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Newton's Laws of Motion
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0:01
(host) This is a terrifying trick. Check it out. The truck accelerates fast and pulls right out from underneath this skater-- this really talented guy from Braille Skateboarding-- pretty nuts. Hey, I'm Dianna Cowern. And welcome to Lesson 4 of Dianna's Intro Physics Class, also known as AP Physics 1 Review, also known as Physics by Dianna. Today's lesson is Newton's Laws of Motion. And today's theme: May the force be with you. It's a little clumsy. May the force be with you. Ah ah wha.
0:28
[record scratches]
0:31
As someone born on Star Wars' Day, May the 4th, that saying never gets old. So the force-- pushing, pulling, what makes things accelerate. How much do they accelerate? There's this relationship between force, mass, and acceleration. And today we're going to understand that relationship quantitatively with math. So that's our lesson today. So let's get started with Newton's first law, inertia. Let's think back about that skater. This trick is really fun for a physicist to see
1:02
because it's unexpected. You kind of want the skater to accelerate with the truck, but he doesn't. Why not? Here's another confusing demo of this same idea. I have a regular balloon hanging from the ceiling, and a helium balloon taped to the ground. I'm in a Porsche which can accelerate really quickly. So which direction do you think the balloons will go? And hit it. The balloons went separate directions. I mean initially they stayed right where they were, but then they went separate ways.
1:27
So before we show how these two weird demonstrations are related and how they're explained by Newton's first law, we actually have to think about why things move. And when you think about motion, you'll quickly come across the name Isaac Newton. Back in his day, in 1600s England, they didn't have cars or trains. So the fastest thing you're going to see around town is probably a cart pulled by a horse. If you asked someone at the time, what makes the cart move?
1:50
They would probably say, "It's the horse." If you take away the horse, the cart stops moving. Like, what's wrong with you? Why would you even ask this? It's obvious. It seems obvious that moving things will stop unless you keep pushing or pulling them. But is that right? We can do something that those people in the past couldn't do. We can go to space. I mean not us, but like some people can go to space. If I'm in outer space, and I throw Olive the Otter, she just goes.
2:19
She moves and keeps on moving. Space does not have air resistance or anything providing friction. So unless she smashes into the moon, or another planet, nothing will stop the otter, and she'll keep moving forever. So we can see something more easily that people in the 17th century could not see. It's not that things in motion need forces to keep them in motion, it's the opposite. On Earth, there's always wind, or air resistance, or friction in wheels, or sliding friction,
2:49
or something, some force that's acting to slow things down. The forces act to change the motion. Absent those forces, things do keep moving, or they never move. There's this really fun party trick where you hit the top of a glass bottle with water in it, and if you hit it hard enough, the bottom of the bottle sometimes breaks out. And the reason why is that thing we just talked about. As you hit the bottle, it moves fast with the hammer. But the water stays behind and creates this area
3:17
of low pressure at the bottom. And the pressure is so low that the water turns to a gas and creates vapor bubbles that quickly collapse with such a violent shockwave, it breaks out the bottom of the glass, all because the water wanted to resist motion. So that's the first and the simplest of the three main ideas that we're going to explore today-- the idea that things keep moving until something stops them. The flip side of this idea is that things that are stopped
3:40
will stay stopped until something moves them. This property implies that anything that has mass. And the property is called inertia. It's inertia, not inershaw. [LAUGHS] Newton was the one who really refined this idea of inertia. And this idea was one of several ideas so important to our understanding of the natural world that we've come to call them laws. In fact, the concept of inertia is Newton's first law. Newton came up with three well-known laws
4:10
and wrote them down in his<i> Principia</i> , which I actually got to hold during a visit to London, which was probably the proudest moment of my physicist life. It was the original manuscript from the 1600s. Ah. Anyways. Inertia is the first of those three laws, and you might hear it stated as something like an object at rest remains at rest, and an object in motion remains in motion unless acted upon by a force. But, basically, Newton's first law is that inertia exists.
4:36
So then what's going on with that skater in the truck? Look carefully. As the truck accelerates, the skater basically stays still. There's so little friction in the wheels of the skateboard that there's very little force acting on the skater. So the truck accelerates right out from underneath while he just sits there, inertiating. And as for the balloons, well, this one is a little trickier. Because the thing that stays behind, resisting motion, is actually the air inside the car.
5:01
It stays behind and ends up getting compressed toward the back of the car which creates a high pressure. And that high pressure is enough to push the very not-dense helium balloon forward, just like helium balloons will rise into the air where the pressure is lower. OK, great. That's Newton's first law. Maybe I should start writing these down.
