study of natural phenomena on the basis of the experiment is possible only under condition of observance of all stages: observation, hypothesis, experiment, theory.Monitoring will identify and compare the facts, the hypothesis makes it possible to give them a detailed scientific explanation, requires experimental confirmation.Carrying out observation of the motion of bodies led to an interesting conclusion: the change in velocity of the body is possible only by the action of another body.
For example, if you quickly run up the stairs, you just need to turn to grab the railing (change of direction) or pause (the change of the speed), so as not to run into the opposite wall.
observations of similar events led to the creation of the physical science studying the reasons for changing the speed of the bodies or deformation.
Basics dynamics
Respond to the perennial question of why the physical body is moving in any way or at rest, the speaker called upon.
consider the rest.Based on the concept of the relativity of motion, we can conclude that there can be absolutely motionless bodies.Any object being stationary relative to one reference body moves relative to the other.For example, the book lying on the table is stationary relative to the table, but if you consider its position with respect to the passing person, then it is natural to conclude the book moves.
Therefore, the laws of motion of bodies covered in the inertial reference systems.What it is?
called Inertial reference system in which the body is at rest or performing uniform and rectilinear motion in the absence of exposure to other subjects or objects.
In the above example, the frame of reference associated with the table can be called inertial.A man in uniform motion in a straight line, can serve as a reference body of ISO.If his motion will be accelerated, then connect it inertial CO impossible.
In fact, such a system can be correlated with the bodies rigidly fixed to the surface of the Earth.However, the planet itself can not serve as a reference body for ISO as uniformly rotating around its own axis.The bodies on the surface have a centripetal acceleration.
What is inertia?
phenomenon of inertia is directly related to the ISO.Think of what happens when a moving car stops abruptly?Passengers are at risk, as are continuing their movement.Stop it can seat in front of a seat belt.This process explains the inertia of the passenger.Is it so?
Inertia - a phenomenon that is expected to maintain a constant speed of a body in the absence of exposure to other bodies.The passenger is under the seat or seats.Inertia phenomenon is not observed.
explanation lies in the properties of the body, and, according to him, instantly change the speed of an object is not possible.It - inertia.For example, the inertia of the mercury in the thermometer allows you to omit the bar if we are old shake the thermometer.
a measure called body mass inertia.The interaction is changing faster than the speed of the bodies with less weight.Car collision with a concrete wall for the final runs almost without a trace.The car is often undergoes irreversible changes: changing the speed, there is a significant distortion.It turns out that the inertia of the concrete wall is much higher than the inertia of the car.
possible in nature to meet with the phenomenon of inertia?A condition in which the body is no relationship with other bodies - deep space, in which the spacecraft is moving with the engine off.But even in this case present gravitational moment.
Basic quantities
study of the dynamics of the pilot involves a level of experience with measurements of physical quantities.The most interesting are:
- acceleration as a measure of the speed of change in the speed of the bodies;designated by the letter a, measured in m / s2;
- weight as a measure of inertia;It denotes the letter m, measured in kg;
- force as a measure of the mutual action of bodies;often denoted by the letter F, measured in N (newtons).
relationship of these variables is set out in three regularities derived the greatest English physicist.Newton's laws are designed to explain the complexity of the interaction between different bodies.As well as the processes to manage them.That is the concept of "acceleration", "power", "weight" Newton's laws associated mathematical relationships.Let's try to understand what it means.
Action Only one force - an exceptional phenomenon.For example, the artificial satellite orbiting the Earth, is affected only by gravity.
resultant
several forces can be replaced by a single force.
Geometric sum of forces acting on the body, called the resultant.
We are talking about the geometric sum, since the force - a vector quantity, which depends not only on the point of application, but also on the direction of action.
For example, if you need to move quite massive wardrobe, you can invite your friends.Together, the desired result is achieved.But you can invite only a very strong man.His force is equal to the action of all the friends.The force applied hero may be called 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 with the most frequent phenomenon.The first law is commonly called the law of inertia, since it establishes the causes of uniform motion or standstill bodies.
body moves uniformly in a straight line or at rest, if he did not carry the force or effect of this offset.
can be argued that in this case, the resultant is zero.In such a condition is, for example, a moving vehicle at a constant speed on a straight stretch of road.The force of gravity is compensated by the reaction force bearing, and the thrust of the engine modulo equal to the force of resistance to movement.
chandelier on the ceiling rests, as the force of gravity is balanced by the tension of its fixtures.
can be compensated only those forces which are attached to the same body.
Newton's second law
Come on.The causes of change in the velocity of bodies, considering Newton's second law.What is he saying?
resultant forces acting on the body, is defined as the product of the mass of the body to be acquired by the forces of acceleration.
2 Newton's law (formula: F = ma), unfortunately, does not establish a cause-and-effect relationship between the basic concepts of kinematics and dynamics.It can not indicate with precision, which is a cause of the acceleration of bodies.
formulate otherwise: the acceleration obtained body is directly proportional to the resultant force and inversely proportional to body weight.
Thus, it can be established that the change in speed is only depending on the force applied thereto, and body weight.
