Chapter 11: Chapter 11: You’re Underestimating Physics Too Much
BRRRING!
The school bell rang.
Physics teacher Jiang Yang walked leisurely into the classroom, a test paper in hand.
"Everyone, put your books away and take out the papers from last month’s exam." Without wasting any words, Jiang Yang placed his thermos on the lectern. "Today, we’re going over the physics test."
The classroom was immediately filled with the RUSTLE of students rummaging for their papers.
Li Dong pulled his test paper out of his desk drawer as well.
points.
On a physics test with a maximum score of 100, this was definitely considered a high score at Seventh Middle School.
But at this moment, Li Dong just found the score boring to look at.
It was all too simple.
’Sigh, if this were the old me, I probably would have been showing this off for days,’ he thought.
After yesterday’s system review, plus the one-hour special training from Newton’s red packet—"Concentration +1"—his entire perspective on physics had been completely transformed.
He wouldn’t have dared to look down on the questions on this test before.
But now, even watching a block slide down an inclined plane, he could "see" the static friction doing positive work.
He could even personally "feel" the pull of the Lorentz force on a charged particle deflecting in a magnetic field.
This was [Physical Perception]!
It was a completely Tier T0 buff.
Even if he encountered a problem he truly didn’t know how to solve, with [Logic 0.1] and [Memory 0.1], he was like a player with a strategy guide. He could instantly search his mind for the relevant concepts and even extrapolate to connect them with topics from University Physics.
Last night, he had not only breezed through all the high school material but had also idly flipped through a few pages of *Feynman’s Lectures on Physics* out of boredom.
So now, he could absolutely crush this test, which had been written by the senior teachers of Seventh Middle School.
Take the second-to-last problem, for example. It was the hardest one on the entire test.
The final, most challenging question on mechanics.
[As shown in the figure, a soft, flexible chain of length L and uniform mass density has a mass per unit length of λ. The chain is inelastic, even when slack. Initially, one end of the chain is suspended from the ceiling, with the other end just touching 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.]
This problem was actually completely beyond the scope of the curriculum. It involved the dynamics of a variable-mass system, specifically the famous "Leibniz Chain" model.
An average high school student, without any advanced training, would typically try to solve it using Newton’s second law, F=ma.
But there was a huge trap here.
When the chain falls to the ground, it’s an inelastic collision, meaning energy is lost!
If you used conservation of energy, the answer would be completely wrong.
To solve this problem, you had to use the Momentum Theorem or integration with the Microelement Method.
For a question like this to appear on a Seventh Middle School monthly exam, the teacher who wrote it must have had a brain fart, or they just copied and pasted it from some Ossai question bank without checking the difficulty.
’I bet almost no one in the class got it right,’ Li Dong thought.
Li Dong had overestimated his classmates at Seventh Middle School. In reality, not a single person in the entire grade had solved it correctly.
That included himself—the version of him who took the test, of course.
But now, on Li Dong’s test paper, the previously blank space for this problem was filled with neat lines of calculations.
He hadn’t used the standard high school method. Because it was an inelastic collision where energy wasn’t conserved, he went straight for Calculus and the Momentum Theorem.
[Solution:]
[Let the falling distance of the chain be x, and its velocity be v.]
[According to the laws of free fall: v^2 = 2gx]
[For a small element of the chain, dm = λdx, about to hit the ground, the rate of change of its momentum is the impulse force, F_impulse.]
F_impulse = dp/dt = v(dm/dt) = v(λdx/dt) = v(λv) = λv^2
[Substituting v^2 = 2gx, we get F_impulse = λ(2gx) = 2λgx]
[At this point, the total force F_total on the ground should be: the weight of the part already on the ground + the impulse force.]
F_total = G + F_impulse = (λx)g + 2λgx = 3λgx
In other words, as the chain falls, the normal force from the ground is three times the weight of the portion of the chain at rest on the ground at that instant!
Simple, brutal, and straight to the point.
This was the overwhelming advantage of using advanced mathematical tools in physics.
Up at the lectern, Jiang Yang was still going through the test, question by question.
Unlike Old Yang, he didn’t spoon-feed the concepts to the students; he just read the answers directly from the key.
"Question one is B. It’s testing Lenz’s Law. No need to elaborate on that, right? It’s a freebie."
"Question two is C. Don’t mess up the force analysis. Use orthogonal decomposition, set up your coordinate system, split it into x and y axes... couldn’t be simpler."
