Qiao Mu thought that it was time to bring Nangong Yan back.
He didn't bring Nangong Yan directly to the capital after taking him out of the First Emperor's mausoleum. Instead, he sent him to Ah Country to resolve the problem of his identity and loyalty.
Time passed quickly, and Qiao Mu was already sitting in the examination hall for the preliminary round of the district physics competition.
Some people imagined that when the spacecraft entered the return to Earth from orbit, they could use the opportunity when the spacecraft needed to decelerate to launch a small space probe to achieve the purpose of saving energy.
As shown in the picture, the spacecraft was flying around the Earth on a circular orbit I. Its orbit radius was k times the Earth's radius (k was greater than 1).
When the spacecraft passed through point A of orbit I, the launch device on the spacecraft worked briefly to pull the probe out along the original direction of motion of the spacecraft, and the probe was able to completely leave the gravitational range of the Earth, that is, the speed when it reached infinity from the Earth was exactly zero. After the spacecraft launched the probe, it moved forward along the oval orbit II, and the distance from its perigee B to the earth's core was approximately the Earth's radius R.
The mass of the spacecraft and the probe could be considered constant during the process. It is known that the gravitational acceleration on the Earth's surface is g.
(1) Find the speed of the spacecraft in orbit I;
(2) If the gravitational potential energy of two particles is zero when they are infinitely far apart, then the mass is M and GMm respectively, where G is the gravitational constant. During the spacecraft's movement along Orbits I and II, the sum of its kinetic energy and gravitational potential energy remained unchanged. After the probe was ejected, the sum of its kinetic energy and gravitational potential energy also remained unchanged.
(1) Find the speed of the probe when it left the spacecraft;
(2) It is known that the speed of the spacecraft passing through points A and B is inverse to the distance from these two points to the earth's core. According to the calculation results, in order to realize the motion process of the spacecraft and the probe, the mass ratio of the spacecraft and the probe should meet what conditions.
Below the question was a picture of the spacecraft returning to Earth.
"This question is interesting."
Qiao Mu thought to herself as she held the pen.
The first question wasn't difficult. It was a very simple question to find the answer that roughly calculated the speed of the universe.
Qiao Mu picked up the brush and started writing.
Solution: Let the mass of the Earth be M, the mass of the spacecraft be m, and the mass of the probe be m. When the spacecraft and the probe are moving in a circular motion around the Earth, the speed is Wo.
According to the law of universal gravitation and Newton's second law, there is (kR) 2/GM (m m')(m m) kR/vo2
The solution is: number k/gR
The first question was very simple, but the second question was a little interesting. The question gave a formula for gravitational potential energy. There were quite a lot of small holes in it. In short, don't panic first. Don't think about why it was infinite or why the gravitational potential energy had a negative sign.
First of all, it's obvious that the kinetic energy and potential energy are constant, and the expression for the conservation of mechanical energy is Ek
Therefore, he could bring Ep into it.
get
1/2 MV2-
The solution is: V '= sign 2gR/k
The second question continued. First, the question gave a condition (in essence, Kepler's second law).
RVA
Generally speaking, writing this step should give one point.
Then, it was obvious that there was mechanical conservation at points A and B.
Qiao Mu realized that there was no other mass here.
"If you can't make a decision, write an equation!"
"The only equation that can communicate these two masses is the conservation of momentum equation.”
Qiao Mu didn't pause at all as she continued writing with her pen.
（m m'）vA mv
Finally, because the speed of the spacecraft passing through points A and B is inverse to the distance from these two points to the core, RvA
The solution is: m-root sign k 1/2/2 root sign 2-1
There were only a few questions on the entire test paper, and Qiao Mu spent half an hour to finish all of them. He was not in the mood to continue sitting in the examination hall and waiting for the end of the examination time.
So he raised his hand and said,"Teacher, I've finished answering. I have to hand in my paper."”
Qiao Mu's actions caused the other examinees in the examination hall to tremble inwardly. Who was this? He was so awesome that he had to hand in his paper before he could even solve a single question.
Inside was a fair and clean student, the representative of Elite High School, Qian San. He even took another glance at Qiao Mu.
"There's actually someone who's faster than me. It seems that the first place this time is a bit of a risk.”
Qian San Yi was a top student at Elite High School. He was also in his third year of high school this year. When he first joined Elite High School, he did not choose it himself. Instead, he was " recruited " by Elite High School at a high price.
Not only did they not have to spend money to study, but they could also get a salary. As long as they won the competition, the school would give them a bonus.
But now, he had nothing to do with the highest reward.
With Qiao Mu around, Qian San had nothing to do with her!
"Qiao Mu, why did you come out so quickly?”
Teacher Liu from Spring Breeze Middle School stopped Qiao Mu and asked as she walked out of the examination hall.
"I've finished all the questions. Teacher, don't worry. They should all be correct.”
"Then are you confident that you can get first place?”
"Teacher, I'm not bragging. As long as no one is playing tricks, I'm sure that all my answers are correct.”
This book comes from：m.funovel.com。