You Really Underestimate Physics

"Ring, ring, ring."

The class bell rang.

The physics teacher, Jiang Yang, strolled into the classroom with a test paper in hand.

"Everyone, put your books away and take out your papers from the last monthly exam." Without wasting words, Jiang Yang set his thermos on the lectern. "Today, we'll go over the physics paper from the last monthly exam."

The classroom immediately filled with the rustling sound of papers being flipped through.

Li Dong also pulled his test paper out of his desk.

88 points.

On a physics test with a perfect score of 100, that was definitely considered a high score at No. 7 High School.

But as Li Dong looked at that score now, he found it utterly dull.

Because it was too easy.

"Sigh, if this had been before, I'd probably have shown it off for days."

After yesterday's systematic review, plus the one-hour special training from Newton's "Focus +1" red packet, his understanding of physics had completely opened up.

Back then, he naturally wouldn't have dared to look down on the questions on this test paper.

But now, even if he watched a block sliding down an inclined plane, he could "see" static friction doing positive work.

He could even personally "feel" the Lorentz force pulling charged particles sideways as they deflected in a magnetic field.

This was [Physics Perception]!

It was absolutely a T0-tier buff.

Even if he encountered a problem he genuinely didn't know how to solve, with [Logic 0.1] and [Memory 0.1], he was like a player gaming with a walkthrough. He could quickly retrieve the relevant knowledge points from his mind, and even draw inferences from them to connect them with university-level physics.

Last night, he had not only gone through all the high school knowledge points, but had even idly flipped through several pages of The Feynman Lectures on Physics.

So this test paper, written by No. 7 High School's senior-year teachers, was something he could completely crush in seconds.

Take the second-to-last question, for instance. It was the hardest question on the entire paper.

It was the final, most difficult mechanics problem.

[As shown in the figure, a soft chain of length L and uniform mass density has a mass per unit length of λ. The chain is inextensible even when slack. Initially, one end of the chain is suspended from the ceiling, while the other end just touches the ground. The suspended end is now released. Find the relationship between the force F exerted by the ground on the chain and the falling distance x during the chain's descent.]

This problem was actually far beyond the syllabus. It involved the dynamics of a variable-mass system—the famous "Leibniz Chain" model.

Ordinary high school students without advanced training would generally try to solve it using Newton's second law, F = ma.

But there was a huge trap here.

When the chain hit the ground, it underwent an inelastic collision, meaning energy was lost!

If energy conservation was used, the answer would definitely be wrong.

To solve this problem, one had to use the impulse-momentum theorem or integrate with infinitesimals.

Putting a problem like this on a monthly exam at No. 7 High School was either the teacher who wrote it having a brain cramp, or the teacher had directly copied it from some Olympiad problem bank without checking the difficulty.

"I bet hardly anyone in the class got it right."

Li Dong had still overestimated the students at No. 7 High School. In truth, no one in the entire grade had solved this problem correctly.

That included himself, of course—the version of himself from the monthly exam.

At that moment, the answer space that had originally been blank on Li Dong's paper was already filled with neat lines of calculations.

He did not use the standard high school method. Since it was an inelastic collision and energy was not conserved, he directly used calculus and the impulse-momentum theorem.

[Solution:]

[Let the chain have fallen a distance x and have velocity v.]

F_impact = dp/dt = vdm/dt = v(λdx/dt) = v(λv) = λv²

[At this moment, the total pressure exerted on the ground, F_total, should be: the weight of the portion already on the ground + the impact force.]

F_total = G + F_impact = (λx)g + 2λgx = 3λgx

In other words, during the chain's fall, the support force exerted by the ground on it was three times its instantaneous static weight!

Simple, brutal, and straight to the point.

This was mathematics serving as a dimensionality-reducing weapon against physics.

At the lectern, Jiang Yang was still going through the test paper question by question.

Unlike Old Yang, he did not chew up the knowledge points and spoon-feed them to the students. Instead, he simply read straight from the answer sheet.

"For the first question, choose B. It tests Lenz's Law. No need to say more about that, right? It was a giveaway."

"For the second question, choose C. Don't mess up the force analysis. Use orthogonal decomposition, set up a coordinate system, split it along the x-axis and y-axis—it couldn't be simpler."

