Newton's laws
Introduction
Newton's laws, depending on how you look at them, represent either the end of the beginning or the beginning of the end of classical mechanics. In any case, this is a turning point in the history of physical science - a brilliant compilation of all the knowledge accumulated up to that historical moment about the movement of physical bodies within the framework of physical theory, which is now commonly called classical mechanics. We can say that Newton's laws of motion began the history of modern physics and the natural sciences in general.
Newton's first law
Given such a serious, historical failure, Newton's first law is formulated in an unconditionally revolutionary way. He claims that if any material particle or body is simply left undisturbed, it will continue to move in a straight line at a constant speed on its own. If a body moves uniformly in a straight line, it will continue to move in a straight line with constant speed. If the body is at rest, it will remain at rest until someone applies pressure to it. external forces. To simply move a physical body from its place, an external force must be applied to it. Let's take an airplane: it will never move until the engines are started. It would seem that the observation is self-evident, however, as soon as we distract ourselves from rectilinear movement, it ceases to seem so. When a body moves inertially along a closed cyclic trajectory, its analysis from the position of Newton’s first law only allows one to accurately determine its characteristics.
Imagine something like an athletics hammer - a cannonball on the end of a string that you spin around your head. In this case, the nucleus does not move in a straight line, but in a circle - which means, according to Newton’s first law, something is holding it back; this “something” is the centripetal force that you apply to the nucleus, spinning it. In reality, you can feel it yourself - the handle of the athletics hammer is noticeably pressing on your palms. If you open your hand and release the hammer, it - in the absence of external forces - will immediately set off in a straight line. It would be more accurate to say that this is how the hammer will behave in ideal conditions (for example, in outer space), since under the influence of the gravitational attraction of the Earth it will fly strictly in a straight line only at the moment when you let go of it, and in the future the flight path will be deviate more in direction earth's surface. If you try to actually release the hammer, it turns out that the hammer released from a circular orbit will travel strictly along a straight line that is tangent (perpendicular to the radius of the circle along which it was spun) with linear speed, equal speed its circulation in "orbit".
Now let's replace the core of an athletics hammer with a planet, the hammer with the Sun, and the string with the force of gravitational attraction: here you have Newton's model of the solar system.
Such an analysis of what happens when one body orbits another in a circular orbit at first glance seems to be something self-evident, but we should not forget that it includes whole line conclusions of the best representatives scientific thought previous generation (just remember Galileo Galilei). The problem here is that when moving in a stationary circular orbit, the celestial (and any other) body looks very serene and appears to be in a state of stable dynamic and kinematic equilibrium. However, if you look at it, only the modulus (absolute value) of the linear velocity of such a body is conserved, while its direction is constantly changing under the influence of the force of gravitational attraction. This means that the celestial body moves with uniform acceleration. By the way, Newton himself called acceleration a “change in motion.”
Newton's first law also plays another important role from the point of view of our natural scientist's attitude to the nature of the material world. He tells us that any change in the nature of the movement of a body indicates the presence of external forces acting on it. Relatively speaking, if we observe how iron filings, for example, jump up and stick to a magnet, or, taking laundry out of the dryer of a washing machine, we find out that things have stuck together and dried to one another, we can feel calm and confident: these effects have become a consequence of the action of natural forces (in the examples given these are the forces of magnetic and electrostatic attraction, respectively).
Newton's second law
If Newton's first law helps us determine whether a body is under the influence of external forces, then the second law describes what happens to a physical body under their influence. The greater the sum of external forces applied to the body, this law states, the greater the acceleration the body acquires. This time. At the same time, the more massive the body to which it is attached equal amount external forces, the less acceleration it acquires. That's two. Intuitively, these two facts seem self-evident, and in mathematical form they are written as follows:
where F is force, m is mass, and is acceleration. This is probably the most useful and most widely used of all physics equations. It is enough to know the magnitude and direction of all the forces acting in a mechanical system, and the mass of the material bodies of which it consists, and one can calculate its behavior in time with complete accuracy.
It is Newton’s second law that gives all of classical mechanics its special charm - it begins to seem as if the entire physical world is structured like the most precise chronometer, and nothing in it escapes the gaze of an inquisitive observer. Tell me the spatial coordinates and velocities of all material points in the Universe, as if Newton is telling us, tell me the direction and intensity of all the forces acting in it, and I will predict to you any of its future states. And this view of the nature of things in the Universe existed until the advent of quantum mechanics.
