Chapter 32: Chapter 19: Coefficient of Friction
[National Junior High Applied Physics Knowledge Competition - School Qualifier]
Question One.
Fill in the blank.
"As shown in the figure, a wooden block with a weight of G = 10N is in uniform linear motion on a smooth horizontal surface. It is subjected to a horizontal pulling force of F = 5N. Therefore, the frictional force on the block is ( ) N."
Chen Zhuo held his pen, his hand hovering in mid-air as he stared at a few words in the problem description.
Smooth horizontal surface.
Uniform linear motion.
His brow twitched involuntarily.
An extremely strong sense of discomfort shot up his optic nerve and straight to his brain.
’Here we go again.’
’It’s this damned, hypocritical, neutered ideal state that only exists for the sake of an exam.’
In the eyes of a junior high test writer, the world was always this simple and crude.
Surfaces were always perfectly smooth, objects were always rigid, the air was always a vacuum...
No deformation, no fracturing, no thermal energy generation, no electromagnetic interactions.
The single, glib word "smooth" in the problem statement completely erased this complex, fascinating microscopic mechanism, reducing it all to that cold "0".
"So crude..."
Chen Zhuo muttered under his breath.
The fingertips of his other hand still seemed to hold the memory of the rough, oxidized surface of the bare capacitor rod he had just been handling in the lab.
That was real physics.
That was the real world, full of noise, interference, temperature drift, and non-linear errors.
To have just withdrawn from that precise world where one had to account for a 0.1Hz frequency drift, only to be suddenly confronted with such a crude problem that "assumed everything was perfect"...
It was like asking a lead surgeon who had just completed a retinal suture to go and slice a plastic board full of styrofoam.
The answer to this question was simple.
Smooth = no friction.
Uniform motion = balanced forces.
If it weren’t smooth, the answer would be f = F = 5N. If it was smooth, the answer was 0.
But he didn’t want to write down that "0".
Even though reason told him that this was just a junior high question, that "0" was the standard answer, the only path to a perfect score.
He couldn’t bring himself to write it.
Looking at the vast blank space after the parentheses, Chen Zhuo felt it was just too empty.
So empty, it felt like it was mocking his intelligence.
Chen Zhuo sighed.
He fumbled around beside his test paper and found a large blank sheet used for drawing mechanical diagrams.
"CLICK."
He extended the lead of his mechanical pencil.
SWOOSH~.
Beneath the simple wooden block, the tip of his pencil drew a thick, jagged line.
That was a rough surface.
Immediately after, a standard coordinate system was established.
The Y-axis pointed vertically upward, the X-axis horizontally to the right.
Gravity, G, pointed vertically downward.
The normal force, N, pointed vertically upward.
But that wasn’t enough.
Chen Zhuo’s gaze went distant. His other hand unconsciously fiddled with his pen cap, while the hand holding the pencil seemed to have a mind of its own, writing a Greek letter next to the force diagram.
μ.
The coefficient of kinetic friction.
Since he had drawn a rough surface, this was no longer a simple matter of ƒ = F.
This was a matter of microscopic molecular interlocking at the contact surface.
This was the macroscopic manifestation of electromagnetic interaction.
The pencil tip rustled against the paper, moving with extreme speed, even developing a fluid, rhythmic cadence.
"Solution: Construct an inertial reference frame, S."
"Let: the surface not be perfectly smooth. Take the coefficient of kinetic friction as μ (μ ≠ 0)."
"Let: air resistance not be negligible. Introduce a drag coefficient, k. Thus, the air resistance is..."
Was that all?
Of course not.
Chen Zhuo’s mind was still racing ahead.
Chen Zhuo frowned.
’Still not rigorous enough.’
’What if I consider the static friction required to start the motion?’
The maximum static friction is usually slightly greater than the sliding friction.
On the blank paper, the once-empty space was now densely packed with formulas and diagrams.
Dashed lines for orthogonal decomposition.
Arrows for force analysis.
Greek letters representing various physical quantities.
The more Chen Zhuo wrote, the smoother his hand moved, and the faster he went.
’This feels so good.’
He didn’t even need to think.
These force diagrams, these steps of orthogonal decomposition, had long been engraved into his very marrow, becoming an instinct more natural than breathing.