5:23
Whoo hoo. All right, Newton's first law--inertia exists.
5:30
But what can force something to change its motion? Well, muscles, cars with engines, gravity that can pull, all these things exert pushes or pulls to accelerate us. And we call these pushes or pulls forces. Funny forces are what force us to change our motion. Who would have thought? When I change your velocity, I accelerate you. Here's a subtle but important distinction. In a lot of situations, accelerating means speeding you up or slowing you down.
5:54
But it could also mean changing the direction of your velocity. Say you're turning left in a car. The road pushes the wheels sideways, but you stay going 30 meters per second. That change in the direction of your velocity counts as an acceleration. That's an idea we're going to explore more in a later lesson when we get to circular motion. Hmm, an orbit. Hmm. OK, so you push something like a cow. We'll make it a square cow for simplicity. I actually have a square cow; look how cute it is.
6:22
How much will the cow speed up? Well, it depends on how hard I push it, right? The force, duh. But it's also going to depend on the mass. That makes sense, right? The more mass of an object is the harder I have to push it to get it to accelerate. And this all brings us to Newton's second law-- an object's mass is the ratio between the force you apply to an object and the acceleration the object will experience. And this is directly related to our first idea of inertia.
6:50
Mass, whether it's the mass of a person, a skater, a cow-- it's the measure of the inertia of an object. It tells you how hard you need to push it in order to accelerate it. Bring the a up, and boom, f equals m a. That is Newton's second law. This is probably the most fundamental and important idea in all of physics. This is the big momma. F equals ma is to physics as the Force is to Jedi. Given a force and a mass, I can tell you the acceleration that you'll experience.
7:21
Measure the force on an object and the acceleration it undergoes, and I can tell you its mass. Start with f equals ma, add 400 years of people doing physics, and I can send a rocket to Mars. <i> (Reporter) Atlas 5 with Curiosity;</i> <i> seeking clues to the planetary puzzle about life on Mars.</i> Wow. But almost as important as f equals ma is the units of force. So the unit of mass is kilograms. The unit of acceleration is meters per second squared.
7:50
So the unit of force is kilograms times meters per second squared. It's a mouthful. So we give it a name. The units of force are called newtons, as an Isaac Newtons, and it's abbreviated as capital N. Discover something big in physics, and you might get a unit named after you. So let's play with our new tool: F equals ma. Let's push our square cow around. Maybe it has a mass of five kilograms. It's a baby cow. We push this baby cow with a force of 10 newtons. What will its acceleration be?
8:21
We'll write down F equals ma, solve for a. A equals F over m. My F was 10, my m was 5. So that equals 10 newtons over 5 kilograms. So my acceleration equals 2 meters per second squared. Ta da. Double the force, and you double the acceleration. If you represent this graphically, you get a really cool way to visualize Newton's second law. So I'm graphing F versus a, and I get this line. What's the slope of this line? The slope of this graph is an object's mass. That's really cool. Fantastic.
9:01
Now we've got the first two of Newton's laws. Newton's first law-- inertia exists. His second law gives us a way to measure it. What can we do with them? I want to pause for a second and go off in a little bit of a tangent related to gravity, but it's an exciting tangent. We never talked about why the force of gravity-- Fg equals mg-- we never talked about why the force of gravity is m times g even though we've already used it a bunch. But now with F equals ma, we can think about why.
9:27
In the case of gravity, a is g. That's the 9.81 meters per second squared, the gravitational acceleration due to the size and the density of earth. And the crazy thing is that any object I drop near Earth's surface will fall with the exact same acceleration if we ignore air resistance. You might have seen that viral video where a bowling ball and a feather fell at exactly the same rate inside of a vacuum. This is why. It's so counter- intuitive though. Heavier objects should fall faster, right?
9:56
So my force of gravity, if I replace g for a, is m times g. And, yes, if you double the mass, then you do double the force. But two doublings end up canceling. And you end up with the same acceleration. Now we can think about a problem with gravity. For example, what force does gravity exert on a tiny cow with mass 1 kilogram? Well, F equals ma, F equals 1 kilogram times 9.81, about 10 meters per second squared. And the force of Earth's gravity on our cow is about 10 newtons. Ta da.
10:37
Gravity isn't the only force though. Let's hoist our cow up into the air with a rope, and look at the forces on it. We're going to do it safely and humanely, of course. Why? Because our cow is afraid of stairs. So now that cow is hanging there from a rope attached to the roof. My cow is not moving even though we know that there's a downward force acting on it from gravity. Its acceleration is zero. But wait, what? F equals ma. Gravity didn't just turn off. So F isn't zero.
