What are the reasons for the movement of bodies. Newton's laws

Indeed, even in ancient times, Aristotle very clearly and convincingly explained the cause of movement. He asked a simple question - if a donkey drags a cart along the road, then what is the reason for the movement of the cart? - has a simple intuitive answer - the reason for the movement of the cart is the action of the donkey.

This answer was not questioned until Galileo, who saw Aristotle’s mistake - the reason for rectilinear uniform motion does not exist at all; if a body is set in motion, then in the absence of interference the body will move indefinitely:
...the degree of speed exhibited by a body lies inviolably in its very nature, while the causes of acceleration or deceleration are external; this can only be noticed on a horizontal plane, because when moving down an inclined plane, acceleration is observed, and when moving up, deceleration is observed. It follows from this that horizontal motion is eternal, for if it is uniform, then it is not weakened, slowed down or destroyed by anything.

This intuitive error is also present in physics lessons: if you ask students before studying this topic (and sometimes after studying it) “What is the reason for the rectilinear uniform motion of, for example, a car on a flat straight road?”, then very often you can hear that the reason car movement in in this case in engine operation. This answer is due to the fact that indeed, if you turn off the engine, the car will stop very quickly.
That is why it is necessary to explain in great detail the basic laws of dynamics, using not only the formulations from the textbook,
Here, for example, are the formulations of Newton’s first, second and third laws that can be found in textbooks:

Author 1 Newton's law 2 Newton's law 3 Newton's law
O.F. Kabardin There are such reference systems relative to which translationally moving bodies maintain their speed constant if other bodies do not act on them. The force acting on the body is equal to the product of the mass of the body and the acceleration imparted by this force. Bodies act on each other with forces directed along the same straight line, equal in magnitude and opposite in direction

S.V. Gromov
Grade 10 Any body, as long as it remains isolated, maintains its state of rest or uniform rectilinear motion If a particle of mass m is acted upon by surrounding bodies with a force F, then this particle acquires such an acceleration a that the product of its mass and acceleration will be equal to the acting force. The interaction forces of two particles are always equal in magnitude and directed in opposite directions along the straight line connecting them

S.V. Gromov
8th grade. Any body, as long as it remains isolated, maintains its state of rest or uniform rectilinear motion. The product of the body’s mass and its acceleration is equal to the force with which the surrounding bodies act on it. The forces with which two bodies interact are always equal in magnitude and opposite towards

I.K. Kikoin There are such reference systems relative to which a translationally moving body maintains a constant speed if other bodies do not act on it (or the action of other bodies is compensated). The force acting on the body is equal to the product of the mass of the body and the acceleration imparted by this force. Bodies act on each other with forces equal in magnitude and opposite in direction

But also return to the original sources:
1 law (in Newton's original formulation)
Every body maintains a state of rest or uniform rectilinear motion, unless it is forced to change it under the influence of acting forces.
Newton wrote in his Principia:
An applied force is an action performed on a body to change its state of rest or uniform linear motion.

Strength manifests itself only in action and does not remain in the body after it ceases. The body then continues to maintain its new state due to inertia alone. The origin of the applied force can be different: from impact, from pressure, from centripetal force.

In addition, it is necessary to conduct a number of demonstration experiments, including the mental experience of Galileo.
Galileo's experiments. Take an inclined plane and place a ball on its top. If the ball rolls down an inclined plane and lands on an uneven horizontal area, it will soon stop. If the horizontal section is level, the ball will roll further. This means that if there were no obstacles to the movement from the horizontal section, then the ball would move indefinitely. This means that in order for a body to move, the influence of another body is not needed. This means that there are no reasons for uniform rectilinear motion.

In addition, Galileo proves the fact that there are no changes in a body moving uniformly and rectilinearly. He says: no experience can prove the presence of rectilinear uniform motion or its absence. If there are no changes - uniform rectilinear movement, like rest - this is a state of the body, not a process.

