(host) Inside this box, I have an egg. And the box is completely closed, so I also have an LED inside so you can see what's going on. As I filmed with the GoPro I have taped inside the box, I'm going to do something to the box. Watch closely what happens.

(Describer) The egg floats, then hits one side and breaks.

Can you guess what I did? Hey, everyone. I'm Dianna. And welcome to Lesson 5 of Dianna's Intro Physics class, also known as AP Physics 1 Review, also known as Physics by Dianna. Today's lesson-- Free Body Diagrams. That's the new tool we're going to introduce today. And my friends, buckle up, because free body diagrams are going to allow us to measure g, the acceleration from gravity on Earth--that gorgeous, delicious 9.81 meters per second squared. We're going to measure it. Here's a teaser on how we're going to measure g. I have strapped myself into a death-defying contraption. It's called an Atwood machine. Once I trigger the release, this machine is designed to let me fall, but very slowly. This is going to allow us to measure the acceleration of gravity near Earth's surface precisely, which is really cool. So today's theme-- Gravitational Field Trip. It's funny, because we're taking a trip in a gravitational field. Gravitational field trip--do you get it? So we want to measure gravity. What is gravity? It's a force--it's actually called a fundamental force. I want to go off on a fun little tangent.

(Describer) She gets paper and misses a thrown marker.

That one was not my fault.

(Describer) She catches the next try.

Gravity is actually called a fundamental force. Are there other forces besides gravity? Yes. There are three more. I know you know one of them-- it's the electromagnetic force. It's the one that makes magnets stick together or push apart.

(Describer) She catches two white balls.

Yeah, these are little magnets in here that stick together. And, strangely, the electromagnetic force is the same force that makes balloons stick to your hair with static electricity. And there are two more forces: the weak nuclear force-- no one remembers that one-- and the strong nuclear force. And you can Google them. That's it. These are the four fundamental forces. There might be more. We don't have any evidence for them, but our known laws of physics don't rule them out. So is gravity the strongest force? Check it out. I can use a magnet the size of a pea-- it's smaller than the size of a pea in here-- to pick up a nail. So this tiny little thing can overcome an entire Earth's worth of gravity. Proportional to mass, gravity is actually a really weak force. There's just a lot of it. But puny as it is, it's still pretty important. And that's the force that we're measuring today. Up until now, we've just accepted that things falling near the Earth accelerate at 9.81 meters per second, squared, which I usually round to 10. But we're going to confirm that number with our experiment on the Atwood machine soon. But first we're going to need a new mathematical modeling tool.

(Describer) She drops the balls.

It's called the free body diagram. A free body diagram is a simple picture that represents all of the forces acting on an object, like a cow. It's a funny phrase, free body diagram. But the word "body" is a physics term for object. And it's free, which doesn't mean it's free like a bird in the sky. Free means we're looking at the cow alone. It may be connected to other cows

(Describer) She holds her square cows.

experiencing forces from the other cows, but we're isolating it. And we're drawing only the forces on that cow-- not physically, but with our math. So how do you make a free body diagram? Let's draw one for a falling bottle of nail polish. I dropped a bottle of black nail polish on the floor once-- it was bad. We're going to ignore air resistance for now. And we're going to ignore these cows. So for a body falling near the Earth, like nail polish, gravity is the only force. I'm going to model it as a point particle, because we do that.

(Describer) She draws a point and arrow.

So that's F sub g. I'm going to represent that on my diagram with this arrow to remind me that it's a vector with a direction.

(Describer) Down.