Newton's third law
It is for this law that Newton most likely gained honor and respect from not only natural scientists, but also humanities scientists and simply the general public. They love to quote him (both on business and without business), drawing the broadest parallels with what we are forced to observe in our everyday life, and they pull him almost by the ears to substantiate the most controversial provisions during discussions on any issues, from interpersonal and ending with international relations and global politics. Newton, however, put a very specific physical meaning into his subsequently named third law and hardly intended it in any other capacity than as an accurate means of describing the nature of force interactions. This law states that if body A acts with a certain force on body B, then body B also acts on body A with a force equal in magnitude and opposite in direction. In other words, when you stand on the floor, you exert a force on the floor that is proportional to the mass of your body. According to Newton's third law, the floor at the same time acts on you with absolutely the same force, but directed not downward, but strictly upward. This law is not difficult to test experimentally: you constantly feel the earth pressing on your soles.
Here it is important to understand and remember that Newton is talking about two forces completely of different nature, and each force acts on “its” object. When an apple falls from a tree, it is the Earth that acts on the apple with the force of its gravitational attraction (as a result of which the apple uniformly accelerates towards the surface of the Earth), but at the same time the apple also attracts the Earth to itself with equal strength. And the fact that it seems to us that it is the apple that falls to the Earth, and not vice versa, is already a consequence of Newton’s second law. The mass of an apple compared to the mass of the Earth is incomparably low, therefore it is its acceleration that is noticeable to the eye of the observer. The mass of the Earth, compared to the mass of an apple, is enormous, so its acceleration is almost imperceptible. (If an apple falls, the center of the Earth moves upward by a distance less than the radius atomic nucleus.)
Conclusion
Taken together, Newton’s three laws gave physicists the tools necessary to begin a comprehensive observation of all phenomena occurring in our Universe. And, despite all the enormous advances in science that have occurred since Newton's time, to design a new car or send a spaceship to Jupiter, you will use the same three laws of Newton.
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MINISTRY OF DEFENSE OF THE RUSSIAN FEDERATION
MILITARY ACADEMY
MILITARY AIR DEFENSE
ARMED FORCES OF THE RUSSIAN FEDERATION
NAMED AFTER MARSHAL OF THE SOVIET UNION A. M. VASILEVSKY
Department Mathematics and physics ____________
Abstract on the topic:
"Newton's Laws"
Completed by: cadet 311 study group Vasiltsov N.Yu.
Checked by: teacher of department No. 15 Ermolenko V.P.
SMOLENSK – 2009
- INTRODUCTION.
The science of those years had a natural-philosophical character, i.e. proceeded from the fact that the directly observed movements of the celestial bodies are their actual movements. From this the conclusion was drawn about the central position of the Earth in the Universe. This system correctly reflected some of the features of the Earth as a celestial body: that the Earth is a ball, that everything gravitates towards its center. Thus, this teaching was actually about the Earth. At the level of its time, it met the basic requirements for scientific knowledge. Firstly, it explained the observed movements of celestial bodies from a single point of view and, secondly, made it possible to calculate their future positions. In the same time theoretical constructions the ancient Greeks were purely speculative in nature - they were completely divorced from experiment.
This system lasted until XVI century, before the advent of the teachings of Copernicus, which received its further justification in the experimental physics of Galileo, culminating in the creation of Newtonian mechanics, which united the movement of celestial bodies and terrestrial objects with unified laws of motion. It was the greatest revolution in natural science, which marked the beginning of the development of science in its modern understanding.
Galileo Galilei believed that the world is infinite and matter is eternal. In all processes, nothing is destroyed or generated - only a change in the relative arrangement of bodies or their parts occurs. Matter consists of absolutely indivisible atoms, its movement is the only universal mechanical movement. The celestial bodies are similar to the Earth and obey the same laws of mechanics.
For Newton, it was important to unambiguously find out, through experiments and observations, the properties of the object being studied and to build a theory based on induction without using hypotheses. He proceeded from the fact that in physics as an experimental science there is no place for hypotheses. Recognizing the imperfection of the inductive method, he considered it the most preferable among others.