Main conclusions:
There are no reasons for uniform rectilinear motion:

If the body is not acted upon by other bodies or the action of the bodies is compensated, then the body moves uniformly and rectilinearly
If a body moves uniformly and rectilinearly, then other bodies do not act on it or the action of the bodies is compensated.
If a body is in a state of uniform rectilinear motion, then the frame of reference associated with it is inertial.
Only in inertial frames of reference does the application of the laws of dynamics take place.

Another problem arises when studying the concept of “inertia”. The easiest way to consider this concept is to put it in contrast to the concept of inertia; it is better remembered. Inertia and inertia are similar words, but have different meanings.
Inertia is the property of bodies to prevent changes in the nature of their movement (speed).
Inertia is a state of uniform linear motion or rest.

The reason that a body begins to move is the action of other bodies on this body. The ball will only roll if you hit it. A person will jump if he pushes off the floor. Some bodies act at a distance. So, the Earth attracts everything around, so if you let go of the ball, it will immediately begin to move down. The speed of movement of a body can also change only when other bodies act on this body. For example, a ball sharply changes its speed when it hits a wall, and a bird makes a sharp turn, pushing the air with its wings and tail feathers.

All of the above examples and many others that we encounter at every step suggest that a body can change its speed only when other bodies act on it. And vice versa, if no other bodies act on the body, then the body will be at rest or move uniformly and in a straight line. G. Galileo first came to this conclusion at the beginning of the 17th century, and a century later I. Newton called it one of the fundamental laws of mechanics.

The ability of a body to maintain its speed is called its inertia. Therefore, the law discovered by G. Galileo and formulated by I. Newton is called the law of inertia or Newton’s first law.

The law of inertia is not valid in all reference systems. For example, in the reference frame associated with a moving car, its driver, when braking sharply, begins to move forward, although no bodies act on him. Standing on a disk that begins to rotate around its axis, we feel how some unknown force forces us to move away from the center of this disk. It is obvious that in these two reference systems - a braking car and a rotating disk, the law of inertia does not hold.

Reference systems in which the law of inertia is satisfied are called inertial reference systems. The reference frame associated with the Earth can be considered inertial, although, as is known, the Earth (like a disk in one of the previous examples) rotates around its axis, but so slowly that only very accurate measurements show non-compliance with the law of inertia in this reference frame.

If the reference body moves uniformly, rectilinearly and translationally relative to the inertial reference system, then the reference system associated with this body is also inertial. Let us prove this using the rule for converting velocities when moving from one reference system to another (see § 2). Let the speed of body M (see Fig. 7), measured in the reference frame C 1 be equal to v 1, then the speed v2 of the same body, but measured in the reference frame C 2, moving relative to C 1 with speed v, is equal to:

v 2 = v 1 - v (7.1)

From (7.1) it follows that changes in the speeds Dv 1 and Dv 2 over a period of time Dt must be the same, since the speed v remains unchanged. Therefore, the acceleration values of the body M, measured in both reference systems, will also be the same. In particular, if body M, which is not acted upon by other bodies, moves without acceleration, that is, uniformly, in the reference frame C 1, then its motion relative to the frame C2 will also be uniform, which means the reference frame C 2 can also be considered inertial. So, for example, if we consider the Earth to be an inertial frame of reference, then a train car moving uniformly, rectilinearly and translationally, can also be considered an inertial frame of reference.

Review questions:

· What does dynamics study?

· What causes the acceleration of a body?

· Define the inertia of a body and formulate the law of inertia.

· What reference systems are called inertial?

· Give examples of inertial reference systems and those in which the law of inertia is not observed.

Rice. 7. The reference frame C2 is inertial, since it moves relative to the inertial frame C1 translationally, uniformly and rectilinearly with speed v. A method is shown for calculating the speed v2 of a body M relative to the system C2 from the known speed v1 of this body in the system C1.

§ 8. FORCE – A MEASURE OF INTERACTION OF BODIES: TYPES OF FORCES AND THEIR MEASUREMENT

") around the 5th century. BC e. Apparently, one of the first objects of her research was a mechanical lifting machine, used in the theater to raise and lower actors portraying gods. This is where the name of science comes from.

