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Study 20 hours? Every day?

Regarding Wu Bin's answer, Lu Gang took out a handkerchief and wiped the sweat on his forehead, and then asked: You mean these 20 hours are all effective study time?

That's probably it.

Wu Bin didn't intend to talk too much, fearing that he would meet someone like Cai Guoping who would get to the bottom of things.

If you can really do it, you are not very powerful. I was also thinking about what learning experience you have that can be used to spread the word. Lu Gang thought for a while, But if you can learn like this, you should understand physics. Is it fun?

Yes, I find physics very interesting! Wu Bin answered affirmatively.

Hahaha, that's the truth, then keep working hard, maybe you will be another 985 seedling.

Thank you, Teacher Lu.

Well, thank you for answering the teacher's question. Let's go back to the classroom.

After Wu Bin left the office, Lu Gang walked to Yu Xuguang's desk and asked, Is it possible that you think 20 hours are effective study time?

I really don't know about this. I never worked so hard when I was studying. After all, I didn't do anything like playing ball and catching insects. Yu Xuguang shook his head.

From 0 to full score in one month...it seems like the only way to do it is by working so hard.

That's not what I'm saying. You can get a score of 70 or 80 with hard work, but it's not that easy to get a perfect score.

Yeah, oh, I have been teaching for a long time, and I can see all kinds of little monsters.

Who says it isn't?

After they finished speaking, the two looked at each other and smiled, feeling emotional.

…

Wu Bin, who was walking back to the classroom, was still wondering whether to study chemistry or trigonometry, when he was stopped by Cai Guoping, who was standing at the door of the class.

Have you finished talking to Teacher Yu?

Well, we're done talking. Wu Bin nodded.

Well, come with me and I'll show you something good.

Ah? Teacher, why don't you be later...

Wu Bin is very uncomfortable now because he has not studied for nearly an hour!

Why are you late? Come quickly. I guarantee you will like it.

After Cai Guoping finished speaking, he dragged Wu Bin towards the office.

As soon as he entered the office, Wu Bin immediately felt a sharp glare. He knew it was from Chen Fang, their class teacher, without even looking.

The reason...of course he himself understands it. Although he often takes time to memorize words and so on, the time he invests in English is still too little compared to physics and mathematics. If he gets a score of 50 or 60 in this exam, it is probably because of his reading. The strategy of choosing B for all questions is correct.

Following Cai Guoping to his desk, Wu Bin saw Cai Guoping handing him a paper and a pen.

Come on, let's do it.

As soon as he saw the paper, Wu Bin's mood immediately improved a lot. He took the pen handed over by Cai Guoping and started reading the questions.

Some people imagine that when the spacecraft enters the return to Earth program from orbit, a small space probe can be launched to save energy by taking advantage of the spacecraft's need to decelerate. As shown in the figure, the spacecraft flies around the earth on a circular orbit I, and its orbit radius is k times the radius of the earth (k is greater than 1). When the spacecraft passes point A of orbit I, the launch device on the spacecraft works briefly to launch the detector in the original direction of movement of the spacecraft, so that the detector can completely escape the gravitational range of the earth, that is, it reaches the speed when it is infinitely far from the earth. is exactly zero, and the spacecraft moves forward along the elliptical orbit II after launching the detector, and the distance from its perigee B to the center of the earth is approximately the radius R of the earth. During the above process, the mass of the spacecraft and detector can be regarded as unchanged. It is known that the acceleration due to gravity on the earth's surface is g.

(1) Find the speed of the spacecraft moving in orbit I;

(2) If it is stipulated that the gravitational potential energy is zero when two particles are infinitely far apart, then the gravitational potential energy Ep of two particles with masses M and m when the distance is r = r divided by GMm, where G is the gravitational constant. During the movement of the spacecraft along orbit I and orbit II, the sum of its kinetic energy and gravitational potential energy remains unchanged. During the motion of the detector after being ejected, the sum of its kinetic energy and gravitational potential energy also remains unchanged.

① Find the speed of the detector when it just leaves the spacecraft;

② It is known that when the spacecraft moves along orbit II, the speed of passing point A and point B is inversely proportional to the distance from these two points to the center of the earth. According to the calculation results, explain what conditions the mass ratio of the spacecraft and detector should meet in order to realize the above motion process of the spacecraft and detector.

Below the title is a picture of the spacecraft returning to Earth.

‘This question is interesting. ’

Wu Bin, who was holding the pen, had his eyes shining.

The first question is not difficult. It is very simple to combine the two equations to find the answer that roughly calculates the first cosmic speed.

Wu Bin picked up the pen and started writing.

Solution: Assume the mass of the earth is M, the mass of the spacecraft is m, and the mass of the detector is m’. When the spacecraft and the detector move in a circle around the earth together, the speed is vo

According to the law of universal gravitation and Newton’s second law, there is (kR) divided by GM (m+m’) (m+m’) kR divided by vo

For an object with mass mo near the ground, mog=GMmo/R

Solution: vo=root k divided by gR

The first question is very simple, but the second question is a bit more interesting. The question gives a formula for gravitational potential energy, and there are quite a few pitfalls in it. In short, don’t panic, don’t think about why it is infinite, why gravity Potential energy has a negative sign, it’s all something you have to think about after you’ve done it.

First of all, it is obvious that the sum of kinetic energy and potential energy remains unchanged, and the expression of mechanical energy conservation is Ek+Ep=0

So you can put the Ep band into it.

get

1/2mv-kR/GMm=0

The solution is: V’ = root kR/2gR GM = root 2vo = root kR 2gR

The second question ② continues. First, the question gives a condition (essentially Kepler’s second law)

That is RvB=kRVA

Generally speaking, writing this step should be enough.

Then it is obvious that there is mechanical conservation at two points AB.

1/2mvB-R divided GMm=1/2mvA-KR divided GMm

After thinking about it, Wu Bin discovered that there was no other mass here.

‘Hmm…don’t settle the equation when something happens! ’

‘The only equation that can communicate these two masses is the momentum conservation equation. ’

Thinking of this, Wu Bin nodded unconsciously and continued writing.

(m+m’)vo=mvA+m’v’

Finally, because the speed of the spacecraft passing point A and point B is inversely proportional to the distance from these two points to the center of the earth, that is, RvB=kRvA

Solution: m' divided by m=1-root k+square root of 2/1 2-1

call……

Wu Bin let out a breath and put down the pen.

Well, the steps are all right and you get all the points, that's ok! Cai Guoping was very pleased after reading this and patted Wu Bin on the shoulder.

It's quite interesting. I'll do it next, teacher. After Wu Bin finished speaking, he moved on to the next question.

But Cai Guoping suddenly pulled out the paper and said, No need to do it. Since you can solve this problem so easily, it should be no problem to participate in the competition.

Competition? Wu Bin was stunned.

Yes, the National High School Physics Competition!

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PS: Some symbols in the question are not easy to type... so I replaced them.