gravity

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This entry is made by Compilation and application of scientific encyclopedia entries of "Science Popularization China" to examine.

The force that an object receives due to the attraction of the earth is called gravity. The force applying object of gravity is earth 。

The direction of gravity is always vertically downward. The magnitude of the gravity on the object is consistent with the quality Is proportional, the calculation formula is: G=mg, g is Scale factor The size is about 9.8N/kg. The gravity changes with the latitude. The weight of an object with a mass of 1kg is 9.8N. The point where gravity acts on an object is called focus 。

Gravity can be used Dynamometer Measurement, stationary or Uniform linear motion The magnitude of the pull or pressure on the dynamometer by an object of 20% is equal to the magnitude of gravity.

The gravity of ground objects is only Universal gravitation A representation of the near surface of the earth.

Chinese name: gravity
Foreign name: Gravity
expression: G=mg or W=mg

Presenter: Isaac Newton
Proposed time: 1687
Applicable fields: Any star in the universe
Applied discipline: Physics

catalog

one brief introduction
▪ Force applying object and force bearing object
▪ Size and orientation
▪ Action point
two definition
▪ Many versions
▪ dispute
▪ Reconstruction reasons

eleven To terrestrial organisms
twelve Human life
thirteen reference
fourteen comment

brief introduction

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Force applying object and force bearing object

It can be approximately considered that the force applying object of gravity is the earth, and the force bearing object is the object on or near the earth's surface.

Size and orientation

The force exerted on an object by the attraction of the earth is called gravity. The direction is always vertical and downward, not necessarily pointing to the geocenter (only at the equator and poles). The magnitude of the gravity on the object at the same point on the ground is proportional to the mass m of the object. Similarly, when m is fixed, the magnitude of the gravity on the object is proportional to Gravitational acceleration G is proportional, expressed by the relationship G=mg. Generally, near the surface of the earth, the g value is about 9.8N/kg, which means that the weight of an object with a mass of 1kg is 9.8N. (9.8N is an average value; g is the smallest at the equator, g=9.79N/kg; g is the largest at the poles, g=9.83N/kg. N is the unit of force, the letter is N, and 1N is about the force to pick up two eggs)

Gravity is not equal to the earth's gravitation 。 Because of the rotation of the earth itself, except for the poles, objects on the ground all move around the earth axis at approximately uniform speed with the earth, which requires a centripetal force pointing vertically to the earth axis. This centripetal force can only be provided by the earth's gravity on objects. We can decompose the earth's gravity on objects into two components, one component F1, The direction points to the earth axis, and the size is equal to the object's approximation around the earth axis Uniform circular motion Required centripetal force; The other component G is the gravity exerted on the object. Where F1=mrw ^ 2 (w is earth rotation angular velocity , r is the radius of rotation of the object), it can be seen that the size of F1 is zero at the two poles, increasing with the decrease of latitude, and it is the maximum F1max in the equatorial region. Since the centripetal force of an object is very small, in general, it can be approximately considered that the gravity of the object is equal to the gravity of the universe, that is, the influence of the earth rotation can be ignored in general. The gravity component of gravity provides Gravitational acceleration The centripetal force component of gravity provides Centripetal acceleration 。

Action point

All parts of an object are affected by gravity. However, from the perspective of effect, we can think that the gravitational action on all parts is concentrated at one point, which is the equivalent action point of gravity, called the object's focus （center of gravity）。

The position of the center of gravity is related to the geometric shape and mass distribution of the object. For an object with regular shape and uniform mass distribution, its center of gravity is at its geometric center, for example, the center of gravity of a bar with uniform thickness is at its midpoint; The center of gravity of the ball is at the center of the ball; The center of gravity of the square plate is at the intersection of two diagonals. The gravity of the earth on an object seems to pull the object down from its center of gravity. If the center of gravity is supported by other objects, the object can maintain balance. But the position of the center of gravity is not necessarily above the object. Can be used Suspension method To determine.

For an object with uneven mass distribution, the position of the center of gravity is related not only to the shape of the object, but also to the distribution of the mass inside the object. The center of gravity of the truck changes with the amount of loading and the loading position, and the center of gravity of the crane changes with the weight and height of the lifted object.

The position of the center of gravity is of great significance in engineering. For example, when the crane is working, if the center of gravity position is not appropriate, it is easy to overturn; If the center of gravity of a high-speed rotating wheel is not on the shaft, it will cause intense vibration. Increasing the support surface of the object and reducing its center of gravity will help to improve the stability of the object.

definition

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Many versions

Gravity is Dynamics One of the most important and basic concepts in. However, various textbooks and reference books at home and abroad have different definitions of the concept of gravity, basically including the following five categories:

1. "The force on an object due to the attraction of the earth."

2. "The gravity of the earth on objects near the earth's surface is called gravity."^[1]

3.“ particle When suspended by a line and relative to the earth at rest, the direction of gravity on the particle is along the suspension line and vertically downward, and its size is numerically equal to the pull of the particle on the suspension line. "

"In fact, gravity is the balance force of the tension between the suspension line and the particle."

"When an object falls freely near the surface of the earth, it has a vertical acceleration g, and the force that produces this acceleration is called gravity."

4. For an object resting on the ground, the gravity is the component of the earth's gravity on the object that cannot produce acceleration, and the effect that can produce acceleration is all distributed to another component, that is, the centripetal force required for the object to rotate with the earth.^[2]

5. "All objects near the ground are attracted by the earth. The force exerted on objects due to the earth's attraction is called gravity."^[3]

Among the above five definitions, categories 1, 2 and 3 are used for approximate research under different circumstances. In order to meet the requirements of low difficulty, the definition of category 5 only touches the edge of gravity slightly, and the reader can only see the ambiguous image of gravity. The fourth type is established in the inertial system, which is narrow but precise in meaning.

Figure 1 Earth Attraction

Category 4 definition can reveal There are two parallel conditions required for the generation of gravity. One is that objects are subject to Universal gravitation The other is the acceleration of objects 。 The fourth kind of definition can be the representative of various definitions, which is called "the original definition of gravity" in the later description. The following is a schematic diagram of the original definition of gravity (Figure 1), showing gravity F Heavy Universal gravitation F lead And centripetal force F towards Relationship between:

It should be noted that these definitions have common defects:

① Only applicable to the area near the ground. Because the definition is established near the ground, it cannot be applied to the space farther away from the ground, let alone the space in the universe. But in Moon 、 Mars The study of the gravity of objects there is indispensable to the study of extraterrestrials or spaceships on the way to space.

