The three students put their heads together and thought hard.
Kang Woo, who was participating in the discussion from a slight distance, turned his attention to the other tables. Much the same thing was happening in the other groups. One student took the lead while the others helped.
There was plenty of spirited discussion, but most of the groups did not seem to be making much progress.
While Kang Woo was looking around instead of concentrating on the task, his eyes met Cha Do-do's. She was standing at the lectern, observing the students.
'Gah!'
The look she gave him was chilling. His homeroom teacher clearly had plenty of complaints about him. Wasn't a teacher supposed to look upon her students with affection? Why was she staring at him as though she wanted to devour him?
Her gaze seemed to reproach him for fooling around instead of cooperating with his group. Feeling guilty, Kang Woo pretended to join the discussion.
“To calculate mass, we need to know the volume and density.”
Son Cha-hee was the one who offered the suggestion. It was one of the most elementary scientific formulas taught in middle school.
“Haaah! What about the Earth's size? We'd need to know its density as well. Wasn't the Earth's density originally calculated from its mass? Wouldn't that mean we're working backward?”
Choi Dae-woo shook his head, unconvinced.
Historically, the first thing scientists had determined was the Earth's size. Assuming the Earth was a sphere, they could estimate its size by measuring the distance between latitudes. They had then calculated the Earth's mass and used the two values to determine its density.
That density had disproved the hypothesis that the Earth was hollow. It had also led to the suggestion that the Earth's center contained heavy materials, namely iron.
“So the density formula doesn't count as an answer?”
Yoon Su-a asked the question.
As Son Cha-hee sank into thought, Kang Woo watched the proceedings with interest.
Just as Son Cha-hee was about to ask the teacher something, a student from a neighboring group beat her to it.
“Ma'am! Can we assume we already know the Earth's density?”
“You may assume that the other important constants are already known.”
“Yes!”
The students suddenly became much more animated.
“Then this one works.”
Yoon Su-a wrote down the density formula.
“Then we can use the law of universal gravitation, or a gravitational-force equation like F = mg, can't we?”
“If we know the gravitational constant or gravitational acceleration, we can work backward to calculate the Earth's mass.”
Son Cha-hee and Yoon Su-a worked together, listing formulas one after another.
“Haaah, if we use the Moon's orbit and Kepler's laws...”
Then Choi Dae-woo came up with a new approach.
There was no doubt that Choi Dae-woo had a particular gift for astronomy. Kang Woo was reminded once again that the boy possessed S-grade potential in both physics and chemistry.
“Then let's write that down too...”
Yoon Su-a organized their answers logically on the sheet they had been given.
Once they had written down four methods, however, they ran out of ideas. Son Cha-hee thought for a while, her brow furrowing more deeply, before giving Kang Woo a nudge.
“Try thinking of something too.”
“As though I know anything about this.”
Kang Woo had no particular intention of involving himself in the children's discussion.
When he showed no interest, Son Cha-hee clicked her tongue in exasperation and returned to the task.
And so the ten minutes passed.
“All right. Now, one person from each group should come forward and write your answers on the board.”
Yoon Su-a went up for Kang Woo's group.
They had written down five answers in all. One more had been added in the meantime. The other groups had come up with anywhere from one to four answers, though the methods they listed were essentially the same.
Only two groups had five answers: Kang Woo's group and the one at the table right beside theirs.
Go Hyeon-seong was a member of that neighboring group. He was the boy who had asked Son Cha-hee about her ideal type on the first day and seemed particularly interested in girls.
Go Hyeon-seong was not the strongest student in his group. That distinction belonged to Jeon Sang-cheol, who had entered as the second-highest-ranked student in their class. He had attended an academy that competed with the one Son Cha-hee had gone to.
The other two boys were Jo Yeong-je and Oh Dong-seop. Jo Yeong-je was a fairly ordinary, diligent student, while Oh Dong-seop openly regarded himself as Jeon Sang-cheol's lackey.
The moment Son Cha-hee saw who was in the group, her expression soured. Just as she regarded Lee Min-chan as her rival, Jeon Sang-cheol was forever declaring that Son Cha-hee was his rival.
