Newton's Laws: Crash Course Physics #5

Summary

In this CrashCourse episode, we dive into Newton's Laws of Motion, essential tools for understanding how forces cause objects to accelerate. From the concept of inertia to the practical application of F = ma, these principles explain why things move (or don't) as they do. Newton’s first law highlights an object’s tendency to remain in its current state until acted upon by an external force, while the second law quantifies the relationship between force, mass, and acceleration. Lastly, the third law, which states that every action has an equal and opposite reaction, sheds light on interactions between objects. Using practical examples like a reindeer sleigh and an elevator, the episode makes these complex concepts accessible and engaging.

Highlights

• Uncover the secret of inertia with Newton's first law's simple yet profound explanation. 🎓
• Master the mathematical magic of F = ma with Newton’s second law. ✨
• Discover the beauty of action-reaction pairs with Newton’s third law. 🔄
• Learn how to draw free body diagrams to visualize and solve physics problems like a pro. 🖊️
• Understand the interplay of forces on objects with engaging examples like reindeer and sleighs. 🛷

Key Takeaways

• Inertia keeps things moving or stationary unless an external force acts on them. 🏐
• Net force equals mass times acceleration, a cornerstone of Newton’s second law. 🚀
• Every action has an equal and opposite reaction, key to understanding interactions. 🤝
• Drawing free body diagrams helps solve force-related problems efficiently. ✏️
• Physics makes the everyday world, including holidays like Christmas, understandable! 🎅

Overview

Have you ever wondered why a ball thrown in the air falls back down, or what keeps a car moving? It all boils down to forces! In this episode, we explore these forces through the lens of Newton's laws. These three laws, introduced by Isaac Newton in the 17th century, remain fundamental to physics today, explaining everything from falling apples to planetary motion.

Newton's first law, often termed the law of inertia, tells us that an object will stay at rest or in uniform motion unless acted upon by a net force. The second law provides a quantitative description of the changes that force can produce in a body. When a net force acts on an object, it accelerates: this acceleration is directly proportional to the force and inversely proportional to the object's mass.

The third law, stating every action has an equal and opposite reaction, explains the nature of interactions. This episode also introduces practical problem-solving techniques, such as creating free body diagrams and understanding forces like tension and normal force. Through vivid examples, these complex concepts are broken down, making physics an intriguing blend of theoretical and real-world phenomena.