Jiang Yang explained quickly, but the students below listened in a fog.

Jiang Yizhou was the only exception, acting unusually active today.

"Teacher! I know this one! The direction of the friction force was judged incorrectly!"

"Teacher! This one should use the work-energy theorem. It's faster than Newton's second law!"

Whenever Jiang Yang threw out a question, Jiang Yizhou was always the first to answer. His voice was loud, and his eyes occasionally glanced toward the back rows.

Jiang Yang naturally liked students who participated so actively and could not help praising him a few more times.

"Not bad. Jiang Yizhou has a solid foundation and very clear thinking. Everyone should learn more from him."

Hearing the praise, Jiang Yizhou answered questions even more eagerly.

Before long, they reached the end of the test paper.

Jiang Yang glanced at the "chain problem" in the second-to-last question and directly flipped past it.

"All right, the second-to-last question is too difficult. It involves variable-mass systems and goes beyond our syllabus, so I won't go over it. I've already given everyone the points for it."

After saying that, he checked the time. "Use the remaining time to correct your mistakes. Hand it in tomorrow as homework."

"Next class, we'll do another test paper."

This was Jiang Yang's teaching style: do test papers, explain them from the answers, then repeat the cycle.

But just then, a hand shot high into the air.

"Teacher!"

The entire class fell silent, and everyone's gaze turned toward Jiang Yizhou.

He stood up.

"Teacher, all of my answers are correct, and I don't have any mistakes. Does that mean I don't need to hand in homework?"

In the back row, Li Dong's mouth twitched.

Was he really that desperate to stand out?

Jiang Yang had not expected this and froze for a moment before smiling.

"All right. Students who got everything right don't need to hand it in."

As soon as he said that, envious looks poured in from all around.

Jiang Yizhou enjoyed the feeling of being the center of attention, but he felt it was not enough.

He looked at Jiang Yang on the lectern again and suddenly said,

"Teacher, since there's still time, could you explain that second-to-last question?"

Jiang Yang's brows furrowed slightly.

"That question goes beyond the syllabus. Even if I explain it, you won't understand."

"Teacher, just explain it."

Jiang Yizhou still would not let it go, a confident smile on his face.

"What if we can understand it? We want to challenge ourselves too and see what exactly makes this kind of difficult problem so hard."

In truth, Jiang Yizhou had his own little scheme.

The problem was difficult, but he had scored a perfect 100 in physics this time.

Since he had gotten a perfect score, that meant he had "solved" that question correctly too.

Though the teacher had awarded everyone the points, he subconsciously felt that the answer he had written on his paper, "F = mg," was probably close enough.

He wanted to use this opportunity to show the whole class that even if it was beyond the syllabus, Jiang Yizhou could still tackle it!

Jiang Yang regretted this terribly now.

He had originally wanted to make some easy questions to boost the students' confidence and make things easier for himself.

But when he had written the paper, he had not paid attention and had directly copied over an Olympiad problem.

He himself had been left confused after looking at the answer last night. Impulse, infinitesimals—it was far too troublesome to explain.

"Well..." Jiang Yang hesitated. "This question, you really don't need to—"

"It's fine, Teacher! Just give us the general idea!" Jiang Yizhou said loudly.

"Or Teacher, why don't you see whether my approach is correct?"

Looking at Jiang Yizhou's aggressive manner, Li Dong helplessly shook his head and casually drew a force diagram of the falling chain on his scratch paper.

"Honestly... ignorance really was fearlessness."

Yet Jiang Yizhou seemed not to notice Jiang Yang's awkwardness. He kept making a fuss and even directly gave his own answer.

"Teacher, is the answer to this question F = mg? Or F = xgλ?"

Jiang Yizhou looked at Jiang Yang expectantly.

"I think it's just a simple gravitational equilibrium problem."

Hearing that answer, Jiang Yang, who had originally wanted to brush it off, had no choice but to take it seriously.

As a physics teacher, no matter how little he wanted to explain the problem, he could not tolerate such a fundamental mistake being passed around in class as the correct answer.

F = mg?

That was seriously underestimating physics!

The favorable impression Jiang Yang had just built up of Jiang Yizhou instantly dropped below zero.

He set his thermos down on the desk. No longer caring whether it would discourage this model student's enthusiasm, he said coldly,

"No!"