② Even near the ground, when calculating the gravity of an object, only the universal gravitation of the earth on the object and the centripetal force of the object rotating with the earth are considered, but the universal gravitation of the sun, the moon and other planets on the object and the centripetal force of the object rotating with the earth around the sun are not considered, which is unacceptable.

dispute

Gravity is the only physical quantity that can exist in many versions at the same time. This phenomenon is unusual. This shows that it is quite difficult to establish the definition of gravity. The definitions of physical quantities in mechanics, such as gravity, elasticity and friction, as well as various physical quantities in heat, optics, electricity and atomic physics, have all established a single accurate version.

There is no one version of gravity definition that can exclude the existence of other versions and occupy its place exclusively in mechanics. The difficulty of establishing the definition of gravity makes the discussion about gravity have to be far avoided by people. This phenomenon, which is more difficult to understand than advanced science, does not conform to the laws of human understanding of nature.

Reconstruction reasons

Like gravity elastic force 、 friction And electric force Magnetic force These forces are real forces that exist objectively. Their definitions are established on the basis of innumerable experiments, and their correctness has been proved by innumerable experiments. But there is no such process in the establishment of gravity definition. Gravity is a virtual force artificially imagined through scientific thinking on the basis of existing theories. It is totally different from the birth of those actual force definitions. This is the internal factor of multiple reconstruction of gravity definition.

Since the definition of gravity is artificially imagined, the definition of gravity can also be artificially changed. Gravity, elasticity, friction and other real forces are not so casual.

New version

In 2012, a new version of the sixth definition of gravity appeared in the mechanics field. The sixth definition of gravity is: within the scope of statics, the support object or the object itself is Non inertial reference system The resultant force of the universal gravitation and inertial forces on an object is called gravity. The new definition is described in detail below:

1. The universal gravitation of objects from other planets and the corresponding inertial force cancel each other.

Taking the celestial body itself as a non inertial system, in the universe, the celestial body that is regarded as a particle, or the artificial celestial body that is tiny relative to the celestial body, or the aircraft that shuts down the engine, are all regarded as the "celestial particle" of the particle, and they are running in orbit. Because the celestial particle is not constrained by other kinds of forces other than the universal gravitation, such as the support force and the driving force of the engine, the universal gravitation of one celestial body to another celestial body will all be used to generate the acceleration of the celestial body, and corresponding to an inertial force. Because the magnitude of this inertial force is equal to the product of the acceleration of the celestial body and the mass of the celestial body, and the magnitude of the universal gravitation from another celestial body is equal to this product, and the direction of this inertial force is opposite to the direction of this universal gravitation, so the universal gravitation of another celestial body to the celestial body and the inertial force corresponding to its generated acceleration cancel each other. In this way, the gravitational force from another celestial body is all used to generate the acceleration force of the celestial body, and the celestial body will not have the effect of weight.

After the celestial body in the universe is regarded as a particle, the motion track and dynamic law of the object are the same as those of the object, so it is reasonable to regard the object and the object as two objects running in the same orbit. Therefore, the gravitational force from other celestial bodies can also counteract the inertial force corresponding to the acceleration it produces. The object does not gain weight from the gravity of other celestial bodies.

2. The universal gravitation of the planet where the object is located and the corresponding inertial force cannot offset each other

The universal gravitation of the planet where the object is located can no longer be offset by the corresponding inertial force. Because the surface of the planet has a supporting force constraint on the object, the universal gravitation of the planet on the object cannot be used to generate the acceleration of the object. Only one part of the acceleration (centripetal acceleration with the rotation of the planet) is generated, and the other part makes the object gain weight.

Later, we will often encounter problems like Article 1 and Article 2, which will not be explained in detail.

3. Under the new definition, the vector expression of gravity of objects on the ground (with the same derivation process on other objects)

Under the new definition, taking the ground as a non inertial system, the vector expression of the gravity on the ground can be derived more closely by using the principle of force balance. (Unified use F Represents gravity, f Represents inertial force, G Represents gravity, N Stands for supporting force. The letters in bold represent vectors, and the following is the vector operation)

The object placed on the support is subject to the universal gravitation of the earth F land And the universal gravitation of the sun F too , the gravitational force of the moon F month And the gravity of other planets. And the inertial force f due to the rotation of the earth land The inertia force corresponding to the universal gravitation of the sun (making objects revolve around the sun with the earth) f too Inertial force corresponding to the universal gravitation of the moon f month , and the inertial forces corresponding to the universal gravitation of other planets. And the support force of the ground N land , etc. When all these forces are balanced with each other, there are:

F land +F too +F month +…+f land +f too +f month +…+N land = 0

Because the universal gravitation of the sun, moon and other planets, except the earth, counteracts the corresponding inertial force. After sorting out, it can be concluded that:

-N land = F land +f land ①

Because of the support force of the ground N land Gravity with objects G Balanced with each other, there are:

-N land = G ②

Substitute formula ② into formula ① to get:

G = F land +f land ③

③ Equation is the vector expression of the gravity on the ground object under the new definition. This formula shows that the gravity of the object is equal to the combined force of the universal gravitation of the earth and the inertial force corresponding to the centripetal acceleration of the object rotating with the earth.

It can be seen that when calculating gravity near the ground, it is also correct that the gravitational force of the sun, moon and other planets does not participate in the calculation.

4. The new definition is equivalent to the original definition, and the original definition is a special case of the new definition

It can be proved that the new definition and " Inertial frame Gravity is the component of the universal gravitation of the earth on objects, and the other component is the centripetal force. " The original definition is equivalent, but the new definition is selected Non inertial frame 。

According to the new definition, the vector expression of the gravity on the ground object is:

G = F land +f land ①

The original definition under the inertial system is: the universal gravitation of the earth F land Is equal to the centripetal force required by the object to rotate with the earth F towards And the gravity of the object G The resultant force of. The expression is:

F land = F towards +G ② , this formula is

G = F land -F towards ③

Because the centripetal force required by the object to rotate with the earth F towards Is equal to the inertia force corresponding to this centripetal force f land And their directions are opposite, that is

-F towards = f land , which is obtained by substituting formula ③

G = F land +f land This formula is the same as formula ①.