And we know that the force is mass times g. That's it. That's my free body diagram. It's not complicated. We can make free body diagrams for projectile motion problems, too, from lesson 3. So neglecting air resistance, here is a soccer ball flying on its parabolic path right here. How would I draw the free body diagram? Gravity is causing a force downward. Here's my soccer ball. I'm drawing it isolated. Here's my force of gravity, F sub g. Are there other forces? You might be tempted to draw a push from the kicker. But no, I say--don't do that. When the soccer ball player's foot is in contact with the ball, there's a huge force accelerating it. But we're drawing the ball after it has left the foot, which means that force is gone. So neglecting air resistance, the free body diagram of an object in projectile motion looks like this. Look familiar? It looks just like the free body diagram of an object falling straight down, which makes perfect sense, because you remember when we looked at projectile motion, the key idea was to separate out left-and-right motion from up and down. And in projectile motion, there are no forces acting left and right. So the only force is down. So the free body diagram of a cow falling and a cow launched in projectile motion are the same. A lot of people get that wrong. So we've been neglecting air resistance for now, but let's think about it for a hot second. In physics, it's good to consider what you're ignoring before you ignore it, and if it's a good reason to ignore it. Air resistance is a force created by air pushing against a moving object. So when you stick your hand out of a moving window, for instance, that is air resistance. It's not wind, because you feel it even if the wind is not blowing. And when the car stops, you stop feeling air resistance. Air resistance clearly changes, depending on your speed. And it always works against your motion. You can start to tease out this relationship with speed when you think about how air resistance slows down a skydiver in a parachute to land softly. So let's make it David Blaine. Let's draw his free body diagram. This is the best stick figure I've drawn so far. There's gravity downwards, proportional to his mass-- Fg equals mg. And what about the force of air resistance? At the top of the flight, he's not moving. Just like in the stopped car, he isn't feeling any air resistance. But as he falls faster, the air resistance increases and it's going to be the opposite of his downward motion. So it's going to be like this--

(Describer) An arrow going up. She writes F sub air.

F of air. But it can't be too big or else the sum of the forces-- like if it was up here-- would be up and he would shoot out of the atmosphere, which would mean that David Blaine would eventually bounce off the air and land on the moon, which I wouldn't put past him. That's clearly not what happens when you're skydiving. So the force of air resistance must eventually hit a limit where it balances the force of gravity down. So these should be equal in length. So the sum of the forces, which are equal and opposite-- sum of the forces, F air minus Fg-- are 0. And actually, I'm going to make this plus because we're summing the forces. So how these are going to cancel out to be 0 is that this is going to be negative.

(Describer) MG.

Either we could have written a minus in front of here or we could say that g is negative. You always want one of them to be positive, one of them to be negative. That's important to keep track of. So just to be clear, he's still moving. He's just not accelerating. He's falling at a constant velocity known as terminal velocity. Here's a cool, weird thing that air does. It curves the path of balls that are rotating. It's called the Magnus effect, which is when the trajectory of a spinning spherical object curves because of air pushing on it. It's why you can bend a soccer ball when you put some spin on it. And if it's really smooth, it bends the opposite way--crazy. But for the most part, we're going to ignore air resistance, though, because it's complicated. If you want more of a taste, the equations look something like this. OK, no more tricky fluid dynamics for now. Let's take a look at the egg in the box. Did you figure out what I did? Check it out--I can make the weight on a scale go up or I can make it go down by seemingly doing nothing. It's magic--or just sufficiently advanced physics. How is it that when I drop the scale of it, the weight goes down and then up and then goes back to normal? Let's take a look. Let's scale it up. Let's think about a person weighing themselves on a scale, seeing how swole she's gotten. Let's draw her free body diagram. So what we're going to do here is we're going to look at the free body diagrams of a person on a scale when she's just standing there and then when she's moving in an elevator at a constant velocity, and then when she's accelerating, and see how they differ. So let's start with the first one, where she's not moving. So what are the forces on her? There's the force downward, from gravity.

(Describer) Arrow down.

But she's not accelerating, so the scale on the floor must be pushing back on her. So that's upwards.

(Describer) Arrow up, f sub s.

My scale force. And these two forces must be equal and opposite. So my magnitudes are equal. And of course, Newton's third law-- if the scale is pushing up on her, then she is pushing down on the scale. There are little springs in the scale getting compressed by that force. And then the dial, or the numbers, which are connected to those springs, shows the reading of that force. It's measuring the weight pressing down on the scale. Here's an interesting story. When we did the zero-g plane-- I know I talk about it all the time-- they actually simulate Earth and Mars gravity by doing specific types of parabolas. And you can feel what it feels like to be on Mars or on Earth. And you fall a whole lot slower. That's true, they actually do it. So the scale is measuring your weight, but technically speaking, the scale measures the force compressing the springs, which means you can fool the scale about an object's true weight. So we're a little closer to seeing what I did with the eggs. Let's put our weight lifter on the scale on the Taipei 101 in Taiwan, which is the 509.2-meter-high tower and the second tallest building in the world. Tallest building gets too much attention. The elevator is being pulled up by a big cable at a constant speed. So does a scale say that she weighs more? Free body diagram. What are the forces on her? So here she is in the box, because we're free bodying her, we're isolating her. So there's gravity down, Fg, which is the same-- mg. And then the elevator floor also pushes up on the scale and the scale pushes up on her. But--and this is the key idea-- she's moving at a constant speed.

