Many people gave a cry of regret. Chen Jian clapped a booklet in his hand and said, "I have already written these, and I will print them soon. You all want to see if you have enough time. But I am not here today to explore arithmetic and geometry. I have talked so much about the previous problem: force, power, the trajectory of the stone in the air, etc. "

Everyone looked at the thick calculation formulas and word counts that they wrote down on the paper, and they were secretly surprised, knowing that mathematics might not be able to get around this problem.

Mathematics is a tool, just like those experimental instruments, it is a tool, but it is the most difficult to master and the easiest to convince everyone.

In four days, I just used the mathematical level of the previous hundreds of years plus this coordinate system and parabolic intuitive system to make a set of tools-only a part of all the tools needed.

And all the tools are taken out, there are many here and there.

A straight plank twelve paces long, a small brass ball, a precise drop timer, three long springs, four books, two pamphlets published by the Academy, three large black planks, several pieces of plaster A pen, three long rulers, a lifting scale, a piece of iron, a magnet, and a bowl.

Chapter 84 Obtaining knowledge through investigation ([-])

After setting up various tools, Chen Jian first took a small copper ball and rolled it on the ground.

The copper ball gradually slowed down and finally stopped.Then Chen Jian put the small ball on the wooden trough that was flat on the ground. This time the copper ball rolled a lot farther, and the speed also slowed down a lot.

"You see, a copper ball rolls a short distance on the ground, but it can roll a long distance on a smooth wooden trough. Similarly, if it is frozen, a sledge can easily slide a long distance on the ice, but if it is on the sand If you play with a sledge on the ground, you will fall into the mud. Right?"

"So can we assume that if it is extremely smooth and completely free of any bumps and frictions, will the ball not be able to stop?"

Everyone nodded. This question is obvious, and it is also a question that many people have thought about. Otherwise, there would be no special sellers of whale oil and castor oil, let alone sleds and sledges in snowy weather.

"Then here comes the problem. Assuming this plane with no friction exists, the ball will keep moving. So what is the reason for this constant movement? Is there an invisible hand pushing it away? Or is it as I guessed? In that way, everything has a tendency to tend to the current state, unless it is changed by an external force? If it is the former assumption, then force is force; if it is the latter assumption, force is force, and force is force, and force is What changes the current trend of an object, not what maintains the current year's trend."

This is the most difficult question to understand. Many people can't turn their minds around, and they can't understand why a small ball moving at a uniform speed has no force. If there is no force, why does it move?

"Based on these two assumptions, we must prove it through experiments. Because sometimes the world is not the same as we imagined, and what we think may not be the truth, which needs to be verified. Before the verification, I would like to ask everyone a question , Do you think there is a force that can make objects fall from a high place to a low place?"

"I think there is no doubt about this. With this force, you can imagine that you are lying on the ground, and someone is stepping on you and pressing you down. If there is an abyss below you, then it is this force that presses on you that brings The man fell."

"We must first clarify a problem. When you are stepped on at the top of the mountain, you feel the same power when you are stepped on at the bottom of the mountain. But the question arises, why is the water falling from a high place more powerful, while the water falling from a low place is more powerful? What about the force of the falling water? That's the whole point of the problem, and that's why I'm talking about force and force separately."

Seeing that everyone was starting to wonder and start to think, Chen Jian finally set up the board, glanced at the brother who operated the water drop timer, and got ready.

"Now we know that the downward force on the ball is the same when it is placed on the ground as it is when it is placed on a high place. So when the ball falls, is the speed the same? Or is the speed increasing? Quick? This cannot be observed directly with the naked eye, but it can be tested with this small wooden trough."

After the connection was completed, Chen Jian repeated the experiment [-] times with different heights and different lengths.

In the end, relying on the drop timer and the inclined plank, a result was obtained that all these people must agree with.Not to agree with his words, but to agree with the experiment repeated twenty times, the drop timer and the ruler right in front of his eyes.

After writing the results, distance and time of each measurement on the wooden board, Chen Jian said: "Now, we can clearly say that the speed of this small ball rolling down the inclined wooden board is getting faster and faster. And if we Get rid of some friction and air... You already know that air is qualitative and invisible, so it will hinder the small ball... Then roughly, it can be seen..."

Turning around, he sorted out the relationship between the distance of time and said: "It can be seen that within the same period of time, the distance the ball rolls from top to bottom is related to the square of time. Why is it related to the square of time? Let's assume that the speed of the ball It is getting faster and faster, but the rate of increase is the same in every minute time-please note that this is the rate of increase and not the speed itself."

After taking out the plaster pen and writing according to this speculation, there was thunderous applause again. According to the simple algorithm of constant speed increase, the answer obtained is basically the same as the conclusion proved by the experiment.

"From this, we can deduce that if a force is applied to an object all the time, if the force remains constant, then the object will continue to accelerate, and the rate of increase in each minute time will be the same."

"Then, if this conclusion is correct, it proves that a small ball moving on a smooth surface does not have a kind of force after we let go. Otherwise, it will get faster and faster instead of staying still. On the contrary, Because of friction, the ball will be slower and slower, which just proves my hypothesis: any object has a tendency to maintain the status quo, no matter whether the status quo is in motion or at rest. If no force is applied to the object , then this object will always remain. Similarly, the force is to change the object to maintain the status quo, not to maintain the status quo.”

"We can call this state of maintaining the current status quo inertia. In other words, the force changes the inertia of the object."

"So if we assume that a stone is not resisted by the air, what shape will it be in the air?"

Turning around again, I wrote it out using a quadratic equation on the Cartesian coordinate system.

