After taking the advice, I became a top student.

Chapter 36 What if the surface isn't smooth?

Xihua University, Huang Xinyuan's dormitory

Late at night, they stopped playing League of Legends and sat in front of their computers waiting for Chen Mo's live stream.

Huang Xinyuan is completely captivated by Chen Mo.

As for the other roommates, they were prepared to expose this fake academic genius.

There's also Liu Zhuoran from Rongcheng No. 2 Middle School. He completely forgot his promise to study harder today. As soon as he got home, he took out his phone and started watching Chen Mo's live stream. Watching others study was much more interesting than studying himself.

After several days of live streaming, Chen Mo's live stream has become quite popular, as many people are already waiting in the live stream room because the broadcast time is fixed.

As soon as Chen Mo started his live stream, there were already dozens of people in the room. The number of people quickly exceeded one hundred and was still climbing higher.

Chen Mo's questions on Zhihu are currently very popular, and he already has nearly a thousand followers on Zhihu. His Douyin followers have exceeded 30,000 and are still growing rapidly. With mutual traffic between Douyin and Zhihu, his self-media account has become quite successful.

[TikTok Spectacular]

[This is weird. A couple of days ago I saw someone livestreaming themselves sleeping, and hundreds of people were watching. Now, even more people are watching others study. You guys are really bored.]

There's a new guy here, can someone explain things to him?

[Explanation my ass, it's almost 10 o'clock, the streamer is about to start answering questions, experts can start asking questions, I'm already ready to kneel down]

[Send 10 hearts to the streamer, "Math is my dad"]

[Did the class beauty talk to you today? Send the anchor a can of yellow peaches*1]

As it got closer to 10 o'clock, viewers started sending virtual gifts.

This spectacle made some casual viewers who had come in to see what was going on, found nothing special, and were about to leave decide to stay and watch a little longer. After all, it seemed like the streamer was about to unleash something amazing.

Their curiosity was instantly piqued.

They wanted to see what it was about this streamer that attracted so many viewers.

A wooden block A of mass m_A = 1.0 kg moves to the right with an initial velocity v_0 = 2.0 m/s on a smooth horizontal surface and collides with a stationary wooden block B of mass m_B = 2.0 kg. The two blocks are connected by a light spring with a spring constant k = 100 N/m, and the spring is initially at its original length. Find the maximum compression of the spring during the motion.

Not long after Chen Mo looked up, a highlighted comment appeared in the live stream.

In the girls' dormitory of Rongcheng No. 1 High School, Shen Qingyi, who was watching a live broadcast, subconsciously started working on this problem, which was a problem about connecting bodies...

However, before she could even begin to think, the boy in the live stream spoke up, "This is a simple problem involving connected bodies. First, let's analyze it: A moves to the right and compresses the spring. The spring exerts a force to the right on B, causing B to start moving. So, when the velocities of A and B are equal, the compression of the spring reaches its maximum."

"With this premise in mind, solving this problem becomes much simpler."

"Because it is a smooth screen, momentum and mechanical energy are conserved. Let the maximum compression of the spring be x_m, and the common velocity of A and B at this time be v. According to the conservation of momentum, we have m_Av_0=(m_A+m_B)v."

陈末一边讲解,一边在草稿纸上写写画画起来,「又根据机械能守恆,我们可以得到,1/2m_Av_0^2=1/2(m_A+m_B)v_2+1/2kx_m^2.」

"By solving the two equations simultaneously, we can calculate that x_m = √6/15, which is approximately 0.163m."

In less than a minute, Chen Mo had already analyzed the question, solved it, and provided the answer, while also reaping some knowledge along the way.

[Holy crap, I'm impressed! Our teacher went over a similar problem today, and I can confidently say the streamer did a perfect job.]

[He's got some skills, but I still don't believe the streamer is just starting to learn physics. He might be a top student in his senior year of high school.]

[Seriously? All you experts in the livestream, is this all you've got? Don't you have any harder challenges? Bring them out, let me see where the streamer's limits are.]

At Qingfeng Times City, Jiang Fan nodded in satisfaction.

The question he just posed, while not particularly difficult, wasn't easy either. The analysis of the critical condition for a spring to reach its maximum compression, as well as the selection of the system and conserved quantities, still required a certain level of expertise.

The fact that the other person was able to do it so easily shows that they have a very solid foundation in physics.

Since that's the case, he typed on the keyboard with both hands and posted another paid comment.

What if the water surface isn't smooth?

A true expert's skill is immediately apparent upon their first move.

Although it was just a simple change to one condition, it instantly raised the difficulty of the problem by several levels.

Physics is different from mathematics. A physics problem, by simply changing a precondition, could very well represent a leap from classical mechanics to quantum mechanics. This is not an increase in difficulty, but a leap forward in the times.

Often, high school physics, in order to simplify things, involves analysis and calculations within the framework of classical mechanics. Although Jiang Fan's modified problem conditions did not reach that level, they still instantly transformed the problem into a competition-level difficulty.

Because when the horizontal surface is not smooth, the momentum of the entire system is no longer conserved, since friction is an external force acting on system A, B, and the spring.

At the same time, mechanical energy is no longer conserved, because friction does negative work, and some mechanical energy will be converted into internal energy.

[Holy crap, there's a real pro in the live stream. With this question changed, I feel like I'm completely lost. By the way, I'm a second-year student at Jiangcheng No. 6 Middle School, and I was in the top 30 in my grade in the last midterm exam.]

I feel okay about it, anyway, I don't know how to do it (just kidding)

In front of the live broadcast room, Shen Qingyi frowned slightly. She felt that the question setter was deliberately making things difficult. Even she couldn't answer this question, so it was definitely not a question that a high school student could answer.

What's the point of setting such a difficult question?

"Adding friction does make it much more difficult, as both conserved quantities are no longer conserved. However, the physical condition for determining the maximum compression still holds: the spring compression reaches its maximum when the two blocks move at the same speed."

After thinking for a while, Chen Mo began to speak.

"?"

Shen Qingyi's gaze sharpened slightly, but a storm raged in her heart. "Could it be that he's really going to tackle this problem?"

"First, let's assume the maximum compression is x_m, and the common velocity of A and B is v. Then, applying the work-energy theorem to A and B respectively, for block A, the frictional force does negative work, and the spring force also does negative work. Therefore, we can obtain the formula..."

−μm_Ag⋅s_A−∫0-x_mF_弹dx=1/2m_Av^2−1/2m_Av_0^2,其中s_A是A的位移,F_弹=kx,积分项为1/2kx_m^2.」

Chen Mo quickly wrote down the equation on the draft paper, explaining, "For block B, friction does negative work and spring force does positive work. We can also get the equation: −μm_Bg⋅s_B+∫0-x_mF_spring dx=1/2m_Bv^2−0."

"Then the difference in displacement between block A and block B is the compression of the spring, so we have x_m = s_A − s_B. Adding the two equations above and eliminating the integral term for the spring, we can get..."

"Finally, applying Newton's second law to the entire system to calculate the acceleration... we can then obtain that the compression of the spring is 0.114m."

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