(Describer) V.

So the acceleration is 0, which means F equals ma; ma is 0. So then the sum of my forces is 0, which means that the force that she is exerting on the scale is exactly the same as when she was standing on the scale in the gym. It's weird, but it's true. But say that I'm in the elevator. And it starts to accelerate upward at 2 meters per second, squared, from stopped. What will the scale read now? Free body diagram. Gravity is the same-- Ft--but now we have some numbers. It's mass times g, so 58 kilograms times 10 meters per second, squared. So my Fg equals 580 newtons. There's still the force from the floor keeping me from falling through the floor. So that's Fs, because actually from a scale,

(Describer) Up.

which is the same as 580 newtons. But there's this extra little force from the elevator, accelerating me upwards. So the sum of my forces equals ma, which equals my Fs plus Fg. My mass is 50 kilograms, my acceleration is 2 meters per second, squared, which I gave you at the beginning. And that equals Fs minus my Fg, 580 newtons; 58 times 2 is 116, so 160 Newtons equals Fs minus 580 newtons. So Fs equals, then, 160 Newtons plus 580. Fs equals 696 newtons-- beautiful. But without acceleration, the scale would have read 580 newtons. And Newton's third law tells us that I am pushing them back on the scale with the same little extra force. So I'm pushing back on the scale with 696 newtons. Another way to think about this is that the spring in the scale is being compressed up into me more, so the dial says that I gained more weight. Because if I weren't accelerating, the scale would just read this same Fg-- 580 newtons. Now, I don't actually become more massive. The force of gravity hasn't changed, but the scale reads more. And I feel like I weighed more, because the elevator is pushing me up. Crazy stuff. And I know I talk about this way too much, but a few years ago I experienced this concept in the most awesome way on the Vomit Comet, the zero-g plane in France--which is that as the plane ascends, it's just like an elevator accelerating upwards. And I felt two g's. And you can see my face drooping like I weigh twice as much. I was then advised to lie down because, at 58 kilograms, I felt like I suddenly weighed 106 kilograms. I did stand up in the later parts of the flight, and it was a workout just to stay upright. So what happens if the elevator starts to slow down at the top of the tower? It's decelerating, so the sum of my forces must be pointing down. The net force is downward. Because the force of gravity is unchanged, the springs in the scale must be pushing up a bit less, so the dial or the numbers on the scale go down a little bit, which means that if you control the acceleration of the elevator, you can change what the scale reads. You could put a set of brakes on the side of the elevator and tune them to slow down gradually so that you ever so slightly lift off the scale and experience a brief moment of weightlessness. That's what happens in a zero-g plane. Your perceived weight on the scale goes to 0. You could brake super fast and slam into the ceiling, so make sure you wear your helmet in an elevator. We should have gotten some padding for the eggs. Now we have our tools and we're ready to measure g with the Atwood machine. What is the Atwood machine? It came from this English mathematician named George Atwood who invented the contraption in 1784 to study constant acceleration. So it's basically this machine on a pulley with a rope.

(Describer) She moves the paper.

Here's my pulley with a rope and two masses on either side. And one mass is a little bit heavier than the other side. So m1 bigger than m2. You can see that in the Atwood machine we made, we have two pulleys so we can keep the person separated from the weights so they don't smack each other. So I'm here with Thea.

(Describer) Outside...

Behind us is the human-sized Atwood machine. Thea made this. Do you remember what the specifications were?

(Describer) Thea Ulrich:

So the specifications for this were basically it had to be human-sized, support Dianna safely, and be as frictionless as possible, because essentially it's a pulley system. We're offsetting two weights and we want to make sure to minimize variables. OK, so these masses will accelerate, but slowly, because they're very close. And by timing the rate of the fall, we can use our free body diagrams and we can figure out g. Now, you might think, why go to all the trouble of very slowly risking Dianna's life on an Atwood machine? Couldn't you just measure gravity by dropping something? Well, even from these heights, things fall too fast. Let's measure it. I'm going to drop this hair clip. We've measured out a meter. And I'm going to time it. Here we go. I'm hoping to get 9.81 meters per second, squared. Ready? Three, two, one, start.

(Describer) She drops it.

OK, I got 0.55 seconds. That gives us about 6.6 meters per second, squared. That's a pretty big error from 9.8. My timing is terrible. And air resistance, once again, makes things difficult and messy. So by slowing everything down, I can measure more precisely. That's the point of the Atwood machine. So the motion of the Atwood machine involves two fundamental ideas. One is that the two masses are connected by a rope, which means that they will accelerate the same amount: here, m1 accelerates down while m2 accelerates up--

(Describer) In the Atwood Machine, M1 is a set of weights hanging from one end of the rope. M2 is Dianna sitting in a hoop hanging from the other end.