2 Newton's law, the formula of which may be a: a = F / m, in a vector is considered fundamental, because it allows you to establish a link between the branches of physics.Here, a - the acceleration vector of the body, F - resultant force, m - weight.
accelerated movement of the car is possible if the engine thrust greater than the force of resistance to movement.With increasing traction and acceleration increases.Trucks are equipped with heavy-duty engines, because their mass is much greater than the mass of a passenger car.
car, designed for high-speed races are facilitated so that they fixed the minimum necessary parts and engine power is increased to the extent possible.One of the most important characteristics of a sports car acceleration time to 100 km / h.The smaller the interval, the better the properties of the speed of the car.
law interaction
Newton's laws, based on the forces of nature, argue that any interaction is accompanied by a couple of forces.If the ball is hanging on a thread, it feels its effect.This thread is also stretched by the action of the ball.
Ends Newton's laws formulation of the third rule.In short it is: action equals reaction.What does it mean?
forces with which bodies exert on each other are equal in magnitude and opposite in direction directed along the line connecting the centers of the bodies.It is interesting that they can not be called compensated because they act on different bodies.
Application of laws
famous problem of "horse and cart" can stump.A horse harnessed to a cart mentioned, shifts it from the spot.According to Newton's third law, the two objects act on each other with equal forces unit, but in practice, the horse can move a cart that does not fit into the basis of laws.
decision will be, given that this system of bodies is not closed.The road has its effect on both bodies.The strength of the friction acting on the horse's hoof, exceeds the value of the friction wheels rolling cart.For the moment motion begins with an attempt to move the cart.If the situation changes, the horse under any circumstances it will not move from their seats.Its hooves would slip on the road, and the traffic will not be.
As a child, rolling each other on a sled, one could encounter in such an example.If you sit on the sled, two or three children, the efforts of one is not enough to move them.
falling bodies on the ground, explained by Aristotle ("Every body knows its place") can be refuted on the basis of the foregoing.The subject is moving to the ground under the influence of the same force as the Earth for him.By comparing their parameters (mass of the Earth is much greater than the mass of the body), in accordance with Newton's second law, argued that the acceleration of an object as many times more than the acceleration of the Earth.We have seen it change in the rate of the body, the Earth does not move from orbit.
limits of applicability
Modern physics does not deny the laws of Newton, but merely sets the limits of their applicability.Prior to the beginning of XX century physics no doubt that these laws explain all natural phenomena.
1, 2, 3 Newton's law fully reveals the reasons for the behavior of macroscopic bodies.Movement of objects with minor speed fully describes these postulates.
Trying to explain to them the basis of the motion of bodies at velocities close to the speed of light, is doomed to failure.The total change in the properties of space and time at these speeds does not allow the use of Newton's dynamics.In addition, laws are changing their views in non-inertial CO.For their use introduces the concept of inertia.
Explain the motion of celestial bodies, the rules for their location and interaction can Newton's laws.The law of gravity is introduced for this purpose.To see the result of attraction of small bodies is impossible, because the power is scanty.
mutual attraction
known legend according to which Mr. Newton, who was sitting in the garden and watch the apple fall, visited a brilliant idea: to explain the motion of objects near the Earth's surface and the movement of celestial bodies on the basis of mutual attraction.It's not so far from the truth.Observations and accurate calculation concerned not only the fall of apples, but also move the moon.Laws of this movement leads to the conclusion that the force of attraction increases with the masses of interacting bodies and decreases with increasing distance between them.
Relying on the second and third laws of Newton's law of universal gravitation is stated as follows: all bodies in the universe attract each other with a force directed along the line connecting the centers of the bodies, proportional to the mass of bodies and inversely proportional to the square of the distance between the centers of the bodies.
mathematical notation: F = GMm / r2, where F - the force of gravity, M, m - masses of interacting bodies, r - the distance between them.The proportionality factor (G = 6.62 x 10-11 nm 2 / kg 2) is called the gravitational constant.
physical meaning: this constant equal to the force of attraction between two bodies of masses of 1 kg at a distance of 1 m. It is clear that small body mass force is so insignificant that it can be neglected.For the planets, stars, galaxies, the force of attraction is so large that completely defines their movement.
That Newton's law of attraction states that you need to run a fuel rockets that can create a jet thrust to overcome the influence of the Earth.The speed necessary for this - the escape velocity of 8 km / s.
Modern technology allows the manufacture of rockets to launch unmanned station as the satellites of the sun to the other planets to explore them.Speed, developed such a device - the escape velocity equal to 11 km / s.
algorithm of laws
Problem solving dynamics obeys a certain sequence of actions:
- To analyze the problem, identify the data type of motion.
- Run drawing showing all the forces acting on the body and the direction of acceleration (if available).Select a coordinate system.
- Write the first or second laws, depending on the availability of acceleration of the body, in vector form.Consider all forces (resultant force, Newton's laws: first, if the speed of the body does not change, the second if there is acceleration).
- equation written in the projections on the selected axes.
- If the resulting system of equations is not enough, to write different: determination of the forces, the kinematics equations, and so on. N.
- Solve the system of equations for the unknown quantity.
- Run check dimensions to determine the correctness of the formula.
- Calculate.
Usually these actions is enough to solve the problem any standard.
