The study of natural phenomena on the basis of experiment is possible only if all stages are observed: observation, hypothesis, experiment, theory. Observation will reveal and compare the facts, the hypothesis makes it possible to give them a detailed scientific explanation, requiring experimental confirmation. Observation of the movement of bodies led to an interesting conclusion: a change in the speed of a body is possible only under the influence of another body.
For example, if you quickly run up the stairs, then at the turn you just need to grab the railing (change of direction), or pause (change in speed) so as not to collide with the opposite wall.
Observations of similar phenomena led to the creation of a branch of physics that studies the causes of changes in the speed of bodies or their deformation.
Dynamics Basics
To answer the sacramental question of why the physical body moves in one way or another or rests, dynamics is called upon.
Consider the state of rest. Based on the concept of relativity of motion, we can conclude: there are no and cannot be absolutely motionless bodies. Any object, being motionless in relation to one reference body, moves relative to another. For example, a book lying on a table is motionless relative to a table, but if we consider its position in relation to a passing person, we make a natural conclusion: the book moves.
Therefore, the laws of motion of bodies are considered in inertial reference systems. What it is?
Inertial is a reference system in which the body rests or performs uniform and rectilinear movement , provided that there are no effects on it of other objects or objects.
In the above example, the reference system associated with the table can be called inertial. A person moving uniformly and rectilinearly can serve as an ISO reference body. If its motion is accelerated, then inertial CO cannot be associated with it.
In fact, such a system can be correlated with bodies rigidly fixed on the surface of the Earth. However, the planet itself cannot serve as a reference body for ISO, since it evenly rotates around its own axis. The bodies on the surface have centripetal acceleration.
What is inertia?
The inertia phenomenon is directly related to ISO. Remember what happens if a moving car stops abruptly? Passengers are at risk as they continue to move. It can be stopped by a chair in front or seat belts. Explain this process by inertia of the passenger. Is it so?
Inertia is a phenomenon involving the preservation of a constant body speed in the absence of other bodies acting on it. The passenger is under the influence of belts or seats. The inertia phenomenon is not observed here.
The explanation lies in the property of the body, and, according to it, it is impossible to instantly change the speed of an object. This is inertia. 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. During the interaction, the speed changes faster for bodies with a lower mass. The collision of a car with a concrete wall for the latter proceeds almost without a trace. The car most often undergoes irreversible changes: the speed changes, there is a significant deformation. It turns out that the inertia of the concrete wall significantly exceeds the inertia of the car.
Is it possible in nature to encounter the phenomenon of inertia? The condition under which the body is not interconnected with other bodies is deep space, in which the spacecraft moves with the engines turned off. But even in this case, the gravitational moment is present.
Core quantities
Studying dynamics at the experimental level involves conducting an experiment with measurements of physical quantities. The most interesting:
- acceleration as a measure of the speed of change in the speed of bodies; designate it with the letter a, measured in m / s 2 ;
- mass as a measure of inertia; marked with the letter m, measured in kg;
- force as a measure of the mutual action of bodies; denoted most often by the letter F, measured in N (newtons).
The relationship of these quantities is set forth in three laws deduced by the greatest English physicist. Newton's laws are designed to explain the complexity of the interaction of various bodies. As well as the processes that control them. It is precisely the concepts of “acceleration”, “force”, and “mass” that Newton’s laws associate with mathematical relationships. Let's try to figure out what this means.
The action of only one force is an exceptional phenomenon. For example, an artificial satellite moving in an orbit around the Earth is only affected by gravity.
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.
This is precisely the geometric sum, since force is 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 a sufficiently massive cabinet, you can invite friends. Together, the desired result is achieved. But you can only invite one, very strong person. His effort is equal to the action of all friends. The force exerted 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 Newton’s laws with the most common phenomenon. The first law is usually called the law of inertia, since it establishes the reasons for the uniform rectilinear motion or the state of rest of bodies.
The body moves uniformly and rectilinearly or rests if it is not subjected to force, or this action is compensated.
It can be argued that the resultant in this case is zero. In this state is, for example, a car moving at a constant speed on a straight section of the road. The action of the attractive force is compensated by the reaction force of the support, and the engine traction force modulo equal to the force of resistance to movement.
The chandelier on the ceiling is at rest, since the force of gravity is compensated by the tension force of its fixtures.
Only those forces that are applied to one body can be compensated.
Newton's second law
We go further. The causes of the change in the speed of bodies are considered by Newton’s second law. What is he talking about?
The resultant of the forces acting on the body is defined as the product of the mass of the body and the acceleration acquired by the action of the forces.
Newton's law 2 (formula: F = ma), unfortunately, does not establish causal relationships between the basic concepts of kinematics and dynamics. He cannot accurately indicate what causes the acceleration of bodies.
