Newton's laws. Newton's second law. Newton's laws - the formulation

The study of the phenomena of nature on the basis of experiment is possible only if all the stages are observed: observation, hypothesis, experiment, theory. The observation will allow to identify and compare the facts, the hypothesis makes it possible to give them a detailed scientific explanation that requires experimental confirmation. Observing the movement of bodies led to an interesting conclusion: the change in the speed of the body is possible only under the influence of another body.

For example, if you quickly run up the stairs, you simply need to grab the rail (change direction) or turn off (by changing the speed) to avoid colliding with the opposite wall.

Observations of similar phenomena led to the creation of a section of physics that studies the causes of changes in the speed of bodies or their deformation.

Fundamentals of Dynamics

Answer to the sacramental question of why the physical body is moving in one way or another, or is at rest, is called dynamics.

Let us consider the state of rest. Proceeding from the concept of the relativity of motion, we can conclude: there can not be absolutely immobile bodies. Any object, being immovable with respect to one reference body, moves relative to the other. For example, a book lying on a table is fixed relative to a table, but if one looks at its position relative to a passing person, then we make a natural conclusion: the book is moving.

Therefore, the laws of motion of bodies are considered in inertial frames of reference. What it is?

Inertial is a frame of reference in which the body rests or performs a uniform and rectilinear motion , provided that other objects or objects are not affected by it.

In the above example, the reference frame associated with the table can be called inertial. A person moving uniformly and rectilinearly can serve as the reference frame for ISO. If its motion is accelerated, then it is impossible to associate an inertial CO with it.

In fact, such a system can be correlated with bodies rigidly fixed on the surface of the Earth. However, the planet itself can not serve as the reference frame for ISO, since it rotates uniformly around its own axis. The bodies on the surface have a centripetal acceleration.

What is inertia?

The phenomenon of inertia is directly related to ISO. Remember what happens if a moving car stops abruptly? Passengers are endangered as they continue their movement. He can be stopped by a seat in front or by seat belts. Explain this process by the inertia of the passenger. Is it so?

Inertia is a phenomenon that presupposes the preservation of a constant velocity of the body in the absence of the influence of other bodies on it. The passenger is under the influence of belts or armchairs. The phenomenon of inertia is not observed here.

The explanation lies in the property of the body, and, according to him, it is impossible to change the speed of an object at once. It is inertness. For example, the inertness of mercury in a thermometer allows you to lower the column if we shake the thermometer.

A measure of inertia is called body weight. When interacting, the speed changes more rapidly for bodies with a smaller mass. The collision of a car with a concrete wall for the latter takes place practically without a trace. The car most often undergoes irreversible changes: the speed changes, there is a significant deformation. It turns out that the inertness of the concrete wall significantly exceeds the inertia of the car.

Is it possible to meet the phenomenon of inertia in nature? The condition under which the body is without interrelation with other bodies is the deep space in which the spacecraft is moving with the engines turned off. But even in this case the gravitational moment is present.

Basic values

The study of dynamics at the experimental level presupposes an experiment with measurements of physical quantities. The most interesting are:

• Acceleration as a measure of the speed of change in the speed of bodies; Denote it by the letter a, measure in m / s ² ;
• Mass as a measure of inertia; Denoted by the letter m, measured in kg;
• Force as a measure of the mutual action of bodies; Is usually denoted by the letter F, measured in H (newtons).

The relationship of these quantities is set out in three laws, derived by the greatest English physicist. Newton's laws are designed to explain the complexity of the interaction of different bodies. And also the processes that control them. It is the concepts of "acceleration", "force", "mass" Newton's laws that are related by mathematical relationships. Let's try to figure out what it means.

The action of only one force is an exceptional phenomenon. For example, an artificial satellite moving in orbit around the Earth is under the influence of only the force of attraction.

Resultant

The action of several forces can be replaced by one force.

The geometric sum of the forces acting on the body is called the resultant.

We are talking about the geometric sum, because the force is a vector quantity that depends not only on the point of application, but also on the direction of the action.

For example, if you need to move a fairly large cabinet, you can invite friends. Together, the desired result is achieved. But you can invite only one, very strong person. His effort is equal to the action of all friends. The force applied by the hero can be called the resultant.

Newton's laws of motion are formulated on the basis of the concept of "resultant".

Law of inertia

Begin to study the laws of Newton from the most common phenomenon. The first law is usually called the law of inertia, since it establishes the causes of uniform rectilinear motion or the state of rest of bodies.

The body moves evenly and rectilinearly or is at rest, if no force acts on it, or this action is compensated.

It can be argued that the resultant is zero in this case. In this state there is, for example, a car moving at a constant speed on a straight section of the road. The action of the force of attraction is compensated by the reaction force of the support, and the thrust of the engine is modulo equal to the force of resistance to motion.

The chandelier on the ceiling rests, since the force of gravity is compensated by the tension of its fastenings.

Compensated can only be those forces that are attached to one body.

Newton's second law

We go further. The causes that cause a change in the speed of bodies, considers the second law of Newton. What is he talking about?

The equal force acting on the body is defined as the product of the body mass by the acceleration acquired under the action of forces.

2 Newton's law (formula: F = ma), unfortunately, does not establish a causal relationship between the basic concepts of kinematics and dynamics. He can not pinpoint what is the cause of the acceleration of bodies.

Let us formulate differently: the acceleration received by the body is directly proportional to the resultant force and inversely proportional to the mass of the body.

Thus, it can be established that the change in speed occurs only in relation to the force applied to it, and the mass of the body.