People have long noticed that they live in a world of moving objects - trees sway, birds fly, ships sail, arrows fired from a bow hit targets. The reasons for such mysterious phenomena at that time occupied the minds of ancient and medieval scientists.

In 1638, Galileo Galilei wrote: “There is nothing more ancient in nature than movement, and philosophers have written many, many volumes about it.” The ancients and especially the scientists of the Middle Ages and the Renaissance (N. Copernicus, G. Galileo, I. Kepler, R. Descartes, etc.) already correctly interpreted certain issues of motion, but in general there was no clear understanding of the laws of motion in the time of Galileo.

The doctrine of the motion of bodies first appears as a strict, consistent science, built, like Euclid’s geometry, on truths that do not require proof (axioms), in Isaac Newton’s fundamental work “Mathematical Principles of Natural Philosophy,” published in 1687. Assessing the contribution to science scientist predecessors, the great Newton said: “If we have seen further than others, it is because we stood on the shoulders of giants.”

There is no movement in general, movement that is not related to anything, and there cannot be. The movement of bodies can only occur relative to other bodies and the spaces associated with them. Therefore, at the beginning of his work, Newton solves the fundamentally important question of space in relation to which the movement of bodies will be studied.

To give concreteness to this space, Newton associates with it a coordinate system consisting of three mutually perpendicular axes.

Newton introduces the concept of absolute space, which he defines as follows: “Absolute space, by its very essence, regardless of anything external, always remains the same and motionless.” The definition of space as motionless is identical to the assumption of the existence of an absolutely motionless coordinate system, relative to which the movement of material points and rigid bodies is considered.

Newton took as such a coordinate system heliocentric system, the beginning of which he placed in the center, and directed three imaginary mutually perpendicular axes to the three “fixed” stars. But today it is known that there is nothing absolutely motionless in the world - it rotates around its axis and around the Sun, the Sun moves relative to the center of the Galaxy, the Galaxy - relative to the center of the world, etc.

Thus, strictly speaking, there is no absolutely fixed coordinate system. However, the motion of “fixed” stars relative to the Earth is so slow that for most problems solved by people on Earth, this motion can be neglected and the “fixed” stars can be considered truly motionless, and the absolutely motionless coordinate system proposed by Newton really exists.

In relation to an absolutely motionless coordinate system, Newton formulated his first law (axiom): “Every body continues to be maintained in its state of rest or uniform rectilinear motion until and unless it is forced by applied forces to change this state.”

Since then, attempts have been made and are being made to editorially improve Newton's formulation. One of the formulations sounds like this: “A body moving in space tends to maintain the magnitude and direction of its speed” (meaning that rest is movement with a speed equal to zero). Here the concept of one of the most important characteristics of movement is introduced - translational, or linear, speed. Typically linear speed is denoted by V.

Let us pay attention to the fact that Newton's first law speaks only about translational (linear) motion. However, everyone knows that there is another, more complex movement of bodies in the world - curvilinear, but more on that later...

The desire of bodies to “maintain their state” and “maintain the magnitude and direction of their speed” is called inertia, or inertia, tel. The word “inertia” is Latin; translated into Russian it means “rest”, “inaction”. It is interesting to note that inertia is an organic property of matter in general, “the innate force of matter,” as Newton said. It is characteristic not only of mechanical movement, but also of other natural phenomena, for example electrical, magnetic, thermal. Inertia manifests itself both in the life of society and in the behavior of individuals. But let's get back to the mechanics.

The measure of the inertia of a body during its translational motion is the mass of the body, usually denoted m. It has been established that during translational motion the magnitude of inertia is not affected by the distribution of mass within the volume occupied by the body. This gives grounds, when solving many problems in mechanics, to abstract from the specific dimensions of a body and replace it with a material point whose mass is equal to the mass of the body.

The location of this conditional point in the volume occupied by the body is called center of mass of the body, or, which is almost the same, but more familiar, center of gravity.

The measure of mechanical rectilinear motion, proposed by R. Descartes in 1644, is the amount of motion, defined as the product of the mass of a body and its linear speed: mV.