Chapters

• 00:00 - 01:00: Introduction to Forces The introduction discusses the basic concept of forces and their role in motion, specifically acceleration. It mentions the contributions of Isaac Newton, emphasizing his three laws that were groundbreaking at the time of their publication in 1687 in his work, 'Principia.' These foundational ideas still influence our understanding of how forces affect motion today.
• 00:30 - 01:30: Newton's First Law and Inertia This chapter introduces Newton's First Law of Motion, focusing on the concept of inertia. It uses everyday examples such as a box on the ground, a reindeer pulling a sleigh, and an elevator, to explain how Newton's Laws apply to common scenarios. The chapter emphasizes that inertia is the tendency of an object to continue its current state, whether at rest or in motion, unless acted upon by an external force.
• 01:30 - 03:00: Newton's Second Law and Net Force This chapter discusses Newton's Second Law, which is often expressed as the principle that an object will not change its motion unless a net force acts upon it. A key aspect of this law is understanding inertia, which is the resistance of an object to changes in its state of motion. This resistance is directly related to mass; the greater the mass of an object, the greater its inertia. For example, a bowling ball is harder to move and stop than an inflatable beach ball of the same size because it has more mass and thus more inertia. Thus, mass can be seen as a measure of the amount of 'stuff' in an object, contributing to its tendency to maintain its current state of motion.
• 03:00 - 04:00: Gravitational Force and Weight This chapter explores the concepts of gravitational force and weight, emphasizing the importance of understanding net force. Newton's second law is a central focus, with the equation F(net) = ma used to explain how forces interact. The chapter uses the example of a hockey puck on a frictionless surface to illustrate how different forces can cancel each other out, leaving a net force that determines the object's motion.
• 04:00 - 05:00: Newton's Third Law and Normal Force This chapter discusses Newton's Third Law and the concept of normal force using the example of a hockey puck on ice. It explains the ideas of force and acceleration, equilibrium, and how objects in equilibrium can still be in motion but with constant velocity. The chapter also touches on the effects of unbalanced forces, highlighting the role of gravitational force in causing movement.
• 05:00 - 07:00: Free Body Diagrams and Tension Force The chapter discusses the concept of Free Body Diagrams and Tension Force through the example of a ball being thrown directly upward. The ball, which has a mass of 5 kg, is influenced by the force of gravity, accelerating it downward at a rate of 9.81 m/s^2. This net force is strictly due to gravity, calculated using the mass and the acceleration (m*a). Since the acceleration can be measured and is equivalent to 9.81 m/s^2 (denoted as small g), this example is used to illustrate how the force of gravity acts on objects.
• 07:00 - 10:00: Elevator Example with Forces This chapter focuses on explaining the concept of gravitational force and how it relates to weight. It begins by examining the force of gravity exerted on a ball, which has a mass of 5 kg. The force of gravity is calculated using the formula F(g) = mg, where small g is the acceleration due to gravity (approximately 9.81 m/s²), thus resulting in a force measured in Newtons. The chapter emphasizes the distinction between weight (measured in Newtons) and mass (measured in kilograms), correcting the common misconception of using kilograms for weight. The idea highlights the fundamental physics principles introduced by Sir Isaac Newton.
• 10:00 - 11:00: Conclusion and Credits The chapter discusses forces acting on objects, emphasizing that gravity isn't the only force to consider when calculating net force. It introduces Newton's third law, which states, 'For every action, there’s an equal but opposite reaction,' fundamentally explaining what is commonly referred to as the normal force—force exerted by a surface perpendicular to the object it supports.

