How to weigh the quality of the earth elegantly

In life, if we want to weigh ourselves or an object, we can know with balance or electronic scales, so what should I do if I want to know the quality of the earth? The earth cannot be said on the scale! Even if Akimid once said, giving me a fulcrum, I can pry up the entire earth. But he couldn't call the quality of the earth. Throughout the ages, many mechanics, geosciences and astronomical physicists are trying to get the quality of the earth. So, let's talk about the quality of the earth today.

Give me a fulcrum, I can pry up the entire earth

In 1687, Newton's "Mathematics of Natural Philosophy" was published, which has a milestone in the history of science. In this book, Newton summarized and developed the research results of his and many previous scientists, which contains the law of gravity. For the law of gravity, Newton said this: "For all objects, it is proportional The quality contained in each object. In the two attractive spheres, if the material at the same distance of the ball is similar, the weight of one ball compared to the other ball is more than the square of the two goals. "

The establishment of the law of gravity has become an epoch -making event of astronomy research. Previously, the leading tools of astronomy research were geometry, and then astronomical research entered the era of mechanics. Later, important astronomical achievements such as the trajectory and regression cycle of the comet, the discovery of the Neptune and Pluto, the discovery and positioning of the asteroids were obtained under the guidance of mechanics, and the theory of the core role was the law of gravity. Use formula as:

Among them, M and M are the quality of two objects; R is the distance between the two objects, and G is a constant, called the universal gravity constant, and F is the force between the two objects. There is also a very important problem here that it is not solved. This is unknown that the gravity constant G is still unknown. British scientist Henry Cavendi Xu cleverly used the experiment to use Newton's law of gravity to become the first person to accurately measure the quality of the earth.

However, between the two ordinary objects, the gravity is very small, and it is usually not detected at all. Two shots with a diameter of only 1/4 inches from one -fourth inch, relying on the gravity between them alone, in one month, Can't go together. Such a weak gravity is difficult to measure in indoor experiments. It can be imagined how difficult it is to determine the gravitational size and the gravitational constant G. However, Teacher Card has his own tricks to use twisting scales. Let's take a look at how he designed the experiment elegantly and cleverly solves this problem! The experimental instrument diagram and brief diagram he used as shown in the figure below:

Now let's describe Cavendi's experiments. The suspension line in the figure is silver -plated copper wire, 40 inches long. A light -quality wooden stick is suspended under the suspension line. The length of the wooden rod is 2D is 6 feet, and the two ends of the wooden rod are fixed with a shot of 2 inches (weighing 1.61 pounds) in diameter. Their quality is recorded as M. The two balls used to attract these two balls are large shots with a diameter of 12 inches (weighing 348 pounds), and their quality is recorded as M. The distance between the big ball and the small ball is about 9 inches. The entire device is symmetrical.

Let's calculate the perpendicularity of a small shotm M. First of all, according to the law of gravity, the gravity of the closest big shotm M is:

It also needs to be attracted to the gravity of another big shotter M ', because that big shotpeter distance it is

So its gravity is:

However, the direction of this force is obliquely intertwined with the wooden stick. Because the sine that can be obtained by the sine that is connected with the MM 'MM', that is,

Because M 'is the division of m in the vertical direction of the wood rod, it is the opposite of the gravity of M to M. Therefore, the difference between the two forces above is the force of M in the vertical direction of the wooden stick.

remember

Consider the torque of the twisting stiffness of the suspension line, that is, the torque of the suspension line corresponding to the corner of the unit of the bottom unit. The corner is θ, and the torque of the two balls at both ends of the wooden stick is 2FD. Therefore, under the condition of balance, there should be:

K, D, etc. in the upper formula are all known. If you can measure the balancing

G. Then it is easy to calculate the quality of the earth. However, when changing the position of the two big ball m, the system can not be balanced immediately, but it must be shocked for a long time to swing back and forth to gradually move. This time will be very long, and sometimes you need to wait for the clock. So Cavendi tried a way to write down the angle of the largest place to swing, and then the average corner of the expected balance point was obtained from their average. Specifically, the maximum angle of the first and third swing is average, and then the maximum angle of the second width is average. As a result, it is roughly the corner of the final balance.

We also know that according to the law of gravity law, the acceleration of free falling body:

So you can get:

It can be obtained by the type*type:

Then there is:

In this way, the quality of the earth is cleverly obtained.

Through experiments, Cavendi estimated that the quality of the earth was 5.965 × 1024kg, about 60 trillion tons, which was quite close to the existing recognized value of 5972 × 1024kg. The experimental design is so clever, so that the experimental accuracy has not surpassed for many years. His twisting experiments are still the main way to measure all gravity constants.

Kwendi

The rigor of Cavendi's experiment is that he successfully shielded the interference of the measurement results with the external factors, such as air flow, etc. with a closed experimental device; The number of reading errors is reduced; in addition, in order to overcome the cyclical errors, such as the effect of temperature, Cavendi promotes the experiment of the earth for several years, thereby effectively reducing the effects of temperature and twisting periodic swing on observation errors. After understanding the quality of the earth, it is easy to calculate the quality of the moon and the sun based on the law of gravity, and then calculate the quality of other planets and celestial bodies in the solar system. Therefore His twisting experiments are also known as the sixth place in the most beautiful physical experiments. Cavendi's scientist little story

Many people say that Cavendi Xu is the richest person among the learned people in Britain in the 18th century, and the most knowledgeable people of rich people. Cavendi Xu is very cultivated, but there is no Gentleman in the UK. He didn't repair the border, and there was almost no clothes that could not be dropped; he was not good at communication, not good at talking, unmarried for life, and living a strange seclusion life. In order to engage in scientific research, Cavendi changed the living room to a laboratory, and there were many observation instruments beside the bedroom bed to observe the phenomena at any time. He used most of the money on the purchase of scientific instruments and books. He accumulated a batch of useful books. In addition to his own use, he also generously for other scholars. He also cherishes his collection of books and organizes well. Regardless of whether others borrow from him or use books by themselves, they must strictly go through the registration procedures. Wherever the book is removed, the restore place must be returned after reading it. Although his wealth is well, his life is very frugal. He wore a few old and old gentlemen. The concept of money is very weak in Cavendi's mind. He accepted a large legacy from his ancestors and became a millionaire, but he was not hesitant at all. On one occasion, one of his servants borrowed money from him due to difficulties in life. He did not hesitate to issue a check of 10,000 pounds, and asked if he was enough. Cavendi permits a scholar who lives to an old and old, until the age of 79 and is still experimenting with the eve of his death.

People specially set a monument for him to commemorate this great scientist. Later, his descendant relative Devon County Duke S.C. Cavendi made a donation of Cambridge University in his property donation and built a laboratory in 1871. It was originally a teaching laboratory named after H. Cavendi Xu Xu. Later, the laboratory was expanded into a scientific research and education center including the entire physics department, and it was named after the entire Kavadi family. The center focuses on independent, systematic, group pioneering experiments and theoretical explorations, and key equipment is advocated by self -control. This laboratory has made great contributions to the progress of physics science. In the past 100 years, Nobel Prize winners have been trained by Cavendi Laboratory. Maxwell, Ryley, J.J. Thomson, Lutherford, etc. have hosted the laboratory.

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