As a rule, moving bodies cannot maintain the same amount of motion for a long time: fuel reserves are consumed in flight, reducing the mass of aircraft, trains slow down and accelerate, changing their speed. What reason causes the change in momentum? The answer to this question is given by Newton's second law (axiom), which in its modern formulation sounds like this: the rate of change in the momentum of a material point is equal to the force acting on this point.

So, the reason that causes the movement of bodies (if at first mV = 0) or changes their momentum (if at first mV is not equal to O) relative to absolute space (Newton did not consider other spaces) are forces. These forces later received clarifying names - physical, or Newtonian, strength. They are usually designated F.

Newton himself gave the following definition of physical forces: “An applied force is an action performed on a body to change its state of rest or uniform linear motion.” There are many other definitions of strength. L. Cooper and E. Rogers, the authors of wonderful popular books on physics, avoiding boring strict definitions of force, with a certain amount of slyness, introduce their definition: “Forces are what pulls and pushes.” It’s not completely clear, but some idea of what strength is is emerging.

Physical forces include: forces, magnetic (see article ““), forces of elasticity and plasticity, resistance forces of the environment, light and many others.

If during the movement of a body its mass does not change (only this case will be considered further), then the formulation of Newton’s second law is greatly simplified: “The force acting on a material point is equal to the product of the mass of the point and the change in its speed.”

A change in the linear speed of a body or point (in magnitude or direction - remember this) is called linear acceleration body or point and is usually denoted a.

The accelerations and speeds with which bodies move relative to absolute space are called absolute accelerations And speeds.

In addition to the absolute coordinate system, one can imagine (with some assumptions, of course) other coordinate systems that move rectilinearly and uniformly relative to the absolute one. Since (according to Newton’s first law) rest and uniform rectilinear motion are equivalent, Newton’s laws are valid in such systems, in particular the first law - law of inertia. For this reason, coordinate systems moving uniformly and rectilinearly relative to the absolute system are called inertial coordinate systems.

However, in most practical problems, people are interested in the movement of bodies not relative to distant and intangible absolute space, or even relative to inertial spaces, but relative to other closer and completely material bodies, for example, a passenger relative to the body of a car. But these other bodies (and the spaces and coordinate systems associated with them) themselves move relative to absolute space non-rectilinearly and unevenly. The coordinate systems associated with such bodies are called mobile. For the first time, moving coordinate systems were used to solve complex problems in mechanics by L. Euler (1707-1783).

We constantly encounter examples of the movement of bodies relative to other moving bodies in our lives. Ships sail across the seas and oceans, moving relative to the surface of the Earth, rotating in absolute space; a conductor serving tea throughout the compartment moves relative to the walls of a speeding passenger carriage; tea spills out of a glass during sudden jolts of the carriage, etc.

To describe and study such complex phenomena, the concepts are introduced portable movement And relative motion and their corresponding portable and relative velocities and accelerations.

In the first of the examples given, the rotation of the Earth relative to absolute space will be a portable motion, and the movement of a ship relative to the surface of the Earth will be a relative motion.

To study the movement of a conductor relative to the walls of a car, you must first accept that the rotation of the Earth does not have a significant effect on the movement of the conductor and therefore the Earth can be considered stationary in this problem. Then the movement of the passenger car is portable movement, and the movement of the conductor relative to the car is relative motion. With relative motion, bodies influence each other either directly (by touching) or at a distance (for example, magnetic and gravitational interactions).

The nature of these influences is determined by Newton's third law (axiom). If we remember that Newton called the physical forces applied to bodies action, then the third law can be formulated as follows: “Action is equal to reaction.” It should be noted that the action is applied to one, and the reaction is applied to the other of the two interacting bodies. Action and reaction are not balanced, but cause acceleration of interacting bodies, and the body whose mass is smaller moves with greater acceleration.

Let us also recall that Newton's third law, unlike the first two, is valid in any coordinate system, and not just in absolute or inertial ones.

In addition to rectilinear motion, it is widespread in nature curvilinear movement, the simplest case of which is motion in a circle. We will consider only this case in the future, calling motion in a circle circular motion. Examples of circular motion: the rotation of the Earth around its axis, the movement of doors and swings, the rotation of countless wheels.