Both in antiquity and in the 17th century, the importance of studying the movement of celestial bodies was recognized. But if for the ancient Greeks this problem had more philosophical significance, then for the 17th century, the practical aspect was predominant. The development of navigation necessitated the development of more accurate astronomical tables for navigation purposes compared to those required for astrological purposes. The main task was to determine longitude, so needed by astronomers and seafarers. To solve this important practical problem, the first state observatories were created (Paris observatories in 1672, Greenwich in 1675). In essence, this was the task of determining absolute time, which, when compared with local time, gave a time interval that could be converted into longitude. This time could be determined by observing the movements of the Moon among the stars, as well as by using an accurate clock set according to absolute time and kept by the observer. For the first case, very accurate tables were needed to predict the position of celestial bodies, and for the second, absolutely accurate and reliable clock mechanisms. Work in these directions was not successful. Only Newton managed to find a solution, who, thanks to the discovery of the law of universal gravitation and the three fundamental laws of mechanics, as well as differential and integral calculus, gave mechanics the character of an integral scientific theory.
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NEWTON'S MECHANICS.
Newton's concept was the basis for many technological advances over time. Many methods were formed on its foundation scientific research in various fields of natural science.
- Newton's laws of motion.
They can be directly applied to the simplest case of motion, when a moving body is considered as a material point, i.e. when the size and shape of the body is not taken into account and when the movement of the body is considered as the movement of a point with mass. In boiling water, to describe the movement of a point, you can choose any coordinate system, relative to which the quantities characterizing this movement are determined. Any body moving relative to other bodies can be taken as a body of reference. In dynamics we deal with inertial coordinate systems, characterized by the fact that relative to them a free material point moves with constant speed.
- Newton's first law.
In life, this law describes the case when, if you stop pulling or pushing a moving body, it stops and does not continue to move at a constant speed. This is how a car stops with its engine turned off. According to Newton's law, a braking force must act on a car rolling by inertia, which in practice is air resistance and friction of car tires on the highway surface. They give the car negative acceleration until it stops.
The disadvantage of this formulation of the law is that it did not contain any indication of the need to classify the movement as inertial system coordinates The fact is that Newton did not use the concept of an inertial coordinate system - instead, he introduced the concept of absolute space - homogeneous and motionless - with which he associated a certain absolute coordinate system, relative to which the speed of the body was determined. When the emptiness of absolute space as an absolute reference system was revealed, the law of inertia began to be formulated differently: relative to the inertial coordinate system, a free body maintains a state of rest or uniform rectilinear motion.
- Newton's second law.
- acceleration – vector quantity(Newton called it quantity of motion and took it into account when formulating the rule of parallelogram of velocities), which determines the rate of change in the speed of motion of a body.
force is a vector quantity understood as a measure of mechanical influence on a body from other bodies or fields, as a result of which the body acquires acceleration or changes its shape and size.
body mass - physical quantity– one of the main characteristics of matter, determining its inertial and gravitational properties.
This law is easy to confirm experimentally; if you attach a cart to the end of a spring and release the spring, then in time t cart will go the way s 1 (Fig. 1), then attach two trolleys to the same spring, i.e. double your body weight and release the spring, then in the same time t they will go the distance s 2 , two times less than s 1 .
This law is also valid only in inertial frames of reference. The first law from a mathematical point of view is special case second law, because if the resultant forces are zero, then the acceleration is also zero. However, Newton's first law is considered as an independent law, because It is he who claims the existence of inertial systems.
- Newton's third law.
Newton extended the effect of this law to the case of both collisions of bodies and the case of their mutual attraction. The simplest demonstration of this law is a body located on a horizontal plane, which is subject to the force of gravity F T and ground reaction force F O, lying on the same straight line, equal in value and oppositely directed, the equality of these forces allows the body to be at rest (Fig. 2).