So the new definition of formula ① is equivalent to the original definition of formula ②.

In Figure 2 of the following diagram, it can also be proved that the new definition is equivalent to the original definition by geometric method.

Figure 2

By gravity F land , Gravity G , and inertial forces f land Constituent parallelogram , is a newly defined schematic. From centripetal force F towards 、 F land and G The composed parallelogram is the schematic diagram of the original definition. It can be seen that in two parallelograms, the inertial force and the centripetal force are equal in size and opposite in direction, the two universal gravitations coincide, and the two gravitations coincide. It is proved that the two definitions are equivalent.

The new definition not only applies to objects on the earth, but also can be widely applied to celestial bodies, artificial celestial bodies and aircraft in the universe. In fact, the earth is also a celestial body in the universe.

Connotation of new concepts

1. The acceleration of an object is one of the important factors that determine the magnitude and direction of gravity. The acceleration is closely related to the reference system, so choosing a suitable reference system can obtain the simplest method for gravity research. If the reference system is not properly selected, sometimes wrong conclusions will appear. (This is quite different from the actual forces such as gravity, elastic force and friction force. The magnitude and direction of these forces are not directly related to the acceleration of the object, so the selection of the reference system does not change the difficulty of their research.) In this definition, the support object or the object itself selected to place the object is a non inertial system.

2. Gravity is the resultant force of gravity and inertial force or a component of gravity, and the resultant force obtained from the combination of forces or the component force obtained from the decomposition of forces are all forces imagined by people. So gravity is a virtual force.

3. Earth, Moon, Mars Artificial earth satellite From the physical point of view, they have no essential difference, and they are all real celestial bodies. According to the new definition (gravity is the resultant force of universal gravitation and inertial force on an object), the same object is placed on different celestial bodies, and the gravity on an object varies greatly. For example, the gravity of the same object on the moon is much smaller than that on the earth, and the gravity on the satellite is zero (completely weightless, in fact, it is only the universal gravity of the satellite on the object is extremely small).

4. The gravity of the same object will change greatly due to the change of acceleration.

5. The distance between celestial bodies is far greater than the diameter of celestial bodies, so celestial bodies can be regarded as particles when calculating the universal gravitation between celestial bodies. Except for the celestial body where the object is located, the universal gravitation of other celestial bodies to the object can offset the corresponding inertial force. But in fact, the volume of celestial bodies (except artificial sky) is very large. The acceleration of the object on the surface of the celestial body is different from that of the celestial particle, and changes at any time. Therefore, the universal gravitation of the object to other celestial bodies cannot completely offset their corresponding inertial forces, thus making the gravity of the object on the surface of the celestial body change. This is the reason why the earth's oceans have tidal changes.

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Universal gravitation

Structure drawing of gravity trolley (2 sheets)

In physics, Universal gravitation It refers to the trend of accelerated approaching between objects.

The attraction of the earth causes nearby objects to fall to the ground.

Gravitation is the reason for the existence of solar system and other galaxies; Without gravitation, celestial bodies cannot attract each other to form celestial systems. Gravity also makes the earth and other celestial bodies revolve around the sun according to their own orbits, Moon According to its own orbit around the earth, the formation of tides, and other natural phenomena observed by people.

Gravitation is the factor that makes objects gain weight.

Overweight and weightlessness

overweight : The phenomenon that the pressure of the object on the support (or the tension on the suspension rope) is greater than the gravity of the object is called overweight.

weightlessness : The phenomenon that the pressure of the object on the support (or the tension on the suspension rope) is less than the gravity of the object is called weightlessness.

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Uniqueness

Gravity is essentially different from elastic force, friction force, electric field force, etc.

Only the universal gravitation and inertial force are qualified to be the components of gravity, because they act on each element of the object at the same time, making the object gain weight.

Elastic force and friction force can only act on parts of the object. The electric field force can only act on the local part of the object, because the charge is distributed in the local part of the conductor when the conductor in the electric field is in electrostatic balance, and the charge is also distributed in the local part of the insulator after the insulator is polarized. The magnetic force can only act on the part of the object, because permanent magnets have magnetic poles, and soft magnets are magnetized in the magnetic field to produce magnetic poles. These forces acting on the local part of the object cannot make the object gain weight like the universal gravitation and inertial force.

Virtuality

1、 Generation of virtual force

The decomposition of force is to imagine a force as several components corresponding to each action effect according to multiple action effects of force, and replace the original force with these imaginary components.

The combination of forces is to imagine the joint effect of several forces as the effect of one force, which is called resultant force. And replace the original components with the imagined resultant force.

The imagined force is a virtual force.

Whether in the inertial system, gravity is defined as a component of gravity, or in the non inertial system, gravity is defined as the combined force of gravity and inertial force. Gravity is imagined, and gravity is a virtual force.

2、 Characterization of gravity virtuality

The real force of objective existence should have its force and force. This is not the case for virtual forces. For example, inertial forces do not have force objects. From a theoretical point of view, gravity is a virtual force, and it is impossible to determine the specific force.

If we make an approximate study and regard gravity as the universal gravitation of the earth to the object near the ground, then the earth is the force and the object is the force for gravity.

Practical test

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The scientificity of the new definition can be tested by the following three examples.

From weightlessness to "gaining weight"

Artificial celestial body with artificial gravity device (2 sheets)

By rotating the satellite to a certain speed, astronauts who were completely weightless could regain their weight similar to that on the ground. As early as the 1960s, this idea appeared in some popular science books, imagining creating a living environment similar to the earth's surface on satellites. But I didn't realize at that time that long-term flight in weightlessness would lead to bone decalcification, muscle relaxation, etc., which would harm the health of astronauts. The expedition to Mars will go through a long period of time. In order to make the health condition allow astronauts to adhere to the scientific research tasks entrusted by mankind, scientists are ready to install them in the cockpit of manned spacecraft“ Artificial gravity device ”The idea is the same as before. The process of making objects in weightlessness regain weight similar to that on the ground, referred to as "gaining weight". The basic principle of gaining weight can be explained by the new definition of gravity. The universal gravitation of each planet received by the astronauts in the cockpit has been offset by the inertia corresponding to the acceleration of each universal gravitation. In the absence of universal gravitation, astronauts can only rely on inertial force to gain weight. This led scientists to think of turning the cockpit. In this way, there is no gravity involved in gaining weight, and the gravity of the astronaut is only equal to the inertial force corresponding to the centripetal force of his rotation with the cockpit. It can be seen that "gaining weight" depends on the other side of its contradiction, "losing weight".

