Newton's laws applied to gumballs in space

You're stuck floating in space, ten feet from your spaceship, with no way to move, except... a sack full of gumballs. What do you do?

Transcript

If you Google the phrase greatest scientist of all time, you will have two names pop up more than any others. One is Albert Einstein. You can make a good case for Einstein. His ideas were foundational for almost all of modern physics. And if you get a PhD in physics, then you'll come up to know him very well. But the other contender is just as qualified as Einstein. And I think he actually has more going for him. That would be Sir Isaac Newton. Today we're going to talk about a small part of what Newton did. That small part is foundational for how we as scientists see the world. This episode is about Newtonian mechanics, or the laws that govern how things move. Things like a car accelerating or an apple falling from a tree. One of the first classes you take in college as an engineer is an introduction to Newtonian mechanics. That is because Newton's laws are so fundamental, they're useful for explaining things we use every day. and you'll be surprised by just how counterintuitive they seem. Isaac Newton was born on Christmas Day in 1642. His father died before he was born, and when he was three years old, his mother left him in the care of his grandmother so that his mother could remarry. Newton was often considered an angry child. He once threatened his mother and stepfather to burn down the house while they were living in with them inside. His attitudes didn't change much as an adult. and he's well known for his sour disputes with Hooke and Leibniz. In his scientific career, he was not necessarily well-liked, but he was certainly well-respected. When Newton was 23, the university he was studying at shut down due to the Great Plague of London, and he had to go home. But instead of sitting on the couch and watching Netflix, he decided to invent calculus. His mathematical innovations during this time would soon provide a foundation for his laws of motion. At that time, the dominant understanding of mechanics and motion came from the writings of Aristotle. Aristotelian physics had been the accepted dogma for nearly 2,000 years. Aristotle said that when you push on an object, for example a book, the book will keep moving as long as you're applying a force to it, but as soon as you stop applying the force, the book will stop moving. This is very intuitive, and it fits with most of our everyday experience. It certainly worked for Aristotle. But since Aristotle lived in ancient Greece, he never had the chance to go ice skating. Consider now that you set a book down on an ice skating rink. It'd better not be a library book or you're in trouble. You exert a force on the book and it moves. But when you take your hand away, the book is still sliding! How does it keep moving even if you're no longer pushing on it? It turns out that Aristotle's physics only works in a world dominated by friction. When you take away the friction, such as on ice, you need a new set of rules. Newton realized this and discovered a set of rules that work even without friction. These rules form the basis for how scientists understand the world for the next 200 years. Newton's mechanics can be summarized in three statements known as Newton's Three Laws. But before I explain them, we're going to have to go on a trip. Your everyday experience is going to deceive you because you live in a world full of air and rough surfaces. where friction dominates just about everything. So to get rid of friction, we're going outer space. Newton's third law. You heard that right. We're going to start with number three in countdown. Imagine you're floating far away in outer space. 10 feet away from you is your spaceship. How do you get back to it? You can't swim, there's no fluid to swim through. You can't pump like on a swing, it won't move you at all. You're totally stuck. But there is hope. You remember that you packed snacks for the trip. You reach into the pocket of your space suit and pull out a gumball. Then you throw the gumball away from the spaceship, and you start moving towards the spaceship. Why? Because of Newton's third law. Newton's third law says that when you push on the gumball to throw it away from you, it pushes back with the same strength that you threw it with. You may have noticed the same thing happening if you've ever shot a gun. The gun pushes on the bullet to get it moving really fast, but the bullet also pushes backward on the gun with the same amount of force, which creates a recoil and might knock you over if you're not careful. Another example, when you stomp your foot on the ground, your foot exhorts a force on the ground, but the ground exerts the same amount of force back on your foot. That's why your foot doesn't go straight through the ground. Newton's third law can be summarized like this. Forces always come in pairs. Every time you exert a force on something, it exerts the force back on you, with equal magnitude but in the opposite direction. Newton's Second Law Scientists love Newton's Second Law, because it lets you do math. But don't worry, I'll do all the math today, you just have to pay attention. Newton's Second Law relates forces, mass, and acceleration. You may already have some intuition for this one. If something has a lot of mass, which means it's heavy, then it will take more force to accelerate it. It's a lot easier to push over the small scrawny boy than the big fat boy. Not that I've ever done either. So returning to our outer space, Newton's second law says that the gumball accelerates you an amount equal to the force with which you throw it divided by your mass. So all else being equal, one gumball will make someone who weighs 100 pounds go twice as fast as someone who weighs 200 pounds. The same is true about the gumball weight. A gumball that weighs 2 grams will make you go twice as fast as the gumball that weighs 1 gram. Or, thinking about it this way, if you throw two gumballs that each weigh 1 gram, then you will go twice as fast as when you just throw one gumball. That makes sense. Now doing some quick calculations that I haven't taught about yet. If you're an average person weighing 70 kilograms and you manage a good throw of 20 meters per second, and the gumball weighs 4 grams, then you'll start moving towards the spaceship at a speed of.001 meters per second. Since your ship is 10 feet away, that means you'll reach it in about 3,000 seconds or a little under an hour. You'd better hope you have more gumballs or you might be floating for a while. Newton's First Law. Here's where your intuition might fail you. On Earth, if something starts moving, then it will eventually come to a stop. Think of the book Sliding on Ice. Once it slides far enough, it'll stop. That's because even on a low friction surface like ice, there is still some friction. But in the vacuum of space, there's no friction, nothing to stop you from going on forever. So if you throw your gumball at the wrong angle, you could miss your ship and fly right past it, then keep on flying forever. This is because of Newton's first law. called the law of inertia. You may have heard it as an object at rest will stay at rest, and an object in motion will stay in motion