Corollaries follow from Newton's three fundamental laws of motion, one of which is the addition of momentum according to the parallelogram rule. The acceleration of a body depends on the quantities that characterize the action of other bodies on a given body, as well as on the quantities that determine the characteristics of this body. Mechanical action on a body from other bodies that changes the speed of movement given body, is called strength. It can have a different nature (gravity, elastic force, etc.). The change in the speed of a body does not depend on the nature of the forces, but on their magnitude. Since speed and force are vectors, the action of several forces adds up according to the parallelogram rule. The property of a body on which the acceleration it acquires depends is inertia, measured by mass. In classical mechanics, which deals with velocities significantly lower than the speed of light, mass is a characteristic of the body itself, independent of whether it is moving or not. Body weight in classical mechanics does not depend on the interaction of the body with other bodies. This property of mass prompted Newton to take mass as a measure of matter and believe that its magnitude determines the amount of matter in a body. Thus, mass came to be understood as the amount of matter.
The amount of matter can be measured, being proportional to the weight of the body. Weight is the force with which a body acts on a support that prevents it from falling freely. Numerically, weight is equal to the product of body mass and the acceleration of gravity. Due to the compression of the Earth and its daily rotation, body weight changes with latitude and is 0.5% less at the equator than at the poles. Since mass and weight are strictly proportional, practical measurement of mass or quantity of matter was possible. The understanding that weight is a variable force on the body prompted Newton to establish and internal characteristics body - inertia, which he considered as the inherent ability of a body to maintain uniform linear motion, proportional to mass. Mass as a measure of inertia can be measured using scales, as Newton did.
In a state of weightlessness, mass can be measured by inertia. Inertial measurement is a common way to measure mass. But inertia and weight are different physical concepts. Their proportionality to each other is very convenient in practical terms - for measuring mass using scales. Thus, the establishment of the concepts of force and mass, as well as the method of measuring them, allowed Newton to formulate the second law of mechanics.
The first and second laws of mechanics relate respectively to the movement of a material point or one body. In this case, only the action of other bodies on a given body is taken into account. However, every action is interaction. Since in mechanics an action is characterized by force, then if one body acts on another with a certain force, then the second acts on the first with the same force, which is fixed by the third law of mechanics. In Newton's formulation, the third law of mechanics is valid only for the case of direct interaction of forces or when the action of one body is instantly transferred to another. In the case of transfer of an action over a finite period of time, this law applies when the time of transfer of the action can be neglected.
etc.................
Introduction
Newton's laws, depending on how you look at them, represent either the end of the beginning or the beginning of the end of classical mechanics. Either way, this is a turning point in history. physical science– a brilliant compilation of all the accumulated historical moment knowledge about the movement of physical bodies within physical theory, which is now commonly called classical mechanics. We can say that history began with Newton's laws of motion. modern physics and generally speaking natural sciences.
Newton's first law
Given such a serious, historical failure, Newton's first law is formulated unconditionally in a revolutionary way. He claims that if any material particle or body is simply left undisturbed, it will continue to move in a straight line at a constant speed on its own. If a body moves uniformly in a straight line, it will continue to move in a straight line with constant speed. If the body is at rest, it will remain at rest until external forces are applied to it. To simply move a physical body from its place, an external force must be applied to it. Let's take an airplane: it will never move until the engines are started. It would seem that the observation is self-evident, however, as soon as we distract ourselves from rectilinear movement, it ceases to seem so. When a body moves inertially along a closed cyclic trajectory, its analysis from the position of Newton’s first law only allows one to accurately determine its characteristics.
Imagine something like an athletics hammer - a cannonball on the end of a string that you spin around your head. In this case, the nucleus does not move in a straight line, but in a circle - which means, according to Newton’s first law, something is holding it back; this “something” is the centripetal force that you apply to the nucleus, spinning it. In reality, you can feel it yourself - the handle of the athletics hammer is noticeably pressing on your palms. If you open your hand and release the hammer, it - in the absence of external forces - will immediately set off in a straight line. It would be more accurate to say that this is how the hammer will behave in ideal conditions(for example, in outer space), because under the influence of force gravitational attraction On the ground, it will fly strictly in a straight line only at the moment when you let it go, and in the future the flight path will deviate more and more in the direction of the earth's surface. If you try to actually release the hammer, it turns out that the hammer released from a circular orbit will travel strictly along a straight line, which is tangent (perpendicular to the radius of the circle along which it was spun) with a linear speed equal to the speed of its revolution in the “orbit”.
Now let's replace the core of an athletics hammer with a planet, the hammer with the Sun, and the string with the force of gravitational attraction: here you have the Newtonian model solar system.
