The world is a mess.Idealization makes physics easy

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Sometimes the universe The analysis is too complicated.

Oops, if you take a tennis ball and throw it through the room, it’s actually too complicated. After the ball leaves your hand, it will gravitationally interact with the earth, causing it to accelerate toward the ground. The ball is spinning as it moves, which means that one side of the ball may have more frictional resistance than the other.The ball also collided with some oxygen and nitrogen molecules in the air-and some These The molecule ends up with Even Air. The air itself is not even constant-the density changes as the ball moves higher, and the air may be moving. (We usually call it wind.) Once the ball hits the ground, even the floor is not completely flat. Yes, it looks flat, but it is located on the surface of a spherical planet.

But nothing is lost. We can still simulate this thrown tennis ball. All we need is some idealization. These are simplified approximations that turn impossible problems into solvable problems.

In the case of tennis, we can assume that all the masses are concentrated on one point (in other words, the ball has no actual size) and the only force acting on it is a constant downward pull. Why can all other interactions be ignored? This is because they did not produce significant (or even measurable) differences.

Is this legal in the physical court? Well, science is the process of building models, including equations for tennis trajectories. After all, if the experimental observations (where the ball lands) are consistent with the model (prediction of the ball landing), then we can start.For tennis idealization, everything is normal Very good. In fact, the physics of throwing a ball has become a test question in the introduction to physics.Other idealizations are more difficult, such as trying to determine the curvature of the earth by observing this The ultra-long terminal at Atlanta Airport. But physicists have been doing this kind of thing.

Perhaps the most famous idealization was done by Galileo Galilei while studying the nature of movement. He tried to figure out what would happen if you didn’t apply force to a moving object. At that time, almost everyone followed Aristotle’s teachings, saying that if no force is applied to a moving object, it will stop and stay still. (Although his work is about 1,800 years old, people think Aristotle is too cool to be wrong.)

But Galileo disagreed. He thought it would continue to move at a constant speed.

If you want to study a moving object, you need to measure the position and time at the same time, so you can calculate its speed, or its position change divided by the time change. But there is a problem. How do you accurately measure the time it takes for an object to move at a high speed in a short distance? If you drop something from a relatively small height (for example, 10 meters), it will take less than 2 seconds to reach the ground. Back around 1600, when Galileo was still alive, this was a very difficult time interval to measure. So, instead, Galileo watched a ball rolling down its orbit.

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