https://youtu.be/61DYxqvyyUA
PHYS 1101: Lecture Thirteen, Part Three
So Newton’s third law defines that for us, the nature of this interaction between objects.
Here’s one statement or one way of summarizing Newton’s third law, “Whenever one body exerts a force on a second body, that second body exerts and oppositely directed force of equal magnitude on the first.”
We’re going to look at what this means in a couple of different scenarios, but one point to make and I’ll emphasize it again is, that every force that’s on an object has a third law pair, so to speak. There is an action reaction force, as it’s often called, that corresponds to every force on a single object.
Let’s look at some scenarios and exercise our thinking about the implications of this statement and what it means. Let’s go back to our simple scenario of a book sitting on a table and let’s do that one level of complication where I have this force from the hand that’s also pushing down on the book. Focused just on the book, what forces do I have? There’s the force of gravity on the book.
Going around the book then I have… let’s start here, I guess, at the right-hand side again, on the top surface there’s contact with the hand. That hand is pushing down. I’m going to call that Force hand.
Continuing around I run into another spot on the book’s surface, this object’s surface where I’m in contact with something, that’s the table. The table surface is pushing up. Again, surfaces always push away. I’m going to call that Fn, our normal force. The size of the normal force roughly balances these two. That’s a good visual check confirming that the acceleration for this book it zero.
So with my focus on a single object and all of the forces on it, every one of those forces has a third law pair. Let’s go through a couple of them and exercise where this action-reaction force pair is or what’s the nature of it. Let’s focus first here on the normal force.
Let me, in fact, slide this force down and put its tail at the surface below the book just to remind us where that force originates, and that’ll help us remember what’s causing that force. This normal force, remember, was the force that the bottom of this book feels from the table, the push up from the table. Okay, every force that’s on this object has a third law pair. It has an action-reaction pair.
Here’s a helpful way, I think, to get at the heart of each pair and identify this equal and opposite force. First of all, isolate one of these forces that you’re going to consider, so one at a time ask yourself, for example, “What’s the third law pair to this force?” Go to the source of contact, where that force originates, mentally picture sliding your hand at that point of contact or between that point of contact.
So imagine your hand is from, it’s between the book and the table. With your hand slid in there you probably can imagine that you’re going to feel pressure on both sides of your hand. On the bottom of your hand you’re feeling the table pushing up, you’re actually feeling this normal force that the table if providing to support the book up. But then on the other side of your hand, on the top part of your hand you’re feeling pressure and you’re feeling a push down.
That force that you’re feeling effectively is what the table feels when your hand is gone. Your table feels that force pushing down. That is the action-reaction pair to the normal force. You can go through that argument with every force on this object to find its pair.
Here’s a rule of thumb. Take this force that you’re interested in, such as the normal force, write it out more explicitly. This normal force, what causes it? This is the force of the table on the book. The agent that’s causing this force on the book is the table, it’s an inanimate agent. It’s this agent that’s experiencing the action-reaction pair. Meaning if you flipped your perspective and now focused on the table as the object, one of the forces on the table would be the force of the book on the table. So literally make that switch in your notation and then read it out loud and see what it says.
After you’ve explicitly written out, this is the force that you’re asking, what’s the third law pair to, write it out, “This is the force that the table puts on the book.” Then switch the order of these two. That force will be the action-reaction pair to this one, meaning, I’m going to write now, “This is the force of the book on the table.”
So if I go back to my picture and now I’m going to go make a copy of the table. We move it off to the side here. And the idea is with this object, with this now being the object what are the forces on this? Well, one of those forces is going to be the force that the table feels pushing down. This is the force of the book on the table. That is the action reaction pair to the force of the table on the book.
If you write it out explicitly like that I think it’s easier to indentify, you just are switching the order of this. This action-reaction pair, this third law pair is what Newton is asserting is always the same magnitude, the length of these arrows should be the same, but opposite direction. The book feels the table pushing up from its perspective. The table feels the book pushing down. The same number of apples of force pushing down is the same number of newtons pushing up.
