"20 hours of study? Every day? ”

In response to Wu Bin's answer, Lu Gang took out a handkerchief and wiped the sweat on his head, and asked: "You mean that these 20 hours are all effective study time?" ”

"I guess so."

Wu Bin didn't plan to talk too much, for fear of meeting someone like Cai Guoping who would get to the bottom of it.

"If you can really do it, it's not ordinary, I think you can have any learning experience that can be popularized." Lu Gang thought for a moment after speaking, "But if you can learn like this, you should understand the fun of physics, right?" ”

"Yes, I think physics is very interesting!" Wu Bin replied in the affirmative.

"Hahaha, that's the truth, then you continue to work hard, maybe it's a 985 seedling again."

"Thank you, Mr. 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, "Do you think 20 hours is an effective study time?" ”

"I really don't know this, I didn't work so hard when I was studying, after all, I didn't pull down playing ball and catching insects or anything." Yu Xuguang shook his head.

"From 0 to perfect in a month...... It seems that only this is the only way to do it. ”

"That's not what you say, you can work hard for seventy or eighty points, but it's not so easy to get a perfect score."

"It's also ha, oops, it's been a long time to teach, and any little monster can be seen."

"Who's to say it isn't."

The two looked at each other and smiled after speaking, and sighed with emotion.

……

Wu Bin, who was walking on the way back to the classroom, was still struggling with whether to watch chemistry or trigonometry, when he was stopped by Cai Guoping, who was standing at the door of the class.

"Finished talking to Teacher Yu?"

"Well, that's it." Wu Bin nodded.

"Okay, come with me, I'll show you something good."

"Huh? Teacher, don't you want to be late......"

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

"What's late, hurry up, make sure you like it."

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

As soon as he entered the office, Wu Bin immediately felt that he was glared at by a sharp eye, and he didn't need to look at him to know that it was from their head teacher Chen Fang.

Why...... Of course, he himself understands that although he often finds time to memorize words or something, the time invested in English is still too little compared to physics and mathematics, and it is estimated that he can have a fifty or sixty points in this exam, which is considered his strategy of choosing B in all reading questions.

Following Cai Guoping to his desk, Wu Bin saw Cai Guoping hand him a roll and handed him a pen.

"Come on, do it."

As soon as he saw the volume, Wu Bin's mood immediately improved a lot, and he took the pen handed over by Cai Guoping and looked at the question.

Some people imagine that when the spacecraft enters the re-Earth program from its orbit, it can take advantage of the spacecraft's need to slow down to launch a small space probe, so as to achieve the purpose of energy saving. As shown in the figure, the spacecraft orbits the Earth in a circular orbit I., and its orbital radius is k times the radius of the Earth (k is greater than 1). When the spacecraft passes through point A of orbit I., the launcher on the spacecraft works for a short time, shoots the probe out of the original direction of motion of the spacecraft, and makes the probe completely out of the gravitational range of the earth, that is, the velocity when it reaches infinity from the earth is exactly zero, and the spacecraft moves forward along the elliptical orbit II after launching the probe, and the distance from perigee B to the center of the earth is approximately the radius of the earth. The mass of both the spacecraft and the probe can be considered unchanged in the above processes. The acceleration due to gravity on the Earth's surface is known to be g.

(1) Find the velocity of the spacecraft in orbit I.

(2) If the gravitational potential energy is zero when two particles are infinitely far apart, then the gravitational potential energy Ep=rm of r when the two particles with masses M and m are at a distance of r, where G is the gravitational constant. The sum of kinetic energy and gravitational potential energy remains unchanged during the motion of the spacecraft along orbit I and orbit II, and the sum of kinetic energy and gravitational potential energy remains unchanged during the motion of the probe after it is ejected.

(1) Find the velocity of the probe when it just leaves the spacecraft;

(2) It is known that the velocity of the spacecraft passing through points A and B is inversely proportional to the distance from these two points to the center of the earth during the movement of the spacecraft along orbit II. According to the calculation results, it is explained what conditions should be met by the ratio of the mass of the spacecraft to the probe in order to realize the above-mentioned spacecraft and probe motion process.

Below is a diagram of the spaceship returning to Earth.

That's a kind of interesting question. ’

Wu Bin's eyes lit up with a pen.

The first question is not difficult, and it is very simple to find the answer to the approximate velocity of the first universe by combining the two equations.

Wu Bin picked up the pen and began to write.

Solution: Let the mass of the earth be M, the mass of the spacecraft be m, and the mass of the probe be be m', and the velocity of the spacecraft and the probe in a circular motion around the earth together is vo

According to the law of gravitation and Newton's second law, there are (kR)² GM(m+m')(m+m') kR vo²

For objects with mass mo near the ground, there is mog=GMmo/R²

Solution: vo = gR of the root number k

The first question is very simple, but the second question is a bit interesting, the question gives a formula of gravitational potential energy, there are quite a lot of small pits, in short, don't panic, don't think about why it is infinite, why gravitational potential energy has a negative sign, this is all something to think about after doing it.

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

So you can substitute the Ep tape into it.

get

GMm = 0 of 1/2 mv²-kR

It is solved: V' = 2 gR of the root number kR = 2 gR of the root number k

The second question (2) continues, first of all, the question gives a condition (in essence, Kepler's second law)

i.e. RvB = kRVA

Generally speaking, writing this step should be a point.

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

GMm of 1/2 mvB²-R = GMm of 1/2 mvA²-KR

Counting this, Wu Bin found that there was no other quality here.

'Hmm...... Don't decide the equation in case of trouble! ’

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

Thinking of this, Wu Bin nodded unconsciously and continued to write.

（m+m’）vo=mvA+m'v'

Finally, the speed of the spacecraft passing through points A and B is inversely proportional to the distance from these two points to the center of the earth, i.e., RvB = kRvA

Solution: m' m = 1 - root number k + 2 out of 1 root number 2-1

"Hoo ......"

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

"Well, the steps are all right, and you can get all the scores!" Cai Guoping was very pleased to see it, and patted Wu Bin's shoulder.

"It's interesting, then I'll do it, teacher." After Wu Bin finished speaking, he meowed to the next question.

But Cai Guoping suddenly pulled 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." ”

"Race?" Wu Bin was stunned.

"Yes, the National High School Physics Competition!"

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PS: Some symbols in the title are not easy to play...... I replaced it.