(describer) In the Atwood machine, m1 is a set of weights hanging from one end of the rope; m2 is Dianna sitting in a hoop, hanging from the other end.

(Dianna) --but at the same exact rate. Key idea number two has to do with the tension in the rope. That tension pulls m2 up. And because the rope isn't stretching or compressing, it pulls m1 with the same magnitude of tension. Those are the two key ideas. One, m1 and m2 accelerate at the same magnitude. And two, the magnitude of the rope's tension on each of them are equal. I'm going to just tell you up front that we're going to neglect the mass of the rope. We're also neglecting the energy used to accelerate the pulley and the friction of the pulley. And we're being negligent to keep this experiment simple. So our procedure to find the acceleration is straightforward. We draw a free body diagram for each mass. So let's do it. Gravity pulls m1-- let's put m1 here. At a magnitude of m1 times g, tension is pulling it up-- that's T; and there's no other forces, so the sum of the forces equals m1 times a, equals T up and mg down. So minus m1g. But hold on. Let me remind you to pay attention to negative signs. They're going to matter here. Down is negative, up is positive. So m1 is accelerating down, so I put a negative sign here, in front of m1. That's it--we're going to save this for later. OK, let's do the procedure for m2. Mass two experiences the force of gravity down and the tension up. So T up and fg is m2g. The sum of the forces on m2 is m2 times a, which equals T minus m2g for my gravitational force. And remember, m2 is accelerating up, which is positive. So no negative sign in front of m2 over here. So now we've done all of the heavy lifting. And all we have left is algebra. I have two equations here. It looks like a bunch of unknowns, but I can make it simpler by using my two key ideas.

(Describer) They're shown again.

First, I remember that the tension, T, is the same for both ends of the rope. So I just solve for T and I set my two equations equal to each other. So let's do it. T equals minus m1a plus m1g. And T in my second equation equals m2a plus m2g. So I just solve and set my two equations equal to each other. So minus m1a less m1g equals m2a plus m2g. So I remember that the accelerations of each are the same. So the a's on each side are the same a. So I can combine those somehow. I want to do that by moving these on the same side-- m1g over here minus m2g equals m2a plus m2a. And I plug the g times m1 minus m2 equals a m2 plus m1. OK, then we solve for g, because we want to measure g, so we solve for g. g equals a times m2 plus m1 over m1 minus m2. So we get that g is the acceleration I measured times the sum of m1 plus m2, over the difference of m1 minus m2. So now we just have to measure the acceleration and we can measure g.

(Describer) (no standard option) At the machine, a man lets M1 fall, raising M2, and measures the time M1 takes to land on the ground.

(describer) At the machine, a man lets m1 fall, raising m2, and measures the time m1 takes to land on the ground.

