the day to day usage of the word force. Force is very specific and very concrete in the context of motion and what causes motion.
Okay. So not leaving something alone, applying a force, we now know means that it causes the object’s velocity to change. That means I have acceleration. In these accelerations that you see that I have drawn at different angles and different directions these are the exact same accelerations that you’ve been learning to identify and pick out from the motion diagram for some object’s trajectory that it follows.
What I’ve summarized here for you is the verbal description of what’s called Newton’s Second Law. A force causes an object to accelerate. That force means that something is touching the object: it’s not left alone. So at the heart of the distinction between what the fundamental idea of motion is really a black and white difference between leaving an object alone, velocity doesn’t change versus not leaving it alone and causing the velocity to change.
And at the heart of it, I keep saying that fundamental heart of it, sorry. Behind it is the distinction of whether we have a force or not. And if we have that force we have acceleration. If we don’t have that force the object is left alone. We don’t have the acceleration.
But this idea of leaving an object alone and therefore there being no force on it, definitely needs some fine tuning. Because you’re probably asking yourself at this point, you know you have this picture of the boy on the skateboard and I have argued or described that as a scenario where the boy is left alone. So let me note here. But what about the boy on the skateboard? Is he really left alone? Nothing touching it as I trying to introduce you to the idea.
And of course you’re saying no he’s not. He’s moving against the ground, there’s going to be some amount of friction. Obviously there can’t be a lot because he’s still keep going like the book would if it were on a sheet of ice. But he’s not being left alone, he’s touching other things.
So let me be more specific. What criteria do you have to satisfy in order for us to conclude that an object is being left alone? And this is being left alone as it impacts the motion. What are the criteria?
I’ve got two scenarios here I want you to compare. Both of these in terms of physics qualify as being left alone. If I had my book, it was out in the middle of space, it’s away from planets, there’s no asteroid touching it. Nothing in contact, it truly is left alone, no forces on this book. Let me note that here below: no forces at all. No forces on the book, it is left alone, nothing is done to it, therefore the acceleration for this book is 0. All we can conclude from that is that there is no change in velocity, there’s no delta-v. I don’t know what the velocity is of this book right at this instant. All I know is that whatever it is be it 0 or some number moving up, down, right, or left, it’s not going to change.
In terms of the motion, no forces on this book are equivalent to the scenario I have drawn over here. Let’s say the same book is out in space, but now there are two hands that are in contact and they’re touching the book on either side, and if you were to ask these two hands how much pressure they feel, how much force they feel they’re applying to the book. They would say it is the exact same amount.
I’m going to draw with an arrow here this hand is pushing with this length to the right on this book, and this hand is pushing with the same amount of sensation in the fingers of pressure to the left. These are directed exactly opposite to each other and with equal amount.
Because, these two forces have equal amounts and are counter opposing to each other, they effectively cancel out. It’s the same effect as not putting any forces on the book at all. And so these two scenarios in terms of the motion, in terms of the physics this class, are equivalent.
So, I’m going to write here for you that both of these pictures have the same effect as far as the motion is concerned. That means that on the left I had no forces on the book, a is 0 and v is 0. The fact that I have two forces but they cancel each other out, leads me to the same consequence effectively I have no force on the book because they cancel. So a is 0, therefore delta-v is 0.
The same statements I made about this book in terms of predicting where it’s headed I can say about this one, since I don’t know anything about its velocity, just looking at it at this one snapshot. I can’t say if it’s headed up, down, right or left. I can tell you that it’s not speeding up or slowing down for both of these cases.
So, the boy on the skateboard above; there are forces on him. But he falls into this category. Whatever forces are on him I know they have to be equal in opposite cancelling each other out, because, if they don’t, he would speed up or slow down and he doesn’t, obviously. So I know from this that this really does qualify as left alone.
I’m going to put it in quotes because there are forces; there is contact between the environment and this object, the boy. But it must be that those cancel. They have competing forces that cancel each other out.
Okay. Question 7 asks if you understand what this is. So I give you three scenarios here and ask you which scenario corresponds to not left alone. Which scenario do I effectively have a resultant force on that book, a net force on that book?
Having fine-tuned what I mean by leaving an object alone, I want to go back up here earlier in the lecture and be more specific. When I said here, that not leaving it alone means that something is touching it, what that really means is that I have to not just a force or a collection of forces. I have to have a net force. If I have just two forces equal and opposite they’re balancing each other out that is the same as having no force at all.
So I’m going to add the word net here and I’m going to add the word net to this statement too. It’s a net force that causes an object to accelerate. I have no forces here at all: therefore the net force is 0. I have two forces here, but they cancel each other out. So the net force here is 0 as well, and that’s why both have 0 acceleration.