Jiang Yang spoke quickly, but the students below were completely lost in a fog.
Only Jiang Yizhou was unusually active today.
"Teacher! I know this one! The direction of the friction is wrong!"
"Teacher! You should use the work-energy theorem for this one, it’s faster than Newton’s second law!"
Whenever Jiang Yang posed a question, Jiang Yizhou was always the first to shout out the answer, his voice booming as he periodically glanced toward the back of the room.
Jiang Yang naturally liked such an enthusiastic student and couldn’t help but praise him a few times.
"Excellent. Student Jiang Yizhou has a very solid foundation and clear thinking. Everyone should learn from him."
Hearing the praise, Jiang Yizhou began answering with even more vigor.
Soon, they reached the end of the test review.
Jiang Yang glanced at the second-to-last "chain problem" and skipped right past it.
"Alright, the second-to-last problem is too difficult. It involves a variable-mass system and is beyond the scope of our curriculum. I won’t be going over it. I’ve already given everyone credit for it."
After speaking, he checked his watch. "For the rest of the period, correct your mistakes. Turn them in as homework tomorrow."
"Next class, we’ll do another practice test."
This was Jiang Yang’s teaching method: do a test, review the test by reading the answers, and repeat the cycle.
But just then, a hand shot high into the air.
"Teacher!"
The class fell silent, and all eyes turned in unison toward Jiang Yizhou.
He was standing up.
"Teacher, my test paper is perfect, there are no mistakes. Does that mean I don’t have to turn in the homework?"
Listening from the back row, the corner of Li Dong’s mouth twitched.
’Does he have to be such a show-off?’
Jiang Yang hadn’t expected this either. He paused for a moment, then smiled.
"Sure. Students with perfect papers don’t have to turn it in."
As soon as he said that, envious gazes landed on Jiang Yizhou from all around.
Jiang Yizhou basked in the feeling of being the center of attention, but he felt it wasn’t enough.
He glanced at Jiang Yang on the stage again and suddenly said,
"Teacher, since there’s still time, could you explain the second-to-last problem?"
Jiang Yang’s brow furrowed slightly.
"That question is beyond the curriculum. You wouldn’t understand it even if I explained it."
"Please, Teacher, just give it a try."
Jiang Yizhou remained persistent, a confident smile on his face.
"What if we can understand it? We also want to challenge ourselves and see what makes a high-difficulty problem so hard."
In reality, Jiang Yizhou had his own little scheme.
The problem was difficult, but he had scored a perfect 100 on this physics test.
Since it was a perfect score, that meant he had "correctly answered" this question too.
Although that was only because the teacher gave everyone credit, he subconsciously felt that the answer he had written on his paper, "F=mg," was probably more or less correct.
He just wanted to use this opportunity to show the entire class that even when faced with a problem beyond the curriculum, he, Jiang Yizhou, could conquer it!
Jiang Yang was now filled with immense regret.
He had originally intended to write some simple questions to boost the students’ confidence, which would also let him slack off a bit.
But when writing the test, he hadn’t been paying attention and directly copied an Ossai problem.
He himself had been confused looking at the solution last night—all that talk about impulse and microelements was just too much trouble to explain.
"Well..." Jiang Yang hesitated. "This question, you guys really don’t need to..."
"It’s okay, Teacher! Just give us the general idea!" Jiang Yizhou said loudly.
"Or, Teacher, you could see if my approach is correct?"
Watching Jiang Yizhou’s aggressive posture, Li Dong shook his head helplessly and casually drew a free-body diagram of the falling chain on his scratch paper.
’So it’s true... the ignorant are fearless.’
However, Jiang Yizhou didn’t seem to notice Jiang Yang’s predicament. He kept pressing, even blurting out his own answer.
"Teacher, is the answer to this problem F = mg? Or maybe F = xgλ?"
Jiang Yizhou looked at Jiang Yang expectantly.
"I think it’s just a simple gravitational equilibrium problem."
Hearing this answer, Jiang Yang, who had been planning to just brush it off, was now forced to get serious.
As a physics teacher, no matter how much he didn’t want to explain the problem, he couldn’t tolerate such a fundamental error being spread in his classroom as the correct answer.
F = mg?
’That’s just looking down on physics!’
The good impression Jiang Yang had just formed of Jiang Yizhou instantly plummeted into the negatives.
He slammed his thermos down on the desk, no longer caring whether he would crush this top student’s enthusiasm, and said coldly,
"Wrong!"