The origin of the earth's ellipsoid

The objects placed on the earth's surface have Centripetal acceleration 。 The centripetal acceleration of objects on the equator is the maximum, and the centripetal acceleration of objects on the poles is equal to zero, and the minimum.

In order to explain why the earth is slightly ellipsoid, the positions of objects at different latitudes should be selected as non inertial frames. The same object is at the equator Centripetal acceleration Maximum, so the inertial force on the object is the largest, but the direction is opposite to the universal gravitation, and the universal gravitation is also the smallest. In this way, the combined force of gravity and inertial force is the smallest relative to other latitudes, that is, gravity is the smallest. The universal gravitation is the largest relative to other latitudes on the two poles, while the centripetal acceleration is zero, that is, the minimum, and the inertial force is also the smallest, so the gravity is the largest. In this way, the same object moves from the equator to the pole, the gravity gradually changes from the minimum to the maximum, and the specific gravity of the object gradually increases. The sea water is the main part of the earth's surface, and the sea water near the equator has the smallest proportion. According to the principle that the liquid level on one side of the connector with a small proportion is higher than that on the other side, the sea water here will protrude a little. This makes the plastic earth, under the effect of gravity distributed in this form, become an ellipsoid with the equator far from the geocenter and the poles close to the geocenter.

Although the sea level is ellipsoid, at any point on the earth's surface, the direction of gravity of the object is always perpendicular to the sea level at its location, or is always perpendicular to the stationary water surface parallel to the sea level.

The cause of tide

Figure 3 The sea surface is spindle shaped in the tide phenomenon

Figure 1

tide The main cause of formation is the effect of the moon and the sun on the ocean. Only analyze here Moon Role of. Due to the effect of the moon on the ocean, the tide rise phenomenon occurs simultaneously in the two regions of the sea surface closest to the moon and the sea surface farthest from the moon (the two regional centers are called perilunar points and apolunar points respectively),

So that the ellipsoidal sea level is superimposed Spindle Shape (as shown in Figure 3). Why is that?

Before the narration, it is agreed to ignore the influence of other planets other than Earth and Moon, and not consider earth rotation And revolution. The view that the tide phenomenon appears spindle shaped sea level is that the rotation of the earth and revolution 。

It is reasonable to think that the actual situation is that the rotation of the earth makes the following process happen at any time: while the earth material at the near moon point leaves, another part of the earth material moves into the near moon point and inherits the movement state of the earth material leaving, so does the far moon point. This keeps both ends of the spindle at the perilunar and apolunar points.

Represented by boldface vector , unified F Represents gravity, f Represents the inertial force G Represent gravity, and take their respective positions as non inertial frames. The following operations are vector operations.

According to Figure 4, the mass of m is taken at the geocenter, and the mass of m is taken at the near moon point near And the mass is m at the far moon point far Take three substances as three objects and take them as three research objects, and set m=m near =m far 。

Figure 4

The earth and the moon are regarded as particles, which means that the moon moves in a circle around the earth. In fact, both the moon and the earth move in a circle around their common center of mass, but the orbit of the earth is much smaller. (The circumferential orbits of two stars with similar mass are approximately equal) The universal gravitation of the earth particle by the moon particle is just the centripetal force of the earth particle moving in a circle around the common center of mass, so the universal gravitation here is equal to the centripetal force. Taking the geocenter as the non inertial system, the inertial force corresponding to this centripetal force is opposite to the direction of the same magnitude of this centripetal force. Therefore, the universal gravitation of the earth particle affected by the moon particle is opposite to the inertial force in the same direction, and they cancel each other out.

The object m is on the center of the earth, and its motion track and dynamic law are exactly the same as those of the earth particle, so m can be regarded as a planet in the same orbit as the earth. So m receives the gravitational force of the moon F month And the corresponding inertia force f month They cancel each other out. here you are F month =f month The following is based on this formula to compare the force.

In fact, the earth is too large to be regarded as a particle. Since the far moon point, near moon point, geocenter, lunar center and the earth moon common center of mass are always on the same straight line, the angular velocity of the two points of the two centers running around the earth moon common center of mass is the same (as shown in Figure 4).

In this way, m near Same angular velocity as m, while m near The orbit radius around the Earth Moon common centroid is smaller than m, which makes the near The centripetal acceleration of is smaller than that of m at the geocenter. The result is m near Inertial force f Near the moon Than m f month Small. And because m Near the moon The distance to the moon is also smaller than m, so m near By the gravitational pull of the moon F Near the moon Greater than m F month 。 with F month = f month It can be seen from the comparison of standards F Near the moon greater than f Near the moon 。 obtain F Near the moon And f Near the moon And m near By the universal gravitation of the earth F Near the ground Reverse. To find m near Gravity of G near ， G near = F Near the ground +（ F Near the moon + f Near the moon ）, m near Gravity received G near Less than the gravitational force of the earth F Near the ground (If there is no effect of the moon G near = F Near the ground ）, that is, due to the effect of the moon, m near Reduced gravity, m near The proportion of is also smaller. If m near It is the sea water here, so there will be flood tide here, which is the same as the principle of the connector mentioned in the previous paragraph. Using the same method to study the m of apogee far , although already F The moon is far away less than f The moon is far away However, the combined force of the two is also opposite to the gravity of the earth. The role of the moon also makes m far The gravity of becomes smaller and the specific gravity becomes smaller. So the sea water at the far moon point will also have high tide. This makes the sea level slightly like a spindle.

The analysis method of the sun's effect on the ocean is the same as that of the moon. The combined action of the two, together with the intersection of their orbital planes, the different topographies and landforms in different regions, and the rotation of the earth, makes the tide phenomenon at specific locations on the earth's surface more complicated.

If there are oceans on the moon, there will also be tides. Because the ratio of the lunar radius to the lunar orbit radius is already very small, the phenomenon will not be obvious.