"Obviously, if there is no air resistance, the stone's flying trajectory is a curve, and the calculation formula is a simple quadratic equation. As long as we know the speed of the stone and the force of the downward pull, we can You can know the position of this stone at any time, time distance, and under any conditions."

"Switching to artillery shells is the same. This can make our artillery technology a lot better than that of Qi."

"So, what is the approximate force of this downward pull? How much acceleration can it provide? We don't have accurate clocks and watches today, so it is difficult to measure, but it can be roughly calculated using geometric methods."

"Just before the calculation, we need to prepare and determine a concept in advance. This concept is like defining a circle and a straight line. It cannot be proved, but it is the basis of the entire geometry. Or that sentence, maybe there are other explanation, but the system needs that foundation."

This time everyone nodded silently, Chen Jian took a deep breath and started the most difficult step.

He took out three springs and demonstrated the parallelogram law of force. This is a theory that everyone has accepted before. Although the philosophical concept of force is vague, they understand the existence of the parallelogram law.

Then he explained the relationship between force and reaction force in a popular way. This explanation did not use too much mathematical reasoning, but used some common phenomena. In addition, the dualistic philosophy of the entire ethnic group easily accepts action force and reaction force. This can be regarded as a good fate hundreds of years ago.

Finally, there is the most important question.

Chen Jian picked up a steelyard, and there was a piece of iron on the scale. After reading the number, Chen Jian said, "This piece of iron weighs two catties."

Then he took out a magnet and put it on the ground, and put the weighing pan on the magnet for weighing.

"Now, this piece of iron weighs three catties. So, gentlemen, why is that?"

"Because you put a magnet under it, and the magnet attracts iron."

One person directly gave the answer, and Chen Jian smiled and said, "Then here comes the question, assuming we live on a huge magnet, does the iron appear to us heavier than it is now? But this piece of iron has not changed. Is it an inherent property of iron? If it is, then the iron will change when it is placed in a place full of magnets, which proves that the iron is not the same as before. But we all know that iron is still the same as before, so can it be said that , Light and heavy are not inherent and constant properties of iron?"

"For another example, why do people have to fall? Could it be that there is a force similar to a magnet, but this magnet not only attracts iron, but can have a kind of attraction to any object, so people will fall. Then suppose In this case, the suction has increased or decreased, have we changed? If we have not changed, does that mean that our nature has not changed?"

"Since we are still us, we are still here, and our essence has not changed, is weight just an external manifestation of a force exerted on us, rather than the essence we possess?"

"In other words, this essence is part of who we are. Chopped, pressed, roasted, frozen... this essence will not change. This essence is what I call The thing formed by the aggregation of particles. As long as the particles are not recombined or disassembled, this essence will not change. Even if the smallest particles that make up our body are taken out one by one, as long as the particles themselves are not broken Or recombined, then our essence has not changed."

Speaking of this, Chen Jian picked up the prepared bowl, smashed it into pieces, and said: "You see, the essence of the bowl has not changed. The bowl is no longer a bowl in our eyes, but it is still a bowl from the perspective of particles." .If we can re-bond these debris, this is still a bowl but not the original bowl. The appearance has changed, but some things have not changed, so if the appearance is regarded as an essence of the bowl, it can be said that the appearance The essence has changed; but the essence of the bowl is not only the appearance, but also the particles, so in terms of the essence of the particles, the bowl has not changed.”

"Why, because bowls have many kinds of essences. What I'm talking about now is one of them. For example, I died and was burned to ashes. Someone pointed to my ashes and said it was Chen Jian, so..."

"So, the essence I'm talking about is called mass. It is the total collection of particles without recombination and particle splitting."

"Mass can be expressed by weight, but it is not weight. You must think about this issue clearly. Just like my hypothesis just now, assuming that the earth we live on has a special magnetic force that can attract everything other than iron, then we Receive this force and express it through weighing.”

"Let's say I weigh 160 pounds, but if I go to another place, the suction power of this place is twice as high as here, and I still haven't changed if I weigh it..."

"It's not difficult to understand, because the scale is a lever, so I am heavier, and the weight is also heavier. But... a different scale will be completely different, such as a spring. If I use a spring, I am 160 pounds here , I became 320 catties when I got there, but I am still me, my essence and quality have not changed, it has become the external environment.”

"So, mass is related to weight, but mass is not weight, it is just an expression of mass after it is subjected to force. If there is no force, there is no weight, but there is still mass."

"This is the most difficult circle to get around, just like force and energy. If everyone can't accept this concept, I can't explain everything after that. Just like, if you don't agree that one plus one equals two, then you can't calculate All subsequent arithmetic problems. There is no reason, just a definition, a concept, and a basis. You ask me why one plus one equals two? I can’t explain it, but it doesn’t mean I can’t use it to calculate difficult problems.”

"Of course, I'm just a hypothesis, so please don't refute it first, but read my inferences on the premise of agreeing with my hypothesis."

Chen Jian wiped his sweat. There was only one step between metaphysics and philosophy. The steam engine model at the beginning was really not important. On the contrary, these two definitions were the most difficult and most important.

If you can't tell the difference between force and energy, mass, force and weight, all subsequent problems can't be explained.

But precisely, these two things are philosophical categories, which are similar to theology in a sense, giving a definition and then making inferences based on this definition.

Mathematics is not science, and quality is not science.

The so-called problem is troublesome here.In fact, a steam engine can be built without scientists and craftsmen, but Chen Jian had to start from here to define the foundation.

The technique is simple, but the way is too difficult.

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