2 Newton's law, whose formula can be this: a = F / m, is considered to be fundamental in vector form, since it makes it possible to establish a connection between the sections of physics. Here, a is the acceleration vector of the body, F is the resultant of the forces, m is the mass of the body.

Accelerated movement of the car is possible if the traction force of the engines exceeds the resistance to movement. With an increase in traction, acceleration also increases. Trucks are supplied with high-power engines, because their mass is much greater than the mass of the passenger car.

The cars created for high-speed races are facilitated in such a way that they are secured with a minimum of necessary details, and the engine power is increased to the possible limits. One of the most important characteristics of sports cars is the acceleration time to 100 km / h. The smaller this time interval, the better the speed characteristics of the car.

Law of interaction

Newton's laws, based on the forces of nature, argue that any interaction is accompanied by the appearance of a pair of forces. If the ball hangs on the thread, then it tests its effect. The thread is also stretched under the action of the ball.

Completes the laws of Newton formulation of the third law. In short, it sounds like this: the action is equal to counteraction. What does it mean?

The forces with which the bodies act on each other are equal in magnitude, opposite in direction and directed along the line connecting the centers of the bodies. It is interesting that they can not be compensated for, because they act on different bodies.

Application of laws

The famous task of "The horse and the cart" can lead to a dead end. The horse, harnessed to the wagon, moves it from its place. In accordance with Newton's third law, these two objects act on each other with equal forces, but in practice the horse can move the cart, which does not fit into the basis of regularity.

The solution can be found if we take into account that this system of bodies is not closed. The road has its effect on both bodies. The frictional force of rest, acting on the horse's hooves, exceeds the rolling friction of the cart wheels in value. After all, the moment of motion begins with an attempt to move the wagon. If the situation changes, the horse will not move it under any circumstances. His hooves will slip along the road, and there will be no movement.

In childhood, rolling each other on a sled, everyone could face such an example. If two or three children sit on the sled, then one effort is not enough to move them.

The fall of bodies to the surface of the earth, explained by Aristotle ("Every body knows its place") can be refuted on the basis of the foregoing. The object moves to the ground under the action of the same force as the Earth to it. Comparing their parameters (the mass of the Earth is much larger than the mass of the body), in accordance with Newton's second law, we assert that the acceleration of an object is as much as the acceleration of the Earth. We observe exactly the change in the velocity of the body, the Earth is not displaced from the orbit.

Limits of applicability

Modern physics Newton's laws do not deny, but only establishes the limits of their applicability. Until the beginning of the twentieth century, physicists did not doubt that these laws explain all the phenomena of nature.

1, 2, 3 Newton's law fully reveals the causes of the behavior of macroscopic bodies. Movement of objects with insignificant speeds is completely described by these postulates.

An attempt to explain on their basis the motion of bodies with velocities close to the speed of light is doomed to failure. A complete change in the properties of space and time at these speeds does not allow the use of Newton's dynamics. In addition, the laws change their appearance in non-inertial JI. For their application, the concept of the force of inertia is introduced.

Explain the motion of astronomical bodies, the rules of their location and interaction may be Newton's laws. The law of universal gravitation is introduced for this purpose. It is impossible to see the result of attraction of small bodies, because the power is scanty.

Mutual attraction

A legend is known according to which Mr. Newton, who was sitting in the garden and watching the fall of apples, visited a brilliant idea: to explain the movement of objects near the surface of the Earth and the motion of cosmic bodies on the basis of mutual attraction. This is not so far from the truth. Observations and accurate calculations involved not only the fall of apples, but also the movement of the moon. The regularities of this movement lead to the conclusion that the force of attraction increases with the mass of interacting bodies and decreases with increasing distance between them.

Relying on Newton's second and third laws, the law of universal gravitation is formulated as follows: all bodies in the universe are attracted to each other with a force directed along the line connecting the centers of bodies proportional to the masses of bodies and inversely proportional to the square of the distance between the centers of the bodies.

Mathematical notation: F = GMm / r ² , where F is the attractive force, M, m are the masses of interacting bodies, r is the distance between them. The coefficient of proportionality (G = 6.62 x 10 ^-11 Nm ² / kg ² ) was called the gravitational constant.

Physical meaning: this constant is equal to the force of attraction between two bodies of 1 kg mass at a distance of 1 m. It is clear that for bodies of small masses the force is so insignificant that it can be neglected. For planets, stars, galaxies, the force of attraction is so enormous that it completely determines their motion.

It is the law of attraction of Newton argues that the launch of missiles requires fuel that can create such a reactive pull to overcome the influence of the Earth. The speed required for this is the first space velocity, equal to 8 km / s.

The modern technology of manufacturing rockets allows to launch unmanned stations as artificial satellites of the Sun to other planets in order to investigate them. The speed developed by such a device is the second space velocity, equal to 11 km / s.

Algorithm for applying laws

Solving the problems of dynamics obeys a certain sequence of actions:

• Conduct an analysis of the problem, identify the data, the type of movement.
• Perform a figure indicating all the forces acting on the body, and the direction of acceleration (if available). Select the coordinate system.
• Record the first or second laws, depending on the presence of the acceleration of the body, in vector form. Take into account all forces (resultant force, Newton's laws: the first, if the speed of the body does not change, the second, if there is acceleration).
• The equation is rewritten in the projections to the selected coordinate axes.
• If the resulting system of equations is not enough, then write down other: the definition of forces, kinematics equations, etc.
• Solve the system of equations with respect to the unknown quantity.
• Perform a dimensional test to determine the correctness of the resulting formula.
• Calculate.

Usually these actions are sufficient for solving any standard problem.