The asteroid will be torn when it approaches Jupiter, which can also be explained by the method here.

application

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In the area near the ground, the study and application of gravity adopt an approximate method. The approximate method ignores the rotation of the earth. Gravity is approximately equal to the universal gravitation. The same object receives the same universal gravitation everywhere. Thus gravity is approximately constant. Under this premise, the concept of gravity in middle school is established. By using the approximate method, the study of dynamics problems involving gravity can be carried out smoothly near the ground, especially the study of projectile motion. In order to comply with the requirements of difficulty, the approximate method is the only choice to study and apply gravity in middle school. However, the definition of gravity adopted here has substantial problems, which will be described in detail in Article 4 of the paragraph [Problem Analysis].

In the approximate study, we are exposed to the universal gravitation in the cloak of gravity. In fact, we are not studying gravity but studying universal gravitation. It is a scientific and reasonable method to make gravity take off its illusory coat and combine with elasticity and friction to form the three basic forces in middle school mechanics (the measurement of gravity will have small systematic errors due to the rotation of the earth, which is allowed by approximate research). As for gravity, the scientific concept of gravity was obtained through in-depth excavation and introduced into university textbooks.

It should be noted that without the premise of setting gravity as a constant force, the concept and definition of gravity in middle school cannot be established.

The application of new concepts and definitions is included in the following contents: [Practice Test], [Phenomenon Essence], [Problem Analysis] and [Smooth Operation of Accelerating Moving Objects].

Essence of phenomenon

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"The phenomenon that the pressure of the object on the support (or the pull on the suspension) is greater than the gravity of the object is called the overweight phenomenon". Conversely, it is called weightlessness.^[3] In this way, the phenomenon is presented to the reader without revealing the essence of the phenomenon, or the mechanism of appearance. The mission of mechanics is not like this. The essence of overweight and weightlessness is discussed as follows.

In the approximate application near the ground, the rotation of the earth is not considered and the universal gravitation is considered to be a constant force. According to the definition of "taking the support for placing objects as a non inertial system, gravity F heavy Is the universal gravitation F of the object lead And inertia force F Habitual The resultant force of ", using the lift as a non inertial system to calculate the gravity of the object placed on the dynamometer in the lift. The gravity of the same object is different under different accelerations. The change of gravity can reflect the essence of overweight and weightlessness (refer to Articles 1 to 4). In the following process, the universal gravitation cannot be changed, but the inertial force can be changed by changing the acceleration, so as to artificially change the gravity.

1. When the acceleration of the lift is zero, the inertial force on the object is zero, and gravity is equal to universal gravitation. Its size can be regarded as the weight of an object under normal conditions, and the normal weight is equal to the size of gravity.

Essence of phenomenon

2. When the acceleration direction of the lift is upward, the reading of the dynamometer becomes larger. The inertial force on the object is downward, and the gravity is equal to the gravity plus the inertial force, so the gravity is greater than the gravity. (The gravity increases, but the universal gravitation remains the same) The object is overweight.

Essence of phenomenon

3. When the acceleration direction of the lift is downward, the reading of the dynamometer becomes smaller. The inertial force on the object is upward, and the gravity is equal to the gravity minus the inertial force, so the gravity is less than the gravity. (The gravity becomes smaller, but the universal gravitation remains the same) The object is weightless.

Essence of phenomenon

4. When the acceleration direction of the lift is downward and the magnitude is equal to the gravitational acceleration, the reading of the dynamometer becomes zero. The inertial force on the object is upward and equal to the gravity. The gravity is equal to the gravity minus the inertial force, and the result is zero. (The gravity becomes zero, but the universal gravitation remains unchanged) The object appears Complete weightlessness 。

Essence of phenomenon

5. Assuming that the earth does not rotate, if the universal gravitation of objects on the earth's surface is set as normal gravity in this case, it can be said that all objects on the ground are in a weak weightlessness state in the real situation.

6. The universal gravitation of the earth on an object placed in a satellite corresponds to the Centripetal acceleration The two forces are equal in magnitude and opposite in direction, making gravity zero and the object completely weightless. In fact, the satellite has a tiny gravitational force on objects, so it is called a microgravity laboratory inside the satellite.

7. If an object in weightlessness is supported again, it will be subjected to new gravity. If the engine of a spaceship is turned on, the objects inside the spaceship and the spaceship itself will also receive new gravity.

8. It should be noted that since gravity acts on every element of the object at the same time, overweight and weightlessness will occur on every element of the object.

9. Overweight, weightlessness and "gaining weight" are all external manifestations of the ever-changing gravity on objects. The gravity of the same object changes due to the change of acceleration. The change of gravity should be the focus of mechanics. Mechanics does not need to deliberately list overweight and weightlessness as a subject to study at a loss.

Acceleration problem

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The definition of gravity was originally established in statics. In middle school textbooks, the study of the motion of projectile (free fall is a special case of projectile) belongs to the category of dynamics. In order to meet the requirements of teaching materials, it is stipulated that gravity is a constant force within the range near the ground, Gravitational acceleration Constant. In this way, the projectile motion can be studied smoothly with the ground as the inertial frame.

However, if we go beyond the area near the ground and study the dynamics of gravity with the ground as the reference system, there will be Newton's law of motion Inconsistencies. Examples are as follows:

Example 1. Taking the ground as a non inertial system, the synchronous satellite is stationary relative to the ground, and should be balanced under force. But on the ground Centripetal acceleration It is much smaller than the centripetal acceleration of synchronous satellite. According to the definition of inertial force, the inertial force of synchronous satellite must be substituted into the centripetal acceleration of the ground as the reference frame. In this way, the inertial force on the geostationary satellite calculated is much smaller than the universal gravitation of the earth on the geostationary satellite. The two forces cannot be offset, and the force on the geostationary satellite is not balanced. This is inconsistent with Newton's law of motion.