Question Two.
"As shown in the figure, the lever is in equilibrium..."
Chen Zhuo glanced at the crude drawing of a seesaw.
He didn’t even have to think about it.
His pencil fell to the paper once more.
’Lever arm?’
’No, that’s torque.’
Μ→=r→×F→
Cross product.
Vector product.
Moment of inertia, I.
Angular acceleration, α.
When he wrote down the formula for the rotational law, ΣM = Iα, he didn’t even realize these were concepts from high school or even university physics.
He just felt that if you were going to calculate rotation, this was a necessity.
This was inertia.
The inertia of thought.
It was like someone used to driving an F1 car. Even if they were just taking a grocery-getter to the supermarket, they would instinctively cut the inside line, hit the apex, and accelerate out of the turn.
「Ten minutes later.」
Chen Zhuo stopped writing.
He looked at the large sheet of paper in front of him, now completely covered in markings.
It had diagrams, formulas, assumptions, and derivations.
It was rigorous, beautiful, and flawless.
The only thing missing was that damned "0".
"..."
Chen Zhuo blinked, a straw dangling from his lips as he froze.
’I went a little overboard.’
He came back to his senses, looked at the sheet full of high school physics formulas, and suddenly found it a bit funny.
If he handed this in, Old Zhou would probably have to study it with a magnifying glass for a good while before cursing, "You psycho."
CREAK.
The door was pushed open a crack.
Liu Xiuying walked in carrying a plate of sliced apples.
"Still working?"
She placed the plate gently on the corner of the desk and leaned over to take a look.
That one glance made her freeze.
Under the desk lamp, on top of the originally neat and tidy test paper, lay a scratch sheet covered in dense, dark markings.
It would have been one thing if it were a language arts test, but this was clearly a physics test.
And those markings...
Those line segments with arrows, those strange symbols that looked like earthworms, and those trigonometric functions that made her head spin just looking at them.
"This... is a junior high question? It’s this hard?"
Liu Xiuying was a little bewildered.
She wasn’t highly educated, but she had seen the homework of the neighbor’s kids, and she had never seen anything drawn like this.
"Why does it look like a bunch of scribbles? And you have to draw so many arrows?"
Chen Zhuo blinked.
"It’s not hard, Mom."
Chen Zhuo nonchalantly picked up a slice of apple and stuffed it into his mouth, hiding the awkward twitch at the corner of his lips.
"I just... wrote out the steps in a bit more detail."
"Oh, more detail is good. It helps avoid mistakes."
Liu Xiuying nodded, impressed despite not understanding a thing. Her faith in her son’s studies was unconditional.
"Alright, eat up and get to bed soon. Don’t stay up too late. You have to get up early tomorrow."
"I know."
Liu Xiuying left, closing the door behind her.
The room returned to silence.
Chen Zhuo stared for a few seconds at the paper he had covered in dense markings.
Chen Zhuo picked up his eraser, intending to wipe it all away.
But after just a couple of strokes, he stopped.
Looking at the dark, smudged eraser shavings, he frowned.
’It’s too messy.’
Besides, why should he have to erase it?
This was the true face of the physical world.
Why should he erase a real derivation just to cater to an oversimplified problem?
Chen Zhuo tossed the eraser aside.
He couldn’t be bothered to erase it.
And he couldn’t be bothered to change it.
He picked up the large sheet of paper, folded it twice, and tucked it inside his test booklet.
Then, on the small blank line for the fill-in-the-blank question, he scrawled the required answer onto the test paper in a slightly messy script.
After writing all that, he tossed his pen down.
He stretched his arms out long and wide.
His joints let out a series of crisp CRACK-CRACK-CRACKs.
’Much better.’
That pent-up, misplaced computational power in his brain had finally been vented, flowing out with those formulas.
He folded his test paper haphazardly, not even bothering to align the edges, and shoved it into his schoolbag.
As for checking his work...
If he needed to check a problem like this, it would be an insult to his intelligence.
Lights out.
Into bed.
Time to sleep.
He rolled over in bed, pulling the blanket up tightly.
When he slapped this test on Old Zhou’s desk tomorrow, the look on his face was going to be priceless.
Chen Zhuo was looking forward to it.
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