The next quiz question has to do with finding the action-reaction pair to this force. This is the force of the hand on the book. Follow those steps and in the text box provided describe the nature of this force. Well if I switch the order of these things I know the agent causing this I need to focus on now as the object. What’s the agent causing this? Well, it’s the hand, so you’re going to want to think about the hand as an object and what are the forces on the hand. That’s question nine for you.
Question ten follows that through and asks, what’s the third law pair to the very last force on our book? That force it the weight, the force due to gravity, the force that’s caused by the gravitational pull of the Earth. For six points, in the text box provided, describe the action-reaction pair to this force. What’s the agent causing this force? That agent, now considered as an object, is experiencing the third law pair to this, the same magnitude, opposite direction.
Okay, here’s a safety tip for Newton’s third law. This is a very common mistake that people make. How I describe avoiding this in words is shown here. That Newton’s third law pair, the action-reaction pair, those two forces are never two forces on the same object.
Here’s the common mistake that people will make. They’ll go to a single object, like this book, and they’ll sketch in, I’m going to sketch it up here, my force due to gravity and then pointing at the point of contact here is the force that’s the table on the book. It’s very common for these two to be identified as the action-reaction pair, because these two are the forces that are balancing to cause the acceleration for this object to be zero.
That’s not what Netwon’s third law says. That’s the second law that you’re invoking there. The third law tells you how one of these forces compares to its companion force, which is on the object responsible for this force.
From the table what all forces do I have? There’s a force representing the downward push from the book. This is the force of the book on table. I know there is the force due to gravity on the table. Then the ground is pushing up and I’m going to explicitly write that one out, “This is the force of the ground on the table.”
The action-reaction pair here, Newton’s third law pair, is this force and this force. They’re forces on different objects, it’s at the contact between these two objects. It’s the force that Object B puts on Object A versus the force that Object A put’s on Object B. Many people want to identify this as the third law pair. No. Don’t do it. It’s not the case. That’s the third law pair.
But, now let’s thing through a couple of scenarios of what it means to assert that these two forces are always the same magnitude, opposite direction, always. This is true if the table and the book together were moving to the right at a constant velocity, or moving up, or down, even if they are accelerating. The force between these two objects is always equal magnitude, opposite direction. That can be counterintuitive at times.
Try your hand at this quiz question. This is a classic example of a scenario that confuses people or their included to think that this is an exception to Newton’s third law. You’ve got a mosquito flying along and collides head on with a car traveling 60 miles per hour. How do the size of the forces that the mosquito exerts on the car and the car exerts on the mosquito, how do they compare?
Newton’s third law is always true. Your eye is definitely drawn to the fact that the mosquito walks away from that collision with a much more catastrophic result than the car, but what your eye is drawn to is the acceleration. The mosquito has a very different acceleration than the car. They both experience the same force, but that force exerted on a mosquito with a very small m leads to a very large acceleration. The poor little body of the mosquito can’t hold up to that kind of acceleration.
The car on the other hand experiences the same force, but that force when you take the mass of the car into account leads to really a negligible acceleration. It’s the acceleration that your eye is primarily drawn to.
It’s often in collisions or, well, I’ll call it abrupt events, like our last homework assignment where the father and the daughter were pushing off of each other, where your eye is drawn to the acceleration and the tendency is to infer that tells you the size of the forces, but that’s not the case. The mass of those two objects makes all the difference in the world. Newton is right, the forces are always the same between these objects. The mass leads to, though, very different accelerations.
Here’s a thought experiment for you to flesh that out some more, that has two scenarios for you to consider. First, imagine a bowling ball is sitting on the ground and you drop a ping pong ball on to the bowling ball. We can all picture what would happen.
During that collision that contact, the action-reaction pair, is indeed equal and opposite between the ping pong ball and the bowling ball. What the ping pong ball feels from the bowling ball is the same, opposite direction, to in turn what the bowling ball feels from the ping pong ball.
If you were to switch it around though and you were to drop the bowling ball onto the ping pong ball we all know the result would be much different. Reconcile this with yourself.
Question 12 is, for five points, has Newton third law pair been violated? Then justify your answer. Notice the weight here. I’m going to read over your answer and I will give you ten points only if your answer makes sense, if you have effectively argued your case, your answer for Number 12.
Think about what is different between the two cases. Something is different. Include that as you justify your answer. Include a discussion about what’s different between the two cases.