Example 2. Move the synchronous satellite out of orbit and place it on the top of an iron tower lower than the synchronous satellite. The synchronous satellite is no longer a satellite and must be supported by the tower top. It is stationary relative to the ground. According to the same principle in Example 1, the calculated inertial force of the synchronous satellite and the support force of the iron tower, the combined force of the two upward forces is less than the gravitational force of the downward earth, and the combined force of the three forces is not zero. How can the object be at rest. This is related to Newton's law of motion Does not match. In the same way, if the synchronous satellite is moved down to any position of the iron tower above the ground, the synchronous satellite will be at rest. However, the force is unbalanced, which is inconsistent with Newton's law of motion. But taking the support point of the tower to the synchronous satellite as a non inertial system, studying gravity in the scope of statics will conform to Newton's law of motion. Because when the object is stationary, the combined force of the support force of the upward tower and the upward inertial force counteracts the gravitational pull of the downward earth, and the force is balanced.

Since the ground is regarded as a non inertial system, when studying the mechanical problems related to gravity in the space outside the ground Newton's law of motion If not, the ground can not be used as a non inertial system to study the projectile motion related to gravity. Then is there any significance of gravity acceleration in this space? Even near the ground, the projectile motion is studied by approximate method, which is theoretically impossible.

Theoretically, gravity has no chance to generate acceleration, because ① gravity cannot exert its ability to generate acceleration when the object is stationary. ② When the projectile moves, the object no longer rotates with the earth due to the constraints of the support, and gravity loses the conditions for existence, Gravitational acceleration It will not appear. (These will be detailed later)

Therefore, in theory, taking the ground as a non inertial frame to study dynamic problems will Newton's law of motion Conflicts occur. So in this case Gravitational acceleration There is no need to exist. However, it is always necessary to study the movement of objects in this space and in the universe, which can only be studied in the inertial system outside the Earth. In this way, the acceleration of the object can only be the gravitational acceleration, and the gravitational acceleration has lost its significance.

Existence conditions

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The definition of gravity is established on the premise of balance between gravity and supporting force. Without support, gravity disappears. For example, empty shell projectile, spacecraft with engine off, artificial satellite, etc., the objects in its interior can not be supported, and gravity can not appear Complete weightlessness 。 It should be noted that although gravity disappears, gravity still exists.

When making an approximate study of the projectile near the ground, gravity is still there“ Gravitational acceleration ”How to explain this? In fact, in the study of this approximation, gravity has been approximated to universal gravitation, and gravitational acceleration has been approximated to universal gravitation acceleration. Therefore, gravity and gravitational acceleration should not be mentioned here. The main explanation is as follows.

There is an important relationship, that is, the universal gravitation or inertial force, because its effect is to make objects gain weight, so their common action is called gravity. This is the relationship between gravity or inertia force and gravity, that is, the relationship between the original name and the effect name. Gravity is an effect force. Since it is the effect force, the effect force will disappear when the effect disappears (the gravity disappears, and the universal gravitation does not disappear). Look at the following example.

Under the inertial reference frame, the object that loses its support force will accelerate. At this time, it is only subject to the effect of gravity, which makes the object gain weight completely invisible on the object. The effect of universal gravitation is no longer to make the object gain weight, but to produce the acceleration of universal gravitation, and the object appears Complete weightlessness At this time, the effect name of gravity is no longer gravity.

The weightlessness of solid objects after removing the support is not easy to be perceived. But when people lose their support, they can feel the loss of gravity in all parts of the body. All parts of the body are light and effortless. The pressure and support between the cells of the human body have disappeared, so there is a feeling of numbness on the body.

The drop without supporting force is spherical when falling, which can also prove that the drop has occurred weightlessness Phenomenon.

Once the object is lost Supportability At the same time, the gravity is lost Complete weightlessness 。 At this time, not only the pressure and support between the object and the support disappeared, but also the pressure and support between all the elements in the object disappeared.

The existence condition of gravity determines that the study of gravity must be within the scope of statics.

problem analysis

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Satellite weightlessness

One is to explain the point of view of satellite weightlessness: Centripetal acceleration , "Its size is equal to the height of the satellite Gravitational acceleration Size of. This is similar to what happens in a lift that descends with gravity acceleration ".^[1]

The following problems must be analyzed:

Without considering the revolution of the earth and the influence of other planets outside the earth, the research is carried out in an inertial system outside the earth. This can not only observe the rotation of the earth, but also observe the correct orbit of the satellite. In this inertial system, the original definition of gravity believes that the universal gravity of the earth on objects can be divided into the centripetal force and gravity which rotate with the earth. Use this way of thinking for the following analysis. (The universal gravitation of the earth is called Earth gravitation for short)

Imagine that there is a bracket on the equator equal to the height of the synchronous satellite. The first step is to place an object on the bottom of the bracket. Under the constraint of the support, the object rotates with the earth Uniform circular motion 。 The gravity of the earth on the object is decomposed into a very small centripetal force and a gravity not much smaller than the gravity of the earth. Next, move the heavy objects from the bottom up gradually and place them at different heights of the support. In this process, the gravity of the earth becomes smaller and smaller, and the centripetal force decomposed becomes larger and larger, and gradually approaches the gravity of the earth. The gravity decomposed becomes smaller and smaller, and gradually tends to zero. Finally, move the object to the top of the bracket. At this time, the centripetal force is equal to the gravity of the earth, and the gravity is small to zero, and the object has become a new synchronous satellite. Its centripetal force is definitely not equal to gravity, so the centripetal acceleration can be equal to Gravitational acceleration Is it? Obviously not. In fact, there is only one effect of gravity on any satellite, generating acceleration. That is, they are all used to provide centripetal force, leaving no effect on the object to gain weight. The effect is gone. The gravity is zero, and the gravitational acceleration is zero. To put it correctly, it should be: "The reason for complete weightlessness is that the satellite Centripetal acceleration The size of is equal to the gravitational acceleration at the height of the satellite.

In explaining the point of view of satellite weightlessness, the law of free fall was applied to the satellite stiffly, saying that "this is similar to what happens in the elevator that descends with the acceleration of gravity", which is paradoxical. If we ignore the rotation of the earth, gravity is gravity. This kind of approximate research can be said as: "This is similar to what happens in an elevator that descends with the acceleration of gravity." It is correct.