unless acted upon by an unbalanced force. So floating still 10 feet away from your spaceship, you'll stay floating there forever. Flying at a constant speed relative to your spaceship, you'll fly right past it and keep on flying forever, unless acted upon by an unbalanced force. What is an unbalanced force? Well first, what's a balanced force? If you throw two gumballs at the same time, one in your right and one in your left, what forces it creates will balance each other out and you won't move anywhere. But throwing just one gumball creates an unbalanced force and causes you to accelerate towards the spaceship. Hitting the spaceship would be another unbalanced force and cause you to stop. Congratulations, you've made it back to your spaceship and now you can go home. Alright, now that we're home, it's time to explore some of what we've learned. Let's review. The first law, also called the law of inertia, says that an object at rest will stay at rest, and an object in motion will stay in motion, unless acted upon by an unbalanced force. Remember the gumball flying through space? It will remain in motion until acted upon by an outside force. Unless it hits something, that means it will keep going on forever without slowing down. 10,000 years in the future, an alien is going for a joyride in his spaceship and he decides to get out for a little spacewalk, but as soon as he steps out of the airlock, from out of nowhere he's hit in the head by a gumball. You don't want to be responsible for that, so don't go throwing gumballs carelessly. The second law said that acceleration of an object is equal to the force applied to it divided by its mass. A larger mass will be harder to accelerate. Go outside and test this for yourself. Find a large boulder and see how difficult it is to roll. Then try a smaller boulder and see how much easier it is. But in both cases, once you get the boulder rolling, it's relatively easy to keep it rolling. We just talked about this, but I'll say it again. An object in motion stays in motion. The third law says that forces come in pairs. When you push on the boulder, the boulder pushes back on you with the same amount of force. It's the same with gravity. The earth pulls you down with a force equal to your weight. But here's a secret. You pull up on the earth with exactly the same force. The earth is attracted to you just as much as you are to it. Every time you jump, the earth is pushed down slightly, and while you're in the air, it's pulled towards you until, when you land, it's in the same position as when you started. But remembering the second law, the earth is much more massive than you are. So while you're pushed up a lot by your jump, the Earth is pushed down only a very, very little bit. But what would happen if you gathered everybody in the world into one location and had them all jump at the same time? The webcomic xkcd asked this question and found an answer. You would push the Earth down by less than the width of an atom. Ouch. Compared to the mass of the Earth... The entire human race is tiny and insignificant. But now that we're on the subject of gravity, one of Newton's other greatest achievements was explaining gravity. He realized that the thing that makes apples fall to the ground is the same as the thing that makes the moon orbit Earth. It's a force that makes everything that has mass attract everything else that has mass. Tell your crush that you have scientific proof that they're attracted to you. Sir Isaac Newton said so. One of the most fundamentally interesting things Newton discovered about gravity was that all objects fall at the same rate, even if they have different weights. A hammer and a feather will both take the same amount of time to hit the ground when dropped from the same height, as long as there's no air resistance. The astronauts on Apollo 15 tested this out when they walked on the moon, because there's no air on the moon to slow the feather down, so now we have video evidence that the hammer and the feather hit the ground at the same time. Speaking of the moon, I mentioned earlier that the Earth's gravity attracts the moon in exactly the same way it attracts apples to the ground. But, you might ask, if the moon is attracted to the Earth like you say, why doesn't it crash into the ground? The answer is, it's trying its best to, but its aim is terrible and it keeps missing. And that's only kind of a joke. The moon is being pulled towards Earth, but it's also moving sideways at the same time. In the time it would take for it to crash into the Earth, it's already way off to the side, 238,900 miles to be exact. It missed! And it keeps falling towards Earth and missing in an internal cycle. That's what we call an orbit. Think of it like this. You throw a baseball. It comes back down and hits the Earth. But if you're Superman, then you can throw it far enough that as it's falling towards the Earth, the Earth is also curving away from it. the Earth is round if you didn't know. If you throw it hard enough, then the Earth curves away at the same rate as the ball falls. So it will do an entire lap of the Earth without hitting the ground. That's called an orbit. Here's something you didn't know. The astronauts on the International Space Station aren't in zero gravity. They still feel about 89% of Earth's gravity. But wait, you might say. I've seen videos of the astronauts in the IOSS. and they clearly don't have gravity there. How else could they just float around? Well, I have an answer for you. They're in freefall. It looks like they're floating in a spaceship, because the spaceship is falling towards the Earth just as fast as the astronauts are. But they're in orbit, so they never hit the ground. As stated earlier, two objects in freefall will fall at the same rate, regardless of their mass. so the space station floor is falling out from under the astronaut's feet at the same rate as the astronaut is falling, which makes him feel completely weightless. Actually, Einstein would say that being in free fall and being in zero gravity are completely equivalent situations, but even ignoring Einstein, Newton's laws are able to explain the situation perfectly. Any questions? I hope you have many. It's time for you to do some googling to try and understand everything I've talked about that grabbed your interest. But before that, I have two questions for you to test your understanding. Number one, a seagull is flying above your head at 10 meters per second. It poops as it's directly above your head. What do you have to do to avoid getting splattered on? The answer? Nothing. Just sit still. The poop is flying with the seagull at 10 meters per second, and it will hit the ground somewhere in front of you. You take a weight on a string and you swing it around your head in a circle, then release it when the weight is right in front of your nose. Which way will it fly? Straight away from you along your line of sight, off to your left or right? Test it out and see for yourself. That's your homework assignment. I can't give you all the answers. I hope you've learned something from this discussion. The next episode of this series will talk about another field of science, my personal specialty, chemistry. Hope to see you next time. This has been Ideas Worth Exploring by Mark McDonald.