(Dianna) So the T we got was approximately 2.15 seconds. The distance was about 2 meters. m1 was about 79 kilograms. And m2 was 65 kilograms. So plugging this all in, g equals-- well first have to d equals 1/2 a T squared. So d is 2 meters equals 1/2 times a times 2.15 seconds, squared. If we solve for a, we get 0.87 meters per second, squared. So we're going to plug that in, then-- 0.87 meters per second, squared. And then we do m1 plus m2-- 79 kilograms plus 65 kilograms over 79 kilograms minus 65 kilograms. And we get g equals 8.9 meters per second, squared-- which is not quite right. The real g is g equals 9.81 meters per second, squared. But the thing is, there were so many places for margins of error. One is friction in the pulleys, which messes with our time. And that error gets squared over here, when we do this calculation. There's also the masses. If we used instead m1 equals 78 kilograms. And we use m2 equals 65.4 kilograms, then we actually do get g equals 9.8 meters per second, squared. So that shows you how sensitive this is to the masses. We also could have slowed it down. We could have made these masses closer together, but what happened then is we got more friction in the pulleys when they were moving slower. So then there's even more error. When we did that, we actually got a value of g equals 2. So we sped it up to get rid of friction, and then we needed more sensitive measurements on our mass. And we were sensitive to within about a kilogram. So this is within the margin of error of our masses. Plus the cable itself weighed about two kilograms. And that changes over the course of the movement. Lots and lots of error. But I say we did pretty good. Yay! We measured g. That's g at this particular elevation, though. We were pretty close to sea level in Los Angeles. Remember, gravity weakens as you move further away from the center of the Earth. Gravity is less at the top of a mountain. If you were standing over a giant uranium mine-- because uranium is a very dense metal-- you would measure a higher g. g over the surface of the Earth varies between 9.76 to 9.83 meters per second, squared. It's not always 9.81. Here's a map NASA made of the gravity anomalies around the planet that shows you will measure different g's, depending on your location. I'm going to show you one last extra trick for solving out machine-type problems, because they show up on exams super often. So a problem might give you two masses and then ask you what the acceleration is. So we need to arrange the algebra to look like this. Solving for acceleration equals g times m1 minus m2 over m1 plus m2. So the algebra looks like this. That's why the masses accelerate slower than freefall. So what I mean is, let's try it in a situation where m1 is twice m2. So m1 equals twice m2. So then my equation works out to a equals g. m1 is twice m2, so 2 m2 minus m2 over 2 m2 plus m2, which equals-- this is m2 over 3 m2 times g. So the acceleration equals 1/3 times g. And I get a equals 1/3 g, so it does work. You can use this trick for any combination of masses. The number of g's you measure is the difference of those two masses over the sum. Gravity only gets to work on the difference of the masses, but it's the sum of the masses that get accelerated. It's like gravity has to accelerate three masses, but only gets to work on the equivalent of one mass. We're used to everything falling at the same rate, because gravitational mass is equal to inertial mass. But in the Atwood machine, that lets us fake out gravity. So that's Lesson 5-- how do to use free body diagrams to calculate forces?

(Describer) She tosses the paper away.

So that's Lesson 5. When they ask you what you learned on YouTube today, here are your two important takeaways. When solving problems using a net force, FBD-- Free Body Diagrams. When solving problems with multiple components, look for variables they have in common. And as always, you must solve the problems. It's the only way to truly, really learn physics.

(describer) Problem one: Draw a free body diagram (FBD)

(Describer) Problem 1: Draw a free body diagram (FBD) for a bottle of nail polish falling straight down. Draw an FBD for a soccer ball kicked at an angle, after the kick. What about during the kick? Problem 2: You are standing on a scale in an elevator that is accelerating upwards at a rate of 2 meters per second-squared. If your mass is 58 kilograms, what does the scale read in Newtons? What would it read if you were decelerating at 2 meters per second-squared (accelerating at negative 2 meters per second-squared)? Problem 3: We built a human-sized Atwood machine using two masses: 65 kilograms and 79 kilograms. The masses fell 2 meters from rest and it took 2.2 seconds. What do we get for g? What are the possible sources of error? Problem 4: You build an Atwood Machine where the masses have a ratio of 4 to 5. What will the acceleration of masses be?

for a bottle of nail polish falling straight down. Draw a FBD for a soccer ball kicked at an angle, after the kick. What about during the kick? Problem two: You are standing on a scale in an elevator that is accelerating upwards at a rate of 2.0 meters per second squared. If your mass is 58 kilograms, what does the scale read, in newtons? What would it read if you were decelerating at 2.0 meters per second squared (accelerating at negative 2.0 meters per second squared)? Problem three: We built a human-sized Atwood machine using two masses: 65 kilograms and 79 kilograms. The masses fell 2.0 meters from rest and it took 2.2 seconds. What do we get for "g"? What are some possible sources of error? Problem four: You build an Atwood machine where the masses have a ratio of 4 to 5. What will the acceleration of masses be?

(Dianna) ...all the problems we did today for you to rework on your own. And you can also search on the internet for free body diagram problems and gravitational acceleration problems for more practice-- you should. And now a message from a very special guest, Bill Nye. Greetings. Bill Nye here. You know the old saying-- everything happens for a reason. Well, that reason is usually physics. Physics is the fundamental science. So enjoy this course. You can't do any better than Professor Cowern. And then get out there and make things happen.

(Describer) Titles: Executive Producer/Host/Writer: Dianna Cowern Lead Writer/Course Designer: Jeff Brock Producer: Laura Chernikoff Video Editor: Spenser Reich Aerialist/Maker: Thea Ulrich Videographer: Levi Butner Curriculum Consultants: Lucy Brock and Samantha Ward Consulting Producer: Vanessa Hill Curriculum Consultant: Andy Brown Physics Girl Accessibility provided by the US Department of Education.

Accessibility provided by the U.S. Department of Education.