There is the word "satellite altitude" in the viewpoint, which indicates that the original intention of the viewpoint is to take the ground as the height starting point and the ground as the reference frame, which leads to problems. First, in the non approximate research (theoretical research), when the ground is the non inertial frame Newton's law of motion It is untenable to study the dynamics of satellites. Second, the dynamics of satellites does not belong to the scope of approximate research, and the ground cannot be used as the inertial frame. Therefore, the reference to "satellite altitude" is not suitable anywhere. The dynamics of satellites can only be correctly studied in an inertial system outside the earth. The dynamics of satellites in this inertial system has nothing to do with the rotation of the earth. However, the virtual force of gravity can only "exist" because of the rotation of the earth, so the problem of satellite weightlessness is not linked to the gravitational acceleration.

Using the new definition of gravity, the satellite is offset by the gravity of the earth and the corresponding inertial force. The gravity of the satellite is zero, but the centripetal force of the satellite is not zero. Or say Gravitational acceleration If it is zero and the centripetal acceleration is not zero, they cannot be equal.

For a satellite in normal operation, if the object in the satellite cannot get support, the gravity of the object cannot exist, and the gravitational acceleration does not exist, but the centripetal acceleration still exists. In this respect, the centripetal acceleration cannot be equal to the gravitational acceleration at the satellite altitude.

In fact, the gravity of satellites and their internal objects is calculated in a non inertial system, while the centripetal force is calculated in another inertial system. The quantity of kinematics should not be compared under the original two reference systems.

Spacecraft weightlessness

Another problem is to explain the viewpoint of spaceship weightlessness: for a spaceship running in a circular orbit near the ground, let its linear velocity be nu "Its orbital radius is approximately equal to the radius of the earth R, and the gravity of the astronaut is approximately equal to his weight measured on the ground mg... It may also be supported by the spaceship cabin F N 。 Gravity and support provided him with the ability to circle the earth Uniform circular motion Required centripetal force ". Through analysis, formulate equations and solve, "When

The cockpit's support for astronauts F N =0. The astronauts are in weightlessness ".^[3]

The following questions need to be considered:

① To get F N =0 is an accurate (idealized) equation, but the value of the satellite orbit radius is approximately the value of the earth radius R, and the value of the earth gravity is also approximately the value of the weight on the ground mg. The process of doing pure theoretical derivation cannot take many approximate values like doing approximate calculation.

② In this point of view, only the spacecraft operating in the orbit near the ground is used to say the problem, and the spacecraft in any orbit is not used to say the problem, nor is it expanded, so it has no broad significance. It does not mean that the spacecraft in any orbit will lose weight.

③ In the opinion, through approximate deduction, the conclusion "when

The cockpit's support for astronauts F N =0. The astronauts are in weightlessness ". "Dang" here basically means "condition". However, as long as the spacecraft is in normal operation in orbit near the ground, weightlessness will occur unconditionally!

④ When equation

F exists when it is not established N ≠ 0, will astronauts not lose weight? No, but the point of view is very like "yes". In fact, even if the linear speed of this spaceship changes, it is no longer

The spacecraft will only change its orbit, and weightlessness must exist unless the engine is turned on or it falls to the ground or other planets.

Weightlessness environment

Another problem is the view that there is a "completely weightless environment": "The astronauts are weightless in a spaceship that moves around the earth at a uniform speed." "In fact, the interior of any aircraft that has its engine turned off and is not subject to resistance is a completely weightless environment. For example, all objects in a container thrown in any direction in the air are weightless. "^[3]

stay Non inertial reference system The essence of the phenomenon of complete weightlessness of an object is that the gravitational force and the inertial force corresponding to the acceleration generated by the gravitational force cancel each other, and the gravity becomes zero, so the object is completely weightless. Once the object is completely weightless, it has nothing to do with the space environment around the object, and has nothing to do with the "completely weightless environment". For example:

① Assuming that the spaceship or the thrown container can be opened like a shell, the object is no longer in the original "completely weightless environment", but the motion law of the object has no change, not still in the Complete weightlessness Is it?

② In orbit, let the big satellite load the small satellite into the big satellite without contacting the small satellite. In this way, the small satellite is in a "completely weightless environment". According to the above view, the small satellite is completely weightless. However, the operating attitude of the small satellite has not changed before and after entering the large satellite, so the small satellite is in a completely weightless state although it is not in a "completely weightless environment" when operating alone.

The above "loading side" can also prove that the projectile itself must be in a state of complete weightlessness.

③ On the outside of the upper end of a long pipe in midair, use a suspension rope to put a system into the pipe, and fix the other end of the suspension rope. Then let the long tube fall freely. At this time, the tube is in a "completely weightless environment", but the object is fixed. Although it is in a "completely weightless environment", it is not weightless.

④ From the upper end of the long pipe placed on the ground, drop a drop of water to make it fall freely. The water drop is spherical because it is in the Complete weightlessness 。 But the place where the water drops pass is not a "completely weightless environment".

In fact, the spaceship itself or the thrown container itself must also be completely weightless. Because the universal gravitation they are subjected to and the corresponding inertial force also cancel each other, the gravity is also zero, of course, weightlessness. Therefore, "totally weightless environment" has no meaning of existence. The weightlessness phenomenon occurs on every element of the object at the same time, which is the matter of the object itself and has nothing to do with the space it is in.

Approximate application

The definition of gravity used in the approximation method is: "All objects near the ground are attracted by the earth, and the force that objects are attracted by the earth is called gravity".^[4]

① Gravity is an important concept in high school mechanics. The application of gravity runs through the contents of mechanics. The definition of gravity given by the approximate method only touches the edge of gravity slightly, giving a vague concept of gravity. When you enter mechanics with gravity doubts, you will encounter many difficulties when you use gravity tools with unknown performance to solve mechanical problems.

② In the approximate study, the unique nature of gravity and the unique role of gravity did not appear. In fact, it uses the universal gravitation in the cloak of gravity to participate in various research processes of dynamics. Although the definition of gravity is given, it is not really applied.

③ In essence, near the ground, gravity itself is gravity with small systematic errors systematic error It is caused by the rotation of the earth. In this case, it is OK to introduce the universal gravitation into the approximate research. It is only necessary to explain that there must be systematic errors in the measurement, which will not affect the application of the universal gravitation near the ground. In this way, the position that gravity occupies in middle school textbooks can be returned to gravity. In this way, in the middle school textbooks, the center of gravity should be changed to the center of mass, the gravitational acceleration should be changed to the gravitational acceleration, and the gravitational potential energy should be changed to the gravitational potential energy. The difficulty of gravity is far greater than that of universal gravitation. At the middle school stage, the content of gravity has exceeded the ability to understand.

