Scholar’s Starry Sea

"Study for 20 hours? Every day?"

For Wu Bin's answer, Lu Gang took out a handkerchief and wiped the sweat on his forehead, and then asked: " Are you saying that these 20 hours are all effective study time?"

"Should be considered."

Wu Bin did not intend to talk too much, afraid of encountering Cai Guoping That's going to get the bottom line.

"If you can really do it, it's not so good. I still think about what you can learn to popularize it." Lu Gang finished thinking about it, "but you can learn this way If you do, you should understand the fun of Physics, right?"

"Yes, I think Physics is very interesting!" Wu Bin answered very positively.

"hahaha, this is the truth, then you continue to cheer, maybe it is a 985 seedling again."

"Thank you Teacher Lu."

"Um , Thank you for answering the teacher’s question, go back to the classroom."

Wait for Wu Bin to leave the office, Lu Gang walked to Yu Xuguang’s desk and asked: "You think 20 hours are effective learning Is time possible?"

"I really don't know this. I didn't fight like this when I was studying. After all, I didn't catch any bugs while playing basketball." Yu Xuguang shook his head.

"A month from 0 points to full marks...It seems that you can only do this by doing this."

"This is not the case. Seventy-eighty points can be worked hard. It’s not that easy to come out with full marks."

"Also, Aiya, I have been teaching for a long time. I can see any monster."

"Who said Not really."

After speaking, the two of them looked at each other and smiled, and they became emotional.

……

Wu Bin, who was walking on the way back to the classroom, was still struggling whether to look at the Chemistry or the trigonometric function, so he was stopped by Cai Guoping, who was standing at the door of the class.

"Have you finished talking with Teacher Yu?"

"Well, I'm finished talking." Wu Bin nodded.

"Well, come with me, I will show you something good."

"Huh? The teacher, please be late..."

Wu Bin is very uncomfortable now, because he hasn't studied for nearly an hour!

"Whether it is late, come hurry up and make sure you like it."

Cai Guoping dragged Wu Bin to the office after he said it.

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

The reason... Of course he understands it himself. Although he often takes the time to recite vocabulary, he still spends too little time in English compared with Physics Mathematics. This exam can have a fifty- Sixty points are estimated to be his strategy of choosing B for all reading questions.

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

"Come, do it and see."

As soon as I saw the paper, Wu Bin's mood immediately improved a lot. After receiving the pen handed over by Cai Guoping, I started to see the question. .

Someone imagined that when the spaceship enters the return to Earth program from the orbit, the spaceship needs to decelerate and launch a small space probe to save energy. As shown in the figure, the spaceship flies around Earth on a circular orbit I, and its orbit radius is k times the Earth radius (k is greater than 1). When the spaceship passes through point A of the orbit I, the launch device on the spaceship works briefly to shoot the detector along the original motion direction of the spaceship, and make the detector completely out of the gravitational range of Earth, that is, the speed when it reaches infinity from Earth It happens to be zero, and the spaceship 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 Earth radius R. In the above process, the quality of the spaceship and the detector can be regarded as unchanged. It is known that the gravitational acceleration on the Earth's surface is g.

(1) Find the velocity of spaceship in orbit I;

(2) If the gravitational potential energy is zero when the two particles are infinitely apart, the masses are M and m respectively The gravitational potential energy Ep=GMm divided by r when the two particles are separated by r, where G is the gravitational constant. During the movement of the spaceship along Orbit I and Orbit II, the sum of its kinetic energy and gravitational potential energy remains unchanged, and the sum of its kinetic energy and gravitational potential energy also remains unchanged during the movement of the probe after being shot.

①Find the velocity of the detector when it leaves the spaceship;

②It is known that the velocity of the spaceship passing through point A and point B is the same as the two points during the movement of the spaceship along the track II. The distance to the center of the earth is inversely proportional. According to the calculation results, explain what conditions should be satisfied by the ratio of spaceship to the mass of the detector in order to realize the motion process of the spaceship and the detector.

Spaceship returns to Earth when the title is drawn.

'This question, Interesting. '

Wu Bin's eyes glowed while holding the pen.

The first question is not difficult. The two simple equations are combined to find the answer to roughly the first cosmic velocity.

Wu Bin picked up the pen and started writing.

Solution: Suppose the mass of Earth is M, the mass of spaceship is m, and the mass of the detector is m'. When the spaceship and the detector make a circular motion around Earth, the velocity is vo

According to Gravity's law and Newton's second law, there is (kR) GM of ² (m+m') (m+m') vo² of kR.

For objects with a mass of mo near the ground, there is mog =GMmoR²

Solved: vo=gR of the root sign of k

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

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

So we can put Ep into it.

Get

1/2 of mv²-kR GMm=0

Then we can solve: V'=root number 2/2 of kR GM=root number 2vo =Round sign 2gR/k

The second question ②Continue, first the question is given a condition (essentially Kepler's second law)

that is, RvB=kRVA

Generally speaking, you should get a point if you write this step.

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

1/2 mvB²-R/GMm=1/2mvA²-KR/GMm

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

'Hmm...I can't settle the equation in case of trouble! '

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

Think of Wu Bin's unconscious nodded, and continue to write.

(m+m')vo=mvA+m'v'

Finally, because of the speed of spaceship through point A and point B, I laughed and the distance between these two points to the center of the earth It is inversely proportional, that is, RvB=kRvA

The solution is: m'th of m=1-root number of k+1 2nd of root number 2-1

"Call... …"

Wu Bin sighed and put the pen down.

"Well, the steps are all right, you can take all the scores!" Cai Guoping was very pleased and slapped Wu Bin on the shoulder.

"It's very interesting. Then I will do it next to the teacher." After Wu Bin finished speaking, he next question.

But Cai Guoping suddenly took 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 taken aback.

"Yes, the National Physics Competition for High School Students!"

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PS: There are some symbols in the title that are not easy to type... so I replaced them.