11:06
And the mass didn't change. So how can a be zero? Well, if there's a downward force of 10 newtons, which we just calculated, then there must be an upward force of 10 newtons balancing it out. Where did that force come from? Well, it comes from the rope pulling up on the cow's weight. The force is called tension. Now we have a new force. My upward tension force, and my downward gravitational force balance out for a net force of 0. And F equals ma makes total sense again--
11:35
no force, no acceleration. And we have a new concept to think about. When you have an acceleration of zero, your net forces must be zero. And it's important to remember, it's not always a single force acting on an object. There can be multiple forces, and they can be fighting each other, canceling out, they might be working together, adding up. But the fun of F equals ma is thinking carefully through all of the forces to figure out their net effect. For example, there's this weird substance
12:01
called pharaoh fluid which is essentially tiny, tiny, tiny iron particles suspended in oil that altogether make up a magnetic liquid that looks like it came straight off an alien spaceship. It looks so weird. And if you wanted to predict how it behaves, you would have to add up the forces on it from gravity, any magnets nearby, from the fluid forces between the trillions of molecules. And it gets quite complicated. We will stick with smaller systems. So let's play some more.
12:28
Let's do a super common problem from physics to see how you sum up forces. Let's keep the same one kilogram cow hanging from a rope and now hang another cow underneath it. Whoa ho ho. Second cow is slightly heavier, 2 kilograms. So now let's think through the forces. F equals ma, a force from gravity on my second cow, m is 2 kilograms, times a is about 10. A is about 10 meters per second squared. So gravity is pulling down on the bottom cow with a force of 20 newtons.
12:57
But if that bottom cow is not accelerating, which it's not, that means the rope between the two cows must have a force pulling up with 20 newtons and down on the top cow with this same 20 newtons. Now we have something interesting. Because the top cow is now experiencing a downward force of 20 newtons from the rope, but it's also still feeling the same gravitational force that it had earlier. Gravity hasn't turned off on the top cow. So the force downward from gravity is still 10 newtons.
13:27
Now we're on this top cow is 30 newtons, but it still has zero acceleration. Which means that there must be a force upward on the top cow that's the same 30 newtons. And you can figure all of this out with F equals ma. Fantastic. We really understand Newton's laws now. But Newton didn't stop there. Oh no. There is a third law. Check it out. This is a soda can being ripped apart by an electromagnet. The basic idea is that a bunch of electricity is flowing around the can and turns the can
13:55
into a temporary magnet so strong that the sides can push against each other. And they push each other so hard that they rip the can apart. But since they don't have anything else to push off of, they push each other with an equal and opposite force. And they fly apart in opposite directions. So cool. OK, goodbye cows. Although actually, I'm still going to need a cow for this part. Imagine that my cow is skating on ice. So there's very little friction. And I push my cow.
14:24
Now imagine it just goes. The cow would accelerate. She would speed up. So there is necessarily a force acting on her from my hand. Can we measure the force? Sure. If I put a spring scale like this one between my hand and the cow, I can actually measure that force. Spring scales like this one or like the scales that you step on are really just measuring forces. They are calibrated to some weird unit called pounds, or in this case, they're calibrated to ounces. My cow is 1.905 ounces.
14:56
If we've calibrated the scale to give measurements in newtons, then we can read off how much force there is in SI unit. I don't think we've actually mentioned yet what SI units are. It's the international system of units, the modern form of the metric system which is the meters, kilograms, seconds, newtons, and everything that we've been using so far. The system that nearly every physics class you'll ever take will use. OK, back to this scale. So I was measuring the force by putting a scale
15:22
between my hand and the cow. Now what happens if we take the exact same situation, and we flip the scale around? Is the number going to change as I push the cow? Well, it's the same scale, same cow, same hand. It's the same acceleration. So the answer is no. The force that we're reading off the scale is going to be the exact same number. That's interesting. Because when we orient the scale one way, we're thinking about the force of my hand pushing on the cow.
15:47
But when we orient the scale the other way, we're thinking of the force of the cow pushing on my hand. And that is Newton's third big idea, Newton's third law. You might have heard this stated like for every force there is an equal and opposite force. Basically, if you push on something-- if I push on the cow, it pushes back. That is Newton's third law. And even if you're not exploding cans, you experience Newton's third law every moment of your life.