As luck would have it, Son Cha-hee's group and Jeon Sang-cheol's group were tied at five answers apiece.
Cha Do-do surveyed the answers written on the board and shook her head, apparently dissatisfied.
“From now on, if you think of another answer, come straight up and write it on the board. The group with the most answers will receive the most points.”
A race against time had begun. But after ten minutes of group discussion had produced only those answers, it was hardly likely that anyone would immediately think of another.
Son Cha-hee puffed out her cheeks as she thought for a long moment, then suddenly raised her hand.
“Would an experiment to determine gravitational acceleration count as a separate method?”
“Yes, it would.”
At that instant, someone from the quick-witted neighboring group dashed toward the board.
Since Son Cha-hee's group and Jeon Sang-cheol's group occupied the tables closest to the front of the classroom, both were well placed to reach it quickly.
The trouble was that Go Hyeon-seong moved much faster than Son Cha-hee. Standing before the board, he cast her a triumphant glance and confidently added two more answers.
- Using the period of a simple pendulum...
- Using a free-fall experiment...
Naturally, all the students in the room understood those methods without needing detailed explanations.
“You! Isn't that cheating? I asked the teacher first!”
“What's cheating about it? The whole point is to get up here and write the answer first.”
Son Cha-hee practically jumped with fury, but Go Hyeon-seong brushed off her complaint without a care.
She appealed to Cha Do-do to arbitrate, but the teacher merely watched their argument with an interested expression.
Five against seven. The gap had suddenly widened.
Struggling to contain her anger, Son Cha-hee asked another question.
“What about a Foucault pendulum?”
“That's the same method as using the period of a simple pendulum.”
Dejected, Son Cha-hee sat down again.
Watching all this, Kang Woo began to understand what was going on.
Pendulum and free-fall experiments were among the problems covered at private academies preparing students for entrance examinations to schools for the gifted. As expected, most of the students' thinking was confined to what they had learned at their academies. They had trouble imagining new methods beyond the curriculum.
'That was rather underhanded.'
Even though he had intended to remain an observer, he could hardly approve of Go Hyeon-seong darting forward and stealing an answer like that.
“Can anyone think of anything else?”
When no more answers appeared, Cha Do-do seemed ready to bring the competition to an end.
Kang Woo glanced around at his group members. Choi Dae-woo looked unperturbed, while Yoon Su-a fiddled with her glasses and kept her eyes fixed on Son Cha-hee.
Son Cha-hee had clenched her fists and was trembling, looking as though she was desperately swallowing her anger.
'She really doesn't want to lose, does she?'
Kang Woo could not help admiring her competitive spirit.
He had not planned on stepping in, but seeing Son Cha-hee looking as though she might cry left him strangely unsettled. Worse, Go Hyeon-seong was standing by the board, clearly enjoying himself as he sneered at them.
All this over a group assessment.
Still, people deserved to be rewarded for the effort they put in. Kang Woo remembered how Go Hyeon-seong had glared at him after failing to get into Son Cha-hee's group, and now the boy had shamelessly snatched away their answers.
With him acting so smug, perhaps someone ought to put him in his place. It was time to see justice done.
'Oh, and I need to change my homeroom teacher's opinion of me, don't I?'
He could help Son Cha-hee while making a new impression on Cha Do-do. Besides, it was a group assessment, so he would benefit too. When he thought of it that way, this seemed like an opportunity he could not afford to miss.
Kang Woo sprang to his feet.
His group members, including Son Cha-hee, turned to look at him. Surprise, expectation, suspicion, bewilderment... Their faces displayed every imaginable reaction.
“Would an experiment to determine the gravitational constant count as well?”
At Kang Woo's question, Cha Do-do gave him a meaningful look.
“Of course it would.”
“Then...”
Kang Woo strode toward the board.
“Hey, brother! Hold on a second!”
Go Hyeon-seong raised a hand to stop Kang Woo and positioned himself to write on the board. But unlike gravitational acceleration, experiments to determine the gravitational constant were not covered in textbooks and received only brief mentions in supplementary study guides.
After hesitating helplessly for a moment, Go Hyeon-seong failed to write anything at all.