Such an analysis of what happens when one body revolves around another in a circular orbit at first glance seems to be something self-evident, but we should not forget that it incorporated a whole series of conclusions of the best representatives of scientific thought of the previous generation (just remember Galileo Galilei). The problem here is that when moving in a stationary circular orbit, the celestial (and any other) body looks very serene and appears to be in a state of stable dynamic and kinematic equilibrium. However, if you look at it, only the module is saved ( absolute value) linear speed such a body, while its direction is constantly changing under the influence of gravitational attraction. This means that heavenly body moves with uniform acceleration. By the way, Newton himself called acceleration a “change in motion.”
Newton's first law also plays another role important role from the point of view of our naturalistic attitude towards nature material world. He tells us that any change in the nature of the movement of a body indicates the presence of external forces acting on it. Relatively speaking, if we observe how iron filings, for example, jump up and stick to a magnet, or, taking laundry out of the dryer of a washing machine, we find out that things have stuck together and dried to one another, we can feel calm and confident: these effects have become a consequence of the action of natural forces (in the examples given these are the forces of magnetic and electrostatic attraction, respectively).
Newton's second law
If Newton's first law helps us determine whether a body is under the influence of external forces, then the second law describes what happens to physical body under their influence. How more amount The more external forces applied to the body, this law states, the greater the acceleration the body acquires. This time. At the same time, the more massive the body to which an equal amount of external forces is applied, the less acceleration it acquires. That's two. Intuitively, these two facts seem self-evident, and in mathematical form they are written like this:
where F is force, m is mass, and is acceleration. This is probably the most useful and most widely used in applied purposes of all physical equations. It is enough to know the magnitude and direction of all forces acting in mechanical system, and mass material bodies, of which it consists, and its behavior over time can be calculated with exhaustive accuracy.
It is Newton's second law that gives all of classical mechanics its special charm - it begins to seem as if all physical world it is designed like the most precise chronometer, and nothing in it escapes the gaze of an inquisitive observer. Call me spatial coordinates and the speed of everyone material points in the Universe, Newton seems to be telling us, show me the direction and intensity of all the forces acting in it, and I will predict to you any of its future states. And this view of the nature of things in the Universe existed until the advent of quantum mechanics .
Newton's third law
It is for this law that Newton most likely gained honor and respect from not only natural scientists, but also humanities scientists and simply the general public. They love to quote him (both on business and without business), drawing the broadest parallels with what we are forced to observe in our everyday life, and are pulled almost by the ears to substantiate the most controversial provisions during discussions on any issues, from interpersonal to international relations and global politics. Newton, however, put into his law, which was later named the third, a completely specific physical meaning and he hardly intended it in any other capacity than as an accurate means of describing the nature of force interactions. This law states that if body A acts with a certain force on body B, then body B also acts on body A with a force equal in magnitude and opposite in direction. In other words, when you stand on the floor, you exert a force on the floor that is proportional to the mass of your body. According to Newton's third law, the floor at the same time acts on you with absolutely the same force, but directed not downward, but strictly upward. This law is not difficult to test experimentally: you constantly feel the earth pressing on your soles.
Here it is important to understand and remember that Newton is talking about two forces of completely different natures, and each force acts on “its own” object. When an apple falls from a tree, it is the Earth that acts on the apple with the force of its gravitational attraction (as a result of which the apple rushes uniformly towards the surface of the Earth), but at the same time the apple also attracts the Earth to itself with equal force. And the fact that it seems to us that it is the apple that falls to the Earth, and not vice versa, is already a consequence of Newton’s second law. The mass of an apple compared to the mass of the Earth is incomparably low, therefore it is its acceleration that is noticeable to the eye of the observer. The mass of the Earth, compared to the mass of an apple, is enormous, so its acceleration is almost imperceptible. (If an apple falls, the center of the Earth moves upward by a distance less than the radius of the atomic nucleus.)
Conclusion
Taken together, Newton’s three laws gave physicists the tools necessary to begin a comprehensive observation of all phenomena occurring in our Universe. And, despite all the colossal advances in science that have occurred since the time of Newton, to design a new car or send spaceship to Jupiter, you will use the same three Newton's laws.