16:13
Unless you're watching this video from the ISS, you're probably sitting or standing right now on Earth. So your body is pushing down on the ground with the same amount of force that the ground is pushing up on you, it's an equal force. If it was pushing back with less force, you would fall through the Earth. And if it was pushing back with more force then you'd be accelerating upwards, which you're not, presumably. So clearly at the interface between you and Earth,
16:37
the forces are equal, opposite, and balanced. It's not always super obvious that the earth is pushing you. But check out this clip of Rodney Mullen doing an ollie. You can see the ground is pushing the skateboard because there's nothing else that could push the skateboard up and accelerate it off the ground. Where else do we see Newton's third law? Let's do a problem. This next problem is a really important one to work because it comes up a lot in physics.
17:00
And you have to be able to break down and think about net forces on objects. So that's what we're good going to do. I need another cow, please. So net forces and objects. Like two square cows on a table. Imagine, again, that they're on ice skates, and we can ignore friction. This cow here has a mass of 4 kilograms, and this other little one has a mass of 2 kilograms. Now if I pull on one cow, they aren't attached. So they come apart. But if I push it, it'll push the other one.
17:28
So I'm essentially pushing both cows. I'll draw that. This is cow 1, this is cow 2. The total mass I'm pushing is six kilograms. And if I push with a force of 12 Newtons, F equals ma, so F is 12. My m is my total mass, 6 kilograms. So my a has to be 2 in order to get 12. So 2 meters per second squared. That's my acceleration. We were able to just figure out what the acceleration was. It's 2 meters per second squared. So what other questions can we ask?
18:00
How about with what force is the first cow, cow 1, pushing on cow 2? Of 1 on 2. We've already found that the two cows are accelerating together at 2 meters per second squared. We've got F equals ma. So I know my acceleration is 2 meters per second squared. And we know the mass of cow 2. It's 2 kilograms. So from cow 2's mass and acceleration, we can find the force on it is 4 newtons. So F of 1 on 2 is 4 newtons. So cow 1 is pushing on cow 2 with a force of 4 newtons.
18:31
Notice that we wrote a little subscript on the F 1,2, means 1 is pushing on 2. So now it's time for Newton's third law. If cow 1 is pushing on cow 2 with a force of 4 newtons, then cow 2 must be pushing back on cow 1 with 4 newtons as well. So my F2, 1 is the same 4 newtons. So now let's think about all the forces on cow 1. Remember how I'm pushing on cow 1 with a force of 12 Newtons? To the right, and I've got that other force from cow 2 pushing left with 4 newtons in the opposite direction.
19:06
So the net force on cow 1 is 8 newtons. Net force on 1, ta da. Now we know the mass of cow 1 is 4 kilograms. So if we apply F equals ma, so we apply F equals ma on cow 1 alone, we've got 8 newtons equals 4 kilograms times acceleration. And we solve to find the acceleration is 2 meters per second squared. We already knew that, though, from our earlier calculation with the total force and the total mass of the two cows together. But it's super cool that we can circle around and use
19:39
Newton's second law and then using Newton's third law and then use Newton's second law again to get the same answer. These problems are fairly simple. But they're also deep because there's a lot of physics going on here. And when he master this way of thinking, the complicated and harder problems will become much more straightforward. That's it. Whoo. That is today's lesson on forces and Newton's laws of motion. And when they ask you what you learned on YouTube today,
20:05
here are your key takeaways, also known as the laws of motion. Number one, inertia exists. Objects tend to stay still if they're still and keep moving if they're moving. Number two, to change an object's motion-- in other words, to accelerate it, you need to apply a force. Force equals mass times acceleration. F equals ma. And number three, when you hit something, it hits back. And because you can only really learn physics by doing the problems, here, again,
20:36
are all the problems we did in the lesson. And you should definitely go work them again at home.
20:56
And, finally, here's a crazy extra little bit of physics that you definitely don't need to know but is way cool. And it's the idea that gravity might actually sometimes push and not always pull. What? Physicists have theorized and are still looking for evidence of situations where gravity is actually repulsive. It pushes things apart rather than pulling them together. These situations would be extreme, extreme cosmic scales between galaxies and galaxy clusters,
21:23
or in extreme conditions like the very, very early universe, right after the Big Bang, when there was a period of crazy expansion. If you stick with physics and eventually take a class in something like cosmology, you get to learn this type of crazy physics. And with that, may the forces be with you. And here is a message for you from a special guest. Hey there. My name's Moiya McTier, and I'm an astrophysicist who studies the motion of the Milky Way Galaxy.
21:48
And I am so pumped for you that you're taking this physics class right now because I didn't find astrophysics until I was a sophomore in college. So I know firsthand that there's no one right time to start studying science. I really hope you enjoy your classes. I wish you the best of luck, and take care.
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