Standing at the board, Kang Woo looked around at the other students. Apparently, none of them knew how the gravitational constant had been determined. He was willing to yield if someone else could provide an answer, but not a single person spoke up.
It seemed that anything unlikely to appear on an exam simply never made its way into their heads.
“Let's look at an experiment to determine the gravitational constant. As it happens, I studied physics quite diligently yesterday...”
“Huh? But you were hanging out with me last night.”
Choi Dae-woo looked thoroughly puzzled.
Honestly, that boy had an uncanny ability to speak up at precisely the wrong moment. Kang Woo pretended not to hear him and continued smoothly.
“I happened to be reading about the history of universal gravitation, and I came across the Cavendish experiment.”
Some students frowned at what seemed like an irrelevant digression. Others racked their brains, vaguely remembering seeing the experiment mentioned in their study guides.
“In the eighteenth century, the British physicist Cavendish devised an experiment using a torsion balance with suspended lead weights to determine the gravitational constant. The value he obtained was remarkably accurate, with an error of less than one percent.”
Kang Woo quickly sketched Cavendish's experimental apparatus on the board.
With that, he added another method to their list.
“But that experiment is rather complicated, isn't it? Another scientist came up with a simpler version! A German scientist named Jolly devised a much more intuitive experimental method using a heavy lead mass. Of course, its margin of error was considerably larger.”
Kang Woo briskly drew Jolly's experiment as well and wrote down the method.
He had added two answers. The groups were now tied at seven apiece.
Kang Woo saw Son Cha-hee's expression brighten, while Go Hyeon-seong and Jeon Sang-cheol looked thoroughly displeased.
Cha Do-do, who had been staring at Kang Woo as though he were an alien, gave a nod.
“You certainly know a great deal about the history of physics. Now both groups have seven answers... Is that all?”
“It would be a shame to stop there, wouldn't it?”
As a former physics professor, he could hardly stop now. If he had started something, he might as well finish it properly.
In truth, a broad question like this could not be answered simply by poring over textbooks. It required a change in the direction of one's thinking. These students had been confined to conventional approaches for so long that perhaps it was time someone showed them what genuinely inventive thinking looked like.
Kang Woo drew a circle on the board, labeled it Earth, and then traced the orbit of a communications satellite around it.
- Applying Kepler's third law to the Earth and an artificial satellite...
- Using the mechanical-energy equation from which the Earth's escape velocity of 11.2 km/s is derived...
Kang Woo explained both methods fluently, without the slightest hesitation. Not only Cha Do-do but all the students were left staring with their mouths open.
Cha Do-do frowned slightly and asked in bewilderment,
“But Kang Woo, didn't you say you hadn't studied ahead...?”
“Like I told you yesterday, I'm something of an enthusiast... I have a habit of digging into particular subjects whenever they catch my interest. It just so happens that I was reading all about gravity last night...”
Kang Woo offered a vague excuse.
He was insisting that the very subject he had happened to study the previous night was the subject of today's lesson. Cha Do-do could think of nothing to say in response. She was almost certain he was lying, but confronting him about it here and now would be another matter entirely.
“Do you have any more?”
“Plenty. But... unless another group has something to add...”
“All right. Go back to your seat.”
When Kang Woo returned to his table, Cha Do-do addressed the class.
“Does anyone have another answer to add?”
Kang Woo's group had nine answers. Jeon Sang-cheol's group had seven, and the next group had four.
“Then Kang Woo's group wins.”
At Cha Do-do's announcement, Choi Dae-woo and Yoon Su-a cheered with delight.
Son Cha-hee, however, had mixed feelings. Her group had won and earned the points, so she ought to have been pleased. Yet she could not help feeling annoyed that the person responsible for their victory was Kang Woo rather than herself.
Worse, hadn't she looked down on Kang Woo because he had never studied ahead? And now he had performed like this!
Son Cha-hee began to grow suspicious of him. The way he had explained the moment of inertia at the café yesterday morning, and the way he had explained gravity today, were both beyond what an ordinary student could manage.
In particular, even if someone like her, who had spent years at an academy concentrating on solving exam problems, knew the material, explaining it in that fashion would be difficult.
'Who on earth is this guy?'
Son Cha-hee regarded Kang Woo with a troubled expression.