기관차는 어떻게 훨씬 더 무거운 긴 기차를 끌 수 있습니까?

Have you ever watched a mile-long freight train rumble by and wondered how one locomotive can pull more than a hundred fully loaded cars? The locomotive weighs maybe 150 metric tons, and each car is about 100 metric tons, which means it’s hauling 10,000 tons. I mean, if you weigh 170 pounds, this would be like pulling three SUVs totaling 12,000 pounds. Ridiculous, right? I’ll give you a hint: It’s not about weight or mass—at least not directly. It’s about friction, which is the resistance to motion between two surfaces that are in contact. Friction gets a bad rap—we use it as a metaphor for something that hinders productivity. But without it, things would not go smoothly. You couldn’t walk; you couldn’t even tie your shoes. You’d drop your latte. Your bicycle tires would spin in place and you’d fall over—luckily, since you’d have no brakes. In fact, all the nuts and bolts holding your bike together would fall off. So, yes, to answer our question about freight trains, we need to understand how frictional forces work. All aboard the physics train! What Is Static Friction? Let’s start with something simple. Place a book on a table and give it a little nudge on the side. Just a light push—not enough to get it moving. Newton's second law says the net force on an object equals the product of its mass and acceleration (Fnet = ma). Since the book isn’t accelerating (a = 0), the net force must be zero, meaning all the forces are balanced. Here’s a diagram: Let’s look first in the vertical direction: We have a downward pull from gravity, and the strength of that force depends on the mass of the book (m) and the gravitational field (g) of the planet you’re on (Fg = mg). But the book isn’t accelerating downward, so there must be an equal force from the table pushing up. We call this a “normal force.” Result: The net vertical force is zero. I know, the idea of an inert table pushing up on a book doesn’t seem very normal. Maybe it’ll help if you realize that gravity doesn’t pull you to Earth’s surface, as people often think—it pulls you to the center of the Earth. The normal force is what keeps you from plunging through the floor. (By the way, “normal” means perpendicular—it’s always perpendicular to the surface.) Horizontally, we also have two forces. There’s the force of you pushing on the book from left to right, and again there must be an equal force pushing in the opposite direction. We call that resisting force static friction—“static” because the book’s not budging. This depends on just two things, the specific materials in contact, captured in a coefficient μs, and the normal force (N): This coefficient μs is just a number, usually between 0 and 1, which you can look up in a table for all kinds of different materials. For rubber tires on asphalt, it’s 0.9; for tires on ice it falls to 0.15 (hence snow chains). And N, as we saw above, equals the gravitational force, which in turn depends on the object’s mass. The greater the mass, the more friction you get. Now, see that less-than-or-equal sign? This says μsN is the maximum static friction force in a given situation. If you push the book with a force of 1 newton, the frictional force will be 1 newton. Double the pushing force and the frictional force also doubles. It does whatever it has to in order to keep the two surfaces stationary—up to a point. If you keep pushing harder, your applied force will eventually exceed μsN and the book will start to slide. At that point, kinetic friction kicks in. Kinetic friction is the resistance you get when the book is sliding across the table. It’s always lower than static friction, because it’s just harder to start something moving than to keep it moving. “OK,” you’re saying, “I got it. Static when stationary, kinetic when in motion.” Ha! Then here’s a paradox: The force that enables you to move—let’s say to walk—is static friction, not kinetic friction. When you push off the ground with your back foot, static friction keeps your foot from sliding out from under you. (For laughs, see my recent article about trying to climb out of an ice bowl.) The same is true for the locomotive: It uses static friction to drive itself forward. Train Tug-of-War Now, suppose we have two identical locomotives chained back-to-back. What happens if they pull in opposite directions? There's a bunch of forces here, but the only new one is what we call the tension force (T) in the chain. This results in an equal force pulling each locomotive in the backward direction. Resisting that pull is the static friction force (Ffs), which is now pushing in the forward direction. Now, since both locomotives have the same mass (even the drivers are the same size), they will have the same normal force (N) and therefor the same maximum static friction. The result is easy to predict: The trains will huff and puff to no avail—it’s a stalemate. What if the train on the right has a higher mass? That means it will have a larger normal force, and therefore a greater ma