Newton's Laws: Crash Course Physics #5 Transcription

• 00:00 - 00:30 We’ve been talking a lot about the science of how things move -- you throw a ball in the air, and there are ways to predict exactly how it will fall. But there’s something we’ve been leaving out: forces, and why they make things accelerate. And for that, we’re going to turn to a physicist you’ve probably heard of: Isaac Newton. With his three laws, published in 1687 in his book Principia, Newton outlined his understanding of motion -- and a lot of his ideas were totally new. Today, more than 300 years later, if you’re trying to describe the effects of forces on
• 00:30 - 01:00 just about any everyday object -- a box on the ground, a reindeer pulling a sleigh, or an elevator taking you up to your apartment -- then you’re going to want to use Newton’s Laws. And yes. I’ll explain the reindeer thing in a minute. [Theme Music] Newton’s first law is all about inertia, which is basically an object’s tendency to keep doing what it’s doing.
• 01:00 - 01:30 It’s often stated as: “An object in motion will remain in motion, and an object at rest will remain at rest, unless acted upon by a force.” Which is just another way of saying that, to change the way something moves -- to give it ACCELERATION -- you need a net force. So, how do we measure inertia? Well, the most important thing to know is mass. Say you have two balls that are the same size, but one is an inflatable beach ball and the other is a bowling ball. The bowling ball is going to be harder to move, and harder to stop once it’s moving. It has more inertia because it has more mass. Makes sense, right? More mass means more STUFF, with a tendency to keep doing what it was
• 01:30 - 02:00 doing before your force came along, and interrupted it. And this idea connects nicely to Newton’s second law: net force is equal to mass x acceleration. Or, as an equation, F(net) = ma. It’s important to remember that we’re talking about NET force here -- the amount of force left over, once you’ve added together all the forces that might cancel each other out. Let's say you have a hockey puck sitting on a perfectly frictionless ice rink. And I know ice isn’t
• 02:00 - 02:30 perfectly frictionless but stick with it. If you’re pushing the puck along with a stick, that’s a force on it - that isn’t being canceled out by anything else. So the puck is experiencing acceleration. But when the puck is just sitting still, or even when it’s sliding across the ice after you’ve pushed it, then all the forces are balanced out. That’s what’s known as equilibrium. An object that’s in equilibrium can still be MOVING, like the sliding puck, but its VELOCITY won’t be changing. It’s when the forces get UNbalanced, that you start to see the exciting stuff happen. And probably the most common case of a net force making something move is the gravitational force.
• 02:30 - 03:00 Say you throw a 5 kg ball straight up in the air -- and then, yknow, get out of the way, because that could really hurt if it hits you... But the force of gravity is pulling down on the ball, which is accelerating downward at a rate of 9.81 m/s^2. So the net force is equal to m a, but the only force acting here is gravity. This means that, if we could measure the acceleration of the ball, we’d be able to calculate the force of gravity. And we CAN measure the acceleration -- it’s 9.81 m/s^2, the value we’ve been calling small g.
• 03:00 - 03:30 So the force of gravity on the ball must be 5 kg, which is the mass of the ball… times small g which comes to 49.05 kilograms times meters per second squared! We use this equation for gravity so much that it’s often just written as F(g) = mg. That’s how you determine the force of gravity, otherwise known as weight. Now, those units can be a bit of a mouthful, so we just call them Newtons. That’s right! We measure weight in Newtons, in honor of Sir Isaac, and NOT kilograms! Kilograms are a measure of mass!
• 03:30 - 04:00 But gravity often isn’t the only force acting on the object. So when we’re trying to calculate a NET force, we usually have to take into account more than just gravity. This is where we get into one of the forces that tends to show up a lot, which is explained by Newton’s third law. You probably know this law as “for every action, there’s an equal but opposite reaction.” Which just means that if you exert a force on an object, it exerts an equal force back on you. And that’s what we call the normal force. “Normal” in this instance means “perpendicular”, and the normal force is always perpendicular
• 04:00 - 04:30 to whatever surface your object is resting on. At least, it is when you're pushing on something big, and macroscopic, like a table. If you put a book down on a table, the normal force is pushing -- and therefore pointing -- up. But if you put it on a ramp, then the normal force is pointing perpendicular to the ramp. Now, the normal force isn’t like most other forces. It’s special, because it changes its magnitude. Say you have a piece of aluminum foil stretched tightly across the top of a bowl, and then you put one lonely grape on top of it.
• 04:30 - 05:00 Because of gravity, that grape is exerting a little bit of force on the foil, and the normal force pushes right back, with the same amount. But then you add another grape, which doubles the force on the foil -- in that case, the normal force doubles too. That’ll keep happening until eventually you add enough grapes that they break through the foil. That’s what happens when the normal force can’t match the force pushing against it. But, what does Newton’s famous third law really mean, though? When I push on this desk with my finger right now, I’m applying a force to it.
• 05:00 - 05:30 And it’s applying an equal force right back on my finger -- one that I can actually feel. But if that’s true -- and it is -- then why are we able to move things? How can I pick up this mug? Or how can a reindeer pull a sleigh? Basically, things can move because there’s more going on, than just the action and reaction forces. For example, when a reindeer pulls on a sleigh, Newton’s third law tells us that the sleigh is pulling back on it with equal force. But the reindeer can still move the sleigh forward, because it’s standing on the ground.
