https://youtu.be/V_9jvFmyj3A
PHYS 1101: Lecture Ten, Part Five
So here are my criteria that I want you to continue to go back to as you try to fine tune your identification of forces on objects because to get the motion correct, understand it properly, you have to be able to identify, and you have to know what all the forces are on an object. Every single force has to be a push or a pull on that object. And it’s always a single object that we’re going to focus on at a time. That push or pull on that object always is going to occur at a very specific contact point on that object.
It will be because some agent, a person, a table, something that’s touching that object is making contact at that point. It doesn’t matter how light that contact is or how strong, there’s a force there. The size of the force depends on how light that touch is or how strong it is. But any contact, you’ve got a force. Force, as you can appreciate from this definition, I think, has both a value and a direction that are important. It’s a vector.
Mathematically, that’s how we’re going to have to treat it. The second bullet down here emphasizes what I pointed out before is that for every force, there’s always an agent or something that’s directly responsible for that force. If you ask yourself, every force that you’re wanting to draw on an object, what the agent is, it can help you catch yourself making a mistake of improperly identifying a force. That agent, it can be animate or inanimate.
My laptop is sitting on this table, and from the laptop’s perspective, it feels it’s in contact with the table. That table is exerting a real force on the bottom of that laptop. If I were to pick up and hold my laptop, I would feel the contact with that laptop so that laptop would be experiencing the same force of support from my hand as it did from the table.
So that’s a case where I have the same force, but you’re seeing it could be due to something animate, like me, or inanimate, like the table. We’re going to work with forces in a lot of our equations. We want to be sure we understand what the equation is, and I’m going to get to that in a minute. Here I want to remind you, or point out that a force is always in units of a Newton. That’s the SI unit for force. And one Newton is equivalent to one kilogram times a meter per second squared.
To give you some physical intuition of what one Newton means, if you were to put a small apple in your hand, your hand would have the sensation of a gentle, downward push from the weight of that apple. The size of that push, that’s about one Newton. So we get to problems, and it says there’s a hundred Newton force on something, you can picture a hundred apples. What does that feel like? That’s what that object is experiencing.
Okay, question eight for your quiz. Let’s see if you can put this together. I show you different motion diagrams, and I want to ask which of these objects is experiencing a net force? And what I’ve argued above is that if I have a net force, that means I have to have a change in velocity. Which of those motion diagrams satisfies that criteria? Which of them is showing acceleration?
Question nine asks you the same thing, but now in the context of a mixture of one-dimensional motion versus trajectories, curved motion, curved paths in two dimensions. Which of these motion diagrams similarly represents a net force? Again, the net force means I have real delta v velocity vectors, which we know means I have acceleration because the definition of acceleration is this delta v vector, the change in the velocity vector divided by time.
I have another question for you to get you to look at it in a slightly different way. Again, it’s just putting pieces together that you know from previous work and applying it to what I’m teaching you now.
Question 10. This motion diagram below shows you that definitely the velocity is changing. This object goes from one to two to three to four, etc. You see the time sequence. What arrow best represents the direction of the net force on the object at instant three?
From net force, I hope you’re making the connection that you need to then be thinking about or asking what’s the acceleration, or what’s the delta v? Where? At instant three. At instant three, what’s the change in velocity? Here’s my summary for you of identifying forces. The first comment I’m going to make is that every single force in this class… This class deals… It’s mechanics. It deals with the motion of day-to-day objects.
Every force, it has to be a contact force. Something is directly touching this object. Pulling on it or pushing on it. There’s only one exception, and that’s the force due to gravity. And we’re going to use w, where the w represents the weight of the object to represent that force. Gravity, with a handful of other forces, is what’s called a long-range force. Meaning, there doesn’t have to be direct contact for this force to exist.
Another example of a long-range force is the magnetic force. If you take two magnets… I’m sure you’ve all experienced this. If you put opposite poles together, they don’t have to be touching for you to feel that there’s a pull between the two. If you change the orientation, and you try to push two poles together that are the same, you’ll feel this push away from each other. Magnetism is another long-range force.
You’ll deal with that in 1102. In 1101, we only have one long-range force, gravity, and it’s somewhat counter-intuitive because none of us have the experience of not experiencing the force of gravity. It’s always there. It’s on every object that we see. It’s on us all the time. So aside from gravity, you just have to then identify the rest of the forces on the object. And all of them have to be from something that’s really in contact with that object.
The gravity force, a few more bullets here point out, the size and the direction, the two questions we have to ask about every vector. How big is it? The magnitude will be the mass of this object times 9.8 meters per second squared. And the direction? The force due to gravity is always straight down. It’s actually pointing straight to the center of the Earth, and from all of our perspective, that just means straight down.
So here are your steps for identifying forces. Use red. Use a specific color pencil, if you’d like, to really hone in on and identify the single object that you’re working with for your problem. Immediately draw a blue arrow down and label it w to represent the force due to gravity. Next, imagine drawing a circle around this object.
Let’s give ourselves an object here so I can illustrate. Here’s my object. It’s some person that’s described in some problem. I’m immediately going to go draw my force due to gravity on that object and label it. Then by step two, I’m saying, “Imagine a hypothetical circle around this object.” Let’s say that in reality this object, we are told, is standing on the ground and maybe is pulling on a rope.
With this imaginary circle that you’ve drawn, start somewhere. Start here at 3 o’clock. Go around clockwise if you want, and be very rigorous as you go around. Any surface that breaks this circle and is making contact with that object, there’s a force at that point. There’s contact there.
So on the ground, we’re going to learn that the ground in truth pushes up on the object. And then, once we’ve got the ground considered, I’m going to keep going around. Nothing’s breaking the circle here. Nothing. Nothing. There’s a rope that’s breaking the circle. That rope is in contact with this person. So I’m going to add another force to represent the tension in that rope.
What these forces, what direction, how big they would be, that’s what we’re going to continue to work on as we go through the next three lectures. What’s critical is that you have to be rigorous to get all forces. If you don’t get them all, then Newton’s second law will let you down. The mathematics won’t properly predict what the acceleration is because it has to be the result of all the forces on some object that lead to some net force or don’t, which then sets the acceleration, which then sets the trajectory for this object.
If we were in a classroom, and I were lecturing to you live, I would at this point show you a real demonstration of shooting a ball straight up into the air. For an online class, the best I can do is show you this animation. So pretend this is a cannon. There’s a spring under here that gives an initial kick to this ball and shoots it straight up into the air. So pretend you’re watching this in real time.
As you watch that movie, I’m going to ask you quiz question number 11. Now if you want, focus on the upward part of this motion. When that ball is on its way up, what list best describes the forces that are acting on it? This is very important question as suggested by the point value that I’m going to give it. I’ll give you eight points if you get this one right.
When that ball is on its way up, choice A is there a force of gravity and the force of this plunger or spring on the ball? Is there B, just the force of gravity? Or C, just the force of the plunger? To answer that question, take the time, and go back, and follow these steps. Follow this advice to help guide you to be sure that your first, intuitive feeling for that question is right. Now, I’ve given you a physical intuition, or I hope I have, for what Newton’s laws, his first and his second law, are.