Lu Shuang took the test paper and read the questions carefully.

As shown in the figure, an elastic baffle is installed at the bottom end of a fixed inclined plane with an inclination angle of θ, and the masses of P and Q two blocks m and 4m respectively, and Q is stationary at A on the inclined plane.

At some point, P collides elastically with Q at a velocity v0 along the inclined plane. The dynamic friction factor between Q and the inclined plane is equal to ta

θ, let the maximum static friction be equal to the sliding friction.

There is no friction between P and the inclined plane, and there is no kinetic energy loss between the collision and the baffle.

Both blocks can be seen as particles, and the bevel is long enough that P will not collide with Q until its velocity is reduced to zero. The magnitude of the gravitational acceleration is g.

(1) Find the respective velocities of P and Q at the moment after the first collision, vP1 and vQ1;

(2) Seek the first

The second collision causes block Q to rise by a height h

；

(3) find the total height H of the block Q rising from point A;

(4) In order to ensure that P will not collide with Q before its velocity is reduced to zero, find the minimum distance s between point A and the baffle.

After reading a set of questions, Lu Shuang roughly understood the content.

After Fang Shitao finished speaking in twenty minutes, Lu Shuang got up and spoke.

"Such a simple question has to use such a complex method, and I doubt the strength of the other classmate. "Unabashedly, it's just mocking you.

Fang Shitao just sat down, his mouth was a little dry after talking for so long, and before he could drink his saliva, he heard someone making a lot of nonsense, and he was immediately unhappy.

"Then I don't know what this classmate thinks? It's also a waste of everyone's time. Fang Shitao sneered mercilessly.

Although it is said that it is just the first day of school, Fang Shitao does not plan to keep a low profile.

"Okay, then since classmate Fang can't, then I'll teach you!" Lu Shuang waved his hand, revealing a reluctant look. As for the rest of the class, they were already surprised.

Anyone who has questioned Lu Shuang. Almost all slapped in the face. For a while, I still have a lot of respect for this Lu-swell-Shuang in the class.

Especially Ye An, after being hit by Lu Shuang and Fang Shitao, he was about to doubt his life. completely lost the mind of offending Lu Shuang.

Lu Shuang is pretending to be × again, and the old horse is not used to landing Lu Shuang. He knocked on the podium directly, cleared his throat and said, "Lu Shuang, is there any other better way to share it with everyone?

Lu Shuang, who was originally going to continue pretending, restrained himself for a moment, and then began to use his own methods.

"(1) For the first collision between P and Q, the direction of the initial velocity of P is taken as the positive direction, which is obtained by the law of conservation of momentum

①

It is obtained from the law of conservation of mechanical energy

②

Synoptic (1) (2).

③

④

Therefore, the velocity of P after the first collision is and the velocity of Q is (2) Let the height of Q rise after the first collision be h1, and the kinematic formula for Q is obtained

⑤

Synonymous (1), (2), (5).

⑥

Let the velocity of P when it moves to the position just before the second collision with Q is, and the kinetic energy theorem is obtained for P after the first collision and before the second collision

⑦

Synonym (1), (2), (5), (7).

⑧

For the second collision between P and Q, the velocities of P and Q after the collision are respectively , which is obtained by the law of conservation of momentum

⑨

It is obtained from the law of conservation of mechanical energy

⑩

Lianli (1), (2), (5), (7), (9), (10).

⑪

⑫

Let the height of Q rise after the second collision be h2, and the kinematic formula for Q is obtained

⑬

Lianli (1) (2) (5) (7) (9) (10) (13).

⑭

Let the velocity of P when it moves to the position just before the third collision with Q is, and the kinetic energy theorem is obtained for P after the second collision and before the third collision

⑮

Synonym (1), (2), (5), (7), (9), (10), (13), (15).

⑯

For the third collision between P and Q, let the velocities of P and Q after the collision be , respectively, which is obtained by the law of conservation of momentum

⑰

It is obtained from the law of conservation of mechanical energy

⑱

Lianli (1) (2) (5) (7) (9) (10) (13) (15) (17) (18).

⑲

⑳

Let the height of Q rise after the third collision be h3, and the kinematic formula for Q is obtained

21

Lianli (1) (2) (5) (7) (9) (10) (13) (15) (17) (18) 21

22

......

In summary, it can be seen that the first

After the collision, block Q rises by a height of （

=1，2，3...... ） 23

(3) When P and Q reach H, the velocity of the two blocks to this point can be regarded as zero, and the whole process of the motion of the two blocks is obtained by the kinetic energy theorem

24

Solution

25

(4) Let the time required from the first collision of Q to the velocity decrease to zero t1, which is obtained by the kinematic formula

26

Let the velocity of P when moving to the bottom of the inclined plane be t2, which is obtained by the kinematic formula

27

28

Let the time of uniform deceleration motion at the point where P decreases to zero after the first collision from point A to Q is t3

29

When the distance between point A and the bezel is the smallest

30

Synaptic 2627282930, you can get the result. ”

"Ahem, I said it too fast, I don't know if I can understand it with the comprehension ability of ordinary people. ”

For a while, Lu Shuang spent less than ten minutes, analyzing and explaining the process at the same time, and the crackling words were like fried beans. Even after a while, the students in the class didn't react.

The class quietly dropped the needle, even the old horse was looking carefully at the moment, thinking about the method of landing double talk, on the whole, this is the most concise way to solve the problem.

Not bad indeed.

"Lu Shuang's speech is very wonderful and detailed, let us applaud Lu Shuang and express our gratitude. Lao Ma put the test paper on the table and said to the other students in the class.

Suddenly, all the students in the class reflected this, and immediately applauded the landing double. Lu Shuang, on the other hand, accepted it calmly.

As far as his Super Saiyan has a brain domain development of up to 15%, isn't this kind of small problem a quick deal?

Lu Shuang accepted the worship of the students, but it was a complete insult to Fang Shitao, the new king. I talked tirelessly for more than 20 minutes, and I didn't see anyone applauding me.

And Lu Shuang crackled and said it, and he successfully solved the problem, and all his limelight was stolen by this surnamed Lu at this time. It's really infuriating!!

Of course, where did Lu Shuang have any effort to care about Fang Shitao's increasingly collapsed heart at this time? instead, he sank his consciousness into his brain and waited for the settlement of Dian Niang.

"You have successfully completed the quest and gained Awakening Points. ”

Okay, no matter how small a mosquito leg is, it's still a piece of meat. As for the rest, it doesn't matter.

On the other hand, Jiang Li, with a pair of beautiful eyes, was even more emotionally complicated, looking at Lu Shuang's appearance in front of him, he didn't know what he was thinking, but he became more and more determined to find Lu Shuang's plan to help with tutoring.

"Okay, Lao Lu, I can't see that you still have a few brushes. Wang Zhou poked Lu Shuang's little arm excitedly, and leaned down to say to Lu Shuang, who had just sat down on the side.

Of course, Lu Shuang knew Wang Zhou's thoughts, smiled at the guy, and then didn't speak again.

In short, after his very punctual slap in the face, this classmate Fang shouldn't really be able to figure out his own positioning. Of course, this backhand sent the past super double so that his ear scraper hurt a little.

After completing the task and getting a little awakening point, what should I do with it! I thought about it and Xiao Li Flying Knife cheats without adding points, and then shook my head, it's not time yet.