Accelerate the smooth operation of moving objects

The following examples all ignore the influence of the earth rotation, and take the research object as a non inertial system, and the research object is stationary relative to the reference system, so that gravity can be studied within the scope of statics. Here, we focus on the smooth operation (non overturning) of accelerating moving objects and the change of gravity. Let the universal gravitation be F lead , inertia force F Habitual , gravity is F heavy 。

1. Within the scope of statics, the train running at the specified speed at the turning point is a non inertial system (in order to make the speed at the turning point just match the required centripetal force, the outer rail here is a certain distance higher than the inner side), and the force on the car when turning is studied. At this time, the carriage Uniform circular motion The direction of centripetal acceleration points to the center of the circle inside the curve, and the inertial force is opposite to the direction of centripetal acceleration. The combined force of gravity and inertia force on the carriage is gravity, which is balanced with the supporting force of the two rails. It can be seen from (Figure 5) that gravity is no longer vertically downward, but is inclined to the outside of the curve, deviates from the vertical direction by an angle θ, that is, it is perpendicular to the plane of the two rails, so that the gravity action line passes through the center of the support surface of the two rails. The gravity is greater than the universal gravitation, and the carriage is overweight.

Practical application: cyclists always lean the body to the inside of the curve at an appropriate angle when turning, so that the action line of the combined force of gravity on people and vehicles can pass through the center of the narrow support surface under the wheels to ride smoothly.

Figure 5

2. In the field of statics, taking the accelerating forward vehicle as the non inertial frame, the force on the ball suspended on the vehicle by the string is studied when the vehicle is stationary. The resultant force of the earth's universal gravitation and inertial force on the ball is gravity, and gravity and the pull of the string balance each other. After balance, the gravity and the string are in the same straight line (the same as when the car is stationary, the gravity and the string are in the same straight line), and the direction of gravity is downward and backward. It can be seen from (Figure 6) that the gravity deviates from the vertical direction by an angle θ, the gravity is greater than the universal gravitation, and the ball is overweight.

Practical application: The person standing on the accelerating car always inclines his body forward at an appropriate angle (no longer vertical to the ground), so that the line of gravity passes through the center of the supporting surface under his feet, so that he can be stable.

Figure 6

3. In the field of statics, the force on the sliding block is studied by taking the sliding block itself which slides down along a smooth slope as a non inertial system. The slider is at rest relative to the reference system. The resultant force of gravity and inertia force of the earth on the sliding block is gravity, and the gravity and the support force of the inclined plane are balanced. After balancing, the direction of gravity points vertically to the support surface of the inclined plane (as the sliding block is resting on a smooth horizontal plane, it points vertically to the support surface). It can be seen from (Figure 7) that the gravity deviates from the vertical direction by an angle of θ, the gravity is less than the universal gravity, and the sliding block is weightless.

Practical application: Skiers who speed up the slide must tilt their bodies forward at an appropriate angle (not perpendicular to the ground. If friction is not considered, they should be perpendicular to the slope, that is, perpendicular to the snow surface on the hillside), so that the line of gravity action passes through the center of the supporting surface under their feet, and then they can slide smoothly.

Figure 7

To terrestrial organisms

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Plants in space grow randomly (2 sheets)

Because of the existence of gravity, it has a profound impact on life on the earth. yes Cell senescence The root cause of. Gravity is the "culprit" of the cycle of life and death of all kinds of creatures on the earth. Because of the effect of gravity, macromolecules, DNA and proteins in cells begin to accumulate in a specific direction after the long-term accumulation of gravity, gradually forming cell aging, which leads to the death of individual organisms.^[5]

Due to the existence of gravity, the roots and stems of plants are affected by gravity, so that the distribution of auxin is uneven. There are few in the far side, and more in the near side. Different organs of plants have different sensitivity to auxin. When the concentration of auxin is high, it is suitable for the growth of stems. Therefore, the stem back of plants grows by gravity. The roots of plants grow towards gravity.

Human life

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Gravity is closely related to human life. Human beings have long used gravity to measure the force on objects. Before the spring appeared, the scale was a tool used by human beings to compare the weight of objects; After the spring appeared, the spring scale was used to weigh the weight. The gravity of the same object changes very little in the space near the ground, so it can be regarded as a constant in daily life, which is the convenience of using gravity as a force measuring unit. Since the gravity of an object is almost constant, Galileo realized that Gravitational acceleration It is also a constant. Galileo's research laid the foundation for Newton's research. Newton published in 1687 Law of universal gravitation Later, the physical origin of gravity was found. Since then, human beings have a more correct understanding of gravity. Newton obtained the concept of universal gravitation by comparing the two phenomena of objects falling to the ground and the moon not falling to the ground. Through the law of universal gravitation and Newton's law of motion , human beings finally understand the basic theory of mechanics and the mechanical movement of objects. According to Newton's concept, gravity is a force beyond the distance. Newton extended gravity to universal gravitation, thus explaining the Kepler's law At the same time, the classical mechanics widely used in engineering is established.

reference

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1. Author: Wang Jiaxuan《 Encyclopedia of China 》Volume 74 (first edition) Mechanical entry: Gravity: China Encyclopedia Press, 1987:596

comment

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Not only Universal gravitation It is the factor that makes the object gain weight. The object accelerates relative to the inertial frame and "appears" in the non inertial frame inertia force It is also an important factor for objects to gain weight.

The acceleration of the accelerated motion of the object with the earth's rotation makes the gravity of the object less than the universal gravity. Is there any difference in essence between this acceleration of the object and the acceleration of the object in other forms of motion? No, Therefore, the acceleration of an object in any form of accelerated motion should be able to determine the size of the weight obtained by the object.

Therefore, the influence of acceleration can be reflected in the calculation of gravity by involving inertial force and universal gravitation in a non inertial system.

Gravity should be the combined force of gravity and inertial force.

In the absence of universal gravitation, the inertial force can independently make the object gain weight. For example, if the astronauts in the artificial satellite have completely lost weight and let the satellite rotate to a certain speed, the astronauts can gain weight similar to that on the earth. This cannot be explained by the original definition of gravity.

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