Circular motion of bodies and material points can occur either around axes or around points.

Circular motion (as well as rectilinear motion) can be absolute, figurative and relative.

Like rectilinear motion, circular motion is characterized by speed, acceleration, force factor, measure of inertia, and measure of motion. Quantitatively, all these characteristics depend to a very large extent on the distance at which the rotating material point is located from the axis of rotation. This distance is called the radius of rotation and is denoted r .

In gyroscopic technology, angular momentum is usually called kinetic moment and is expressed through the characteristics of circular motion. Thus, the kinetic moment is the product of the moment of inertia of the body (relative to the axis of rotation) and its angular velocity.

Naturally, Newton's laws are also valid for circular motion. When applied to circular motion, these laws could be formulated somewhat simplistically as follows.

First law: a rotating body strives to maintain relative to absolute space the magnitude and direction of its angular momentum (i.e., the magnitude and direction of its kinetic momentum).
Second law: the change in time of angular momentum (kinetic momentum) is equal to the applied torque.
Third law: the moment of action is equal to the moment of reaction.

There is no movement, said the bearded sage.
The other fell silent and began to walk in front of him.
He could not have objected more strongly;
Everyone praised the intricate answer.
But, gentlemen, this is a funny case
Another example comes to mind:
After all, every day the sun walks before us,
However, stubborn Galileo is right.
A. S. Pushkin

What is mechanical movement? What does the relativity of mechanical motion mean? What characteristics describe mechanical movement? What causes mechanical movement? What was “stubborn Galileo” right about?

Lesson-lecture

RELATIVITY OF MECHANICAL MOTION. Movement as a change in the position of a body in space relative to other bodies over time is called mechanical movement. The body relative to which motion is considered, the coordinate system associated with it and the clock for measuring time form reference system.

Galileo also established the character relativity of motion. Since ancient times, people have been interested in the question of whether there is any absolutely at rest frame of reference. The ancient philosopher Ptolemy believed that our Earth is such a system, and the rest of the celestial bodies and other objects move relative to the Earth. Figure 61, a shows a diagram of the movement of celestial bodies according to Ptolemy.

Rice. 61. System of planetary motion: according to Ptolemy (a); according to Copernicus (b, modern ideas)

Copernicus proposed describing the motion of the planets in a different frame of reference, where the Sun is stationary. The pattern of planetary motion in this case looks as shown in Figure 61, b.

During the time of Galileo, disputes about the correct description of the motion of the planets were serious. But due to the relativity of motion, both descriptions can be considered equivalent; they simply correspond to the description of motions in different reference systems. The Sun, along with other stars, moves around the center of the Galaxy. The galaxy, like other galaxies observed by astronomers, is also moving. Something that could be considered absolutely motionless in the Universe has not been discovered.

So what is “stubborn Galileo” right about? At first glance, it may seem that the movement pattern according to Copernicus is simpler than the movement pattern according to Ptolemy. But this simplicity is apparent. To observe the movement of planets around the Sun, we need to move away from solar system over a considerable distance, which we cannot do even at the present time. We observe movement while on our planet, and we observe, as Pushkin wrote, that “the sun walks before us.” Maybe Galileo shouldn’t have been stubborn? It turns out that this is not entirely true. Descriptions of motion in different frames of reference (Ptolemy and Copernicus) are equivalent as long as we examine kinematics movements, i.e. we do not consider the reasons causing movements.

Mechanical motion is relative in nature, that is, motion always occurs relative to some reference system. With a kinematic description of motion, all reference systems are equivalent.

MOVEMENT CHARACTERISTICS. Until now we have talked only about a qualitative description of movement. But in natural sciences It is important to be able to describe processes quantitatively. To do this, generally speaking, is not so easy. Try to describe the movement of a bird in flight. But if you are not interested in individual details, you can model the bird's movement as the movement of some small object. In physics, the concept is used to denote such an object material point.

