Xueba's Sea of ​​Stars

Chapter 19 National High School Physics Competition

"Study 20 hours? Every day?"

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

"It should be."

Wu Bin didn't intend to talk too much, he was afraid that he would meet someone like Cai Guoping who would ask questions.

"If you can really do it, you're not so good. I'm still thinking about what you can learn to spread." Lu Gang finished thinking for a while, "But if you can learn like this, you should understand physics. Is it fun?"

"Yes, I think physics is very interesting!" Wu Bin answered with certainty.

"Hahaha, that's the reason, then you keep working hard, maybe you'll be another 985 seedling."

"Thank you, Teacher Lu."

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

When Wu Bin left the office, Lu Gang went to Yu Xuguang's desk and asked, "Do you think it's possible that 20 hours are valid study time?"

"I really don't know. I never worked so hard when I was studying. After all, I didn't fail in playing ball and catching bugs." Yu Xuguang shook his head.

"From 0 points to full marks in one month... It seems that it can only be achieved through hard work."

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

"That's right, oops, it's been a long time teaching, and I can see all kinds of little monsters."

"Who said it wasn't."

The two looked at each other and smiled, feeling emotional.

……

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

"Have you finished talking with Teacher Yu?"

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

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

"Ah? Teacher, why don't you wait later..."

Wu Bin is very uncomfortable now because he has not studied for nearly an hour!
"Why is it late, hurry up and 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 glared by a sharp stare. He didn't even need to look at him to know that it was from their homeroom teacher, Chen Fang.

The reason... Of course he himself understands that although he often finds time to memorize words and so on, compared with physics and mathematics, he still spends too little time on English. It is estimated that he can score [-] or [-] in this exam. The strategy of selecting all questions B is correct.

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

"Come on, let's see."

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

Someone imagines that when the spacecraft enters the program of returning to the earth from the orbit, a small space probe can be launched when the spacecraft needs to slow down, so as to achieve the purpose of energy saving.As shown in the figure, the spaceship flies around 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 spaceship passes through point A of orbit Ⅰ, the launching device on the spaceship works briefly to launch the probe along the original direction of movement of the spaceship, and make the probe just completely out of the gravitational range of the earth, that is, to reach the speed when it is infinitely far away from the earth. is exactly zero, and the spacecraft moves forward along the elliptical orbit II after launching the probe, and the distance from its perigee B to the center of the earth is approximately the radius R of the earth.In the above process, the mass of the spacecraft and the detector can be regarded as unchanged.The acceleration due to gravity on the Earth's surface is known as 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 the two particles are infinitely far apart, then the gravitational potential energy Ep=GMm of r when the two particles with masses M and m are separated by r, 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 constant, and the sum of its kinetic energy and gravitational potential energy also remains unchanged during the motion of the probe after it is ejected.

①Find the velocity of the probe when it just left the spacecraft;

② It is known that during the movement of the spaceship along the track II, the speed of passing through 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, in order to realize the motion process of the spacecraft and the detector, what conditions should be satisfied by the mass ratio of the spacecraft and the detector.

Below the title is a picture of the spaceship returning to Earth at that time.

'This question is a bit interesting. '

Wu Bin's eyes sparkled while holding the pen.

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: Suppose the mass of the earth is M, the mass of the spaceship is m, and the mass of the probe is m', when the spaceship and the probe move around the earth together, the speed is vo
According to the law of universal gravitation and Newton's second law, there are (kR) points of GM (m+m') (m+m') kR points of vo
For an object with a mass mo near the ground, mog=GMmo/R
Solution: vo=gR of the square root of k
The first question is very simple, but the second question is a bit more interesting. The question gives a formula for gravitational potential energy. There are quite a few pitfalls in it. In short, don’t panic. Don’t think about why it is infinite and why gravity is 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 belt into it.

get
2/1mv-kR/GMm=0
Just solve: V'= 2/2 of root kR GM=root 2vo=[-]/k of root gR
The second question ②Continue, the first question gives a condition (the essence is Kepler's second law)

That is, RvB=kRVA
Generally speaking, writing this step should have one point.

Then obviously there is mechanical conservation at two points AB.

2/1 of mvB-R of GMm=2 of 1mvA-KR of GMm
Counting this, Wu Bin found that there is no other quality here.

'Hmm... I don't decide to formulate the equation when things happen! '

'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 through 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
解得：m'分之m=1-根号k+1分之2分之根号2-1
"call……"

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

"Well, the steps are all right, you can get all the points, that's ok!" Cai Guoping patted Wu Bin's shoulder very relieved after reading it.

"It's very interesting. I'll do it again, teacher." After Wu Bin finished speaking, he moved on 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."

"Competition?" Wu Bin was taken aback.

"Yes, the National High School Physics Competition!"

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PS: Some symbols in the title are not easy to type... I just replaced them.

(End of this chapter)