Become a master from now on

Chapter 148 Look at me, read the question! (Ask for a monthly ticket subscription!!)

Somewhere on the level ground, two small balls A and B are thrown at the same velocity v0 with different throwing angles, and their ranges are the same.It is known that the time TA that ball A moves in the air is TA, and the time TB that ball B moves in the air is calculated.The magnitude of the acceleration due to gravity is g, regardless of air resistance.

Another problem is to find the density.

When looking at the sun from the earth, the opening angle to the diameter of the sun is 0.53, the length l1 km of the latitude 110 on the earth's surface is taken, the gravitational acceleration on the earth's surface is g10 m/s2, and the period of the earth's revolution is T365 days.Try to calculate the ratio of the density of the Earth and the Sun using only the above data.Assume that the Sun and the Earth are spheres with uniformly distributed masses.

"what……"

After Fang Chao finished watching, his expression changed slightly.

These two questions seem simple, but they are definitely not low in difficulty. Fang Chao also has a certain understanding of physics, but at first glance, he has no way to list the steps to solve the problem in the first place.

"How's it going? Do you dare to talk too loudly?"

Zheng Zhiqiu looked at Fang Chao with a smile. It was not easy to see the slumped appearance of Xueba. From simple to complex, boy, physics is not as simple as you think.

The two physics questions in front of him did surprise Fang Chao, but the more challenging they were, the more he wanted to try them.

For Xueba, isn't solving one problem after another just like those foodies discovering brand new delicacies?That kind of fragrance, that kind of color, especially the kind of pleasure when it enters the stomach and becomes a part of the body.

It really feels like flying into the sky.

"Teacher Zheng, give me some time and let me untie it and show it to you."

Fang Chao raised his head and looked at Zheng Zhiqiu.

Zheng Zhiqiu glanced at Fang Chao and said, "It's okay, you continue to work on your questions, I won't disturb you, I will watch the news."

Zheng Zhiqiu has the habit of paying attention to the news on weekdays. The school will subscribe to newspapers for teachers of every grade, and they are all fresh newspapers of the day. Now it is not an exam, so there is no need for him to stare at Fang Chao to answer.

Upon hearing this, Fang Chao devoted himself completely to the two physics problems Mr. Zheng gave him.

This takes into account the issue of the projection angle. When the projection angle is small, the movement time is short, but the horizontal velocity is relatively high. On the contrary, the movement time is long but the horizontal velocity is small, so it is entirely possible that their ranges are the same. The decomposition of motion and the characteristics of horizontal motion... the idea of ​​solving this problem is given.

After Fang Chao wanted to understand the train of thought of the question, he started to write without any hesitation.

He took the lead in drawing a plane Cartesian coordinate system x-axis and y-axis on a blank space, the origin of which was the projectile point, and began to list the equations.

Solution: For any projectile ball there is

x=v0cosθ*t
y=v0sinθ*t1/2*gt
From this, the equation of the trajectory of the ball was obtained, and Fang Chao deduced it.

And such a question is divided into two modes of motion, one is the uniform deceleration linear motion in the vertical direction, and the other is the uniform direct motion in the horizontal direction.

It is precisely because Fang Chao understands this point that he knows the problem of this question.

I have to say that this question is quite interesting, and it is not easy to solve it. If it is not for the fact that the physics level has been raised to LV2, it may take a long time for Fang Chao to solve this question, at least tonight. Maybe I should ask Mr. Zheng for advice.

When y=0, solving x is the horizontal range.

So x=v0sin2θ/g
Thus, the movement time T of the ball can be obtained.

Since the ranges of the two balls A and B are the same, we have
sin2θA=sin2θB
So 2θA=π-2θB
So far, the subsequent steps are basically logical.

Fang Chao wrote a few more equations.

Hence the final answer to this question.

The running time of ball B in the air is √4v0-(Tag)/g
"Fruit ice!"

"It's done!"

Fang Chao breathed a long sigh of relief and looked at the time. It took 21 minutes.

This speed is not fast, but it is certainly not slow either.

With Fang Chaocai's physical level of LV2, it still needs to consume some brain cells to deal with such a problem.

But overall, the effect is still good, both in terms of steps and answers, it is very unsatisfactory.

Zheng Zhiqiu caught Fang Chao's sigh of relief. He immediately put the newspaper aside and asked, "Have you finished your answer?"

"I've solved the first question, Mr. Zheng."

"So fast?"

Zheng Zhiqiu was taken aback. This question was already of moderate difficulty for a physics competition. It would probably take more than half an hour for a normal contestant to answer it. However, it only took Fang Chao about ten minutes from reviewing the question to finishing answering. Zheng Zhiqiu was a little surprised by the time.

He folded the newspaper and put it aside, then said directly, "Show me the answer to your first question first."

"Ah? Teacher, I haven't solved the second question yet."

"I see what does your first question have to do with your second question? Hurry up, don't blot the ink." Zheng Zhiqiu urged.

Fang Chao handed the answer to the first question to Zheng Zhiqiu, "Teacher Zheng, here you are."

After receiving the manuscript handed over by Fang Chao, Zheng Zhiqiu continued, "Why are you looking at me? Look at the question and do the second question."

Fang Chao: "..."

Teacher Zheng, it’s so difficult for you to communicate.

I originally thought you would chat with me about the first question, but you just let me do the question, so cold, ruthless, and unreasonable.

So Fang Chao obediently started to do the second question.

The second question already involves astrophysics.

"Humph."

Fang Chao snorted twice, ready to flex his fists.

"What are you humming?" Zheng Zhiqiu looked up, looking at Fang Chao with some displeasure. This is not a good habit.

"No, teacher, I have a stuffy nose. Let me breathe a few times to get some air."

"Hurry up and do the questions."

"Oh."

Fang Chao didn't even dare to hum, the physics teacher Zheng was too scary, a majestic aura pervaded, like a mountain suppressed, Fang Chao was so frightened that he shivered, he could only relieve the pressure by doing questions.

Hey, I can only give you 2 stars for the difficulty of this question.

The first question is not exciting enough.

It can barely fit between the teeth.

Watch me fix you!
Three minutes later, Fang Chao made a move.

When the earth revolves around the sun, according to the law of universal gravitation and Newton's law
GMsMe/R=Me(2π/T)r
Among them, G is the gravitational constant, Me and Ms are the masses of the earth and the sun respectively, r is the distance between the sun and the earth, and T is the revolution period of the earth.

Let θ=2Rs/r
Get GMs/Rs cubic = 8 (2π/T) (1/θ) cubic
For an object with mass m on the surface of the earth, GMem/Re=mg is obtained from the law of universal gravitation and Newton's law
In the formula, Re is the radius of the earth, according to the meaning of the title, 2πRe=360l
Substitute into the formula GMe/Re cubic = πg/180l
Let ρs and ρe represent the densities of the sun and the earth respectively, then we have

ρs=Ms/(4/3)πRs cubic, ρe=Me/(4/3)πRe cubic,
ρs/ρe=gTθ/180l*32π=3.92.

"Finished solving the problem, done!"

(End of this chapter)