The movement of a material point is described most simply. This happens by introducing coordinate systems. When a material point moves, its coordinates change.

An important characteristic of the motion of a material point is trajectory. A trajectory is an imaginary line in space along which a material point moves. However, sometimes the trajectory can be seen. For example, tracer bullets leave a trace in the form of a luminous line in the dark. Another example is the trail of a “shooting star” (meteor) in the atmosphere. We can see the trajectories of stars in the celestial sphere if we take a photograph celestial sphere by opening the camera lens for a long time (Fig. 62).

Rice. 62. Photos: meteor shower (a); movement of stars captured with long exposure (b)

Let us recall that the characteristic of motion, showing how much the coordinates change over time, is called speed. Movement in which the speed remains constant in magnitude and direction is called uniform movement. The change in speed is called acceleration. A material point moves with acceleration if the speed changes in numerical value, in direction, or simultaneously in value and direction.

So far we have talked about the movement of a material point. How to describe the movement of more complex objects? To do this, you need to mentally break the object into separate points and describe the movement of each point. In the simplest case, for example, when a soccer ball or the Earth moves around the Sun, such movement can be represented as forward motion plus rotation. In more difficult case, for example, when a bird is flying, the movement of each point will have to be described separately. That's exactly what they do computer programs, animating the movements of a character on the monitor screen.

REASONS FOR THE MOVEMENT. The branch of mechanics that describes the reasons for changes in the motion of bodies is called dynamics. Historical development dynamics did not go the easy way.

The ancient Greek philosopher Aristotle believed that in order for a body to move uniformly, some force must be applied to it. Galileo, having carried out a series of experiments, came to the conclusion that a body moves uniformly in the case when it does not interact with other bodies. You can verify that this is not entirely true through simple experience (at least mental). Imagine that on a subway train there is a ball in the middle of an empty carriage. What will happen to the ball when the carriage starts moving? Without additional forces, the ball will begin to move with acceleration. To clarify Galileo's formulation, Newton introduced the concept inertial reference frame. An inertial frame of reference is a system in which a body, in the absence of interaction with other bodies, is at rest or moves uniformly. In our example, the subway car is a non-inertial frame of reference. Such a system is any reference system moving with acceleration relative to an inertial reference system.

To describe the movement of an object, a coordinate system is introduced. The simplest movement - the movement of a material point - is described as a change in coordinates. To describe the movement of complex objects, it is necessary to describe the movement of each point. into which you can mentally break down an object.

It turns out that, strictly speaking, there are no inertial frames of reference in nature. For example, the teacher's desk in your classroom rotates with the Earth, and therefore moves with acceleration. However, in many cases, for example, when demonstrating school experiments, such a reference system can be considered as approximately inertial. But if we try to describe the movement of the planets in this reference system, it will be completely wrong. To describe the motion of planets, an inertial frame of reference can be approximately considered to be a system whose center is at the center of the Sun, and whose axes are oriented along the stars. It is for this reason that the movement of celestial bodies in the Copernican system is described better than in the Ptolemaic system.

We thus come to the conclusion, which is known as Newton's first law: in an inertial frame of reference, a body that does not interact with other bodies is at rest or moves uniformly.

But uniform motion is only a particular, practically unrealizable case of motion. All bodies that we actually observe move with acceleration. The reasons for motion with acceleration are formulated in Newton's second law, which you are also familiar with from your physics course.

The acceleration of a body in an inertial frame of reference is proportional to the sum of all forces acting on it, and inversely proportional to the mass of the body.

What is the meaning of the relativity of mechanical motion?
What causes the movement of bodies?
Along a raft moving along the river, perpendicular to the speed of the raft and at twice the speed higher speed currents, a man walks. Draw the trajectory of the person’s movement relative to the shore.

What is the reason for the movement? Aristotle – movement is possible only under the influence of force; in the absence of forces, the body will be at rest. Galileo - a body can maintain motion even in the absence of forces. Force is necessary to balance other forces, for example, the force of friction Newton formulated the laws of motion.

Slide 4 from the presentation "Interaction of bodies, Newton's laws".

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Physics 10th grade summary