• 05:30 - 06:00 When it takes a step, it’s pushing backward on the ground with its foot -- & the ground is pushing it forward. Meanwhile, the reindeer is also pulling on the sleigh, while the sleigh is pulling right back. But the force from the GROUND PUSHING the reindeer forward is STRONGER than the force from the sleigh pulling it back. So the animal accelerates forward, and so does the sleigh. So, one takeaway here is that: there would be no Christmas without physics! But, now that we have an idea of some of the forces we might encounter, let’s describe what’s happening when a box is sitting on the ground.
• 06:00 - 06:30 The first thing to do -- which is the first thing you should ALWAYS do when you’re solving a problem like this -- is draw what’s known as a free body diagram. Basically, you draw a rough outline of the object, put a dot in the middle, and then draw and label arrows, to represent all the forces. We also have to decide which direction is positive -- in this case, we’ll choose up to be positive. For our box, the free body diagram is pretty simple. There’s an arrow pointing down, representing the force of gravity, and an arrow pointing up, representing the force of the ground pushing back on the box.
• 06:30 - 07:00 Since the box is staying still, we know that it’s not accelerating, which tells us that those forces are equal, so the net force is equal to 0. But what if you attach a rope to the top of the box, then connect it to the ceiling so the box is suspended in the air? Your net force is still 0, because there’s no acceleration on the box. And gravity is still pulling down in the same way it was before. But now, the counteracting upward force comes from the rope acting on the box, in what we call the tension force. To make our examples simpler, we almost always assume that ropes have no mass and are completely
• 07:00 - 07:30 unbreakable -- no matter how much you pull on them, they’ll pull right back. Which means that the tension force isn’t fixed. If the box weighs 5 Newtons, then the tension in the rope is also 5 Newtons. But if we add another 5 Newtons of weight, the tension in the rope will become 10 Newtons. Kind of like how the normal force changes, with the grapes on the foil. But in this case, it's in response to a pulling force instead of a push. The key is that no matter what, you can add the forces together to give you a particular net force -- even though that net force might NOT always be 0. Like, in an elevator.
• 07:30 - 08:00 So let’s say you’re in an elevator -- or as I call them, a lift. The total mass of the lift, including you, is 1000 kg. And its movement is controlled by a counterweight, attached to a pulley. The plan is to set up a counterweight of 850kg, and then let the lift go. Once you let go, the lift is going to start accelerating downward - because it’s HEAVIER than the counterweight. And the hope is that the counterweight will keep it from accelerating TOO much. But how will we know if it’s safe? How quickly is the lift going to accelerate downward?
• 08:00 - 08:30 To find out, first let’s draw a free body diagram for the lift, making UP the positive direction. The force of gravity on the lift is pulling it down, and it’s equal to the mass of the lift x small g -- 9810 Newtons of force, in the negative direction. And the force of tension is pulling the lift UP, in the positive direction. Which means that for the lift, the net force is equal to the tension force, minus the mass of the lift x small g.
• 08:30 - 09:00 Now! Since Newton’s first law tells us that F(net) = ma, we can set all of that to be equal to the lift’s mass, times some downward acceleration, -a. That’s what we’re trying to solve for. So, let’s do the same thing for the counterweight. Gravity is pulling it down with 8338.5 N of force in the negative direction. And again, the force of tension is pulling it up, so that the net force is equal to the tension force, minus the mass of the counterweight times small g.
• 09:00 - 09:30 And again, because of Newton’s second law, we know that all of that is equal to the mass of the counterweight, times that same acceleration, “a” -- which is positive this time since the counterweight is moving upward. So! Putting that all together, we end up with two equations -- and two unknowns. We don’t have a value for the tension force, and we don’t have a value for acceleration. But what we’re trying to solve for is the acceleration. So we use algebra to do that. When you have a system of equations like this, you can add or subtract all the terms on each
• 09:30 - 10:00 side of the equals sign, to turn them into one equation. For example, if you know that 1 + 2 = 3 and that 4 + 2 = 6, you can subtract the first equation from the second to get 3 = 3. And in our case, with the lift, subtracting the first equation from the second gets rid of the term that represents the tension force. We now just have to solve for acceleration -- meaning, we need to rearrange the equation to set everything equal to “a.” We end up with an equation that really just says that “a” is equal to the difference
• 10:00 - 10:30 between the weights -- or the net force on the system -- divided by the total mass. Essentially, this is just a fancier version of F(net) = ma. And we can solve that for “a”, which turns out to be 0.795 m/s^2. Which is not that much acceleration at all! So, as long as you aren’t dropping too far down, you should be fine. Even if the landing is a little bumpy. In this episode, you learned about Newton’s three laws of motion: how inertia works, that net force is equal to mass x acceleration, how physicists define equilibrium, and all
• 10:30 - 11:00 about the “normal” force and the “tension” force. Crash Course Physics is produced in association with PBS Digital Studios. You can head over to their channel to check out amazing shows like: BrainCraft, It’s OK To Be Smart, and PBS Idea Channel. This episode of Crash Course was filmed in the Doctor Cheryl C. Kinney Crash Course Studio with the help of these amazing people and our Graphics Team is Thought Cafe.