We formulate another way: the acceleration received by the body is directly proportional to the resultant of forces and inversely proportional to the mass of the body.
So, it can be established that a change in speed occurs only depending on the force applied to it, and body weight.
Newton’s law 2, the formula of which can be as follows: a = F / m, in vector form is considered fundamental, since it makes it possible to establish a connection between the branches of physics. Here, a is the acceleration vector of the body, F is the resultant of forces, m is the mass of the body.
Accelerated car movement is possible if the engine thrust exceeds the resistance to movement. With increasing traction, acceleration also increases. Trucks are equipped with high power engines, because their mass is much higher than the mass of a passenger car.
Fireballs created for high-speed races are facilitated in such a way that a minimum of necessary parts is fixed on them, and engine power is increased to the extent possible. One of the most important characteristics of sports cars is the acceleration time to 100 km / h. The shorter this time interval, the better the speed properties 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 a thread, then it experiences its action. In this case, the thread also stretches under the influence of the ball.
The laws of Newton are completed by the formulation of the third law. In short, it sounds like this: 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. Interestingly, they cannot be called compensated, because they act on different bodies.
Application of laws
The famous task “Horse and Cart” can be confusing. A horse harnessed to the said wagon moves it from its place. In accordance with Newton’s third law, these two objects act on each other with forces equal in magnitude, but in practice a horse can move a cart, which does not fit into the foundations of the law.
There is a solution, given that this system of bodies is not closed. The road has an effect on both bodies. The rest friction force acting on the horse’s hooves exceeds the rolling friction force of the cart wheels. After all, the moment of movement begins with an attempt to move the wagon. If the situation changes, then the horse will under no circumstances move it. His hooves will slip along the road, and there will be no movement.
In childhood, riding each other on a sled, everyone could encounter such an example. If two or three children sit on the sled, then the efforts of one are clearly not enough to move them from their seats.
The fall of bodies on the surface of the earth, explained by Aristotle ("Every body knows its place") can be refuted on the basis of the foregoing. An object moves toward the earth under the same force as the Earth toward it. Comparing their parameters (the mass of the Earth is much greater than the mass of the body), in accordance with Newton’s second law, we affirm that the acceleration of an object is as much as the acceleration of the Earth. We observe precisely the change in the speed of the body, the Earth does not move from orbit.
Limits of applicability
Modern physics does not deny Newton’s laws, but only sets the limits of their applicability. Until the beginning of the 20th century, physicists had no doubt that these laws explain all natural phenomena.
1, 2, 3, Newton's law fully reveals the causes of the behavior of macroscopic bodies. The 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 Newtonian dynamics. In addition, laws change their appearance in non-inertial COs. For their application, the concept of inertia force is introduced.
Explain the motion of astronomical bodies, the rules of their location and interaction can Newton's laws. The law of gravity is introduced for this purpose. It is impossible to see the result of the attraction of small bodies, because the power is minuscule.
Mutual attraction
A legend is known according to which Mr. Newton, who was sitting in the garden and watching the fall of apples, was visited by a brilliant idea: to explain the movement of objects near the surface of the Earth and the movement of cosmic bodies based on mutual attraction. It is not so far from the truth. Observations and accurate calculations concerned not only the fall of apples, but also the movement of the moon. The laws of this motion lead to the conclusion that the force of attraction increases with increasing masses of interacting bodies and decreases with increasing distance between them.
Based on Newton’s second and third laws, the law of gravity 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 the bodies, proportional to the masses of the 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 force of attraction, M, m are the masses of interacting bodies, r is the distance between them. The proportionality coefficient (G = 6.62 x 10 -11 Nm 2 / kg 2 ) is called the gravitational constant.
Physical meaning: this constant is equal to the force of attraction between two bodies with masses of 1 kg 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 gravity is so huge that it completely determines their movement.
It is Newton’s law of attraction that states that to launch rockets you need fuel that can create such a thrust to overcome the influence of the Earth. The speed required for this is the first cosmic speed of 8 km / s.
Modern technology for the manufacture of rockets allows you to launch unmanned stations like artificial satellites of the Sun to other planets in order to explore them. The speed developed by such an apparatus is the second space velocity equal to 11 km / s.
Law Enforcement Algorithm
The solution of dynamic problems obeys a certain sequence of actions:
- Perform an analysis of the problem, identify data, type of movement.
- Perform a drawing indicating all the forces acting on the body, and the direction of acceleration (if any). Choose a coordinate system.
- Write down the first or second laws, depending on the presence of acceleration of the body, in vector form. Take into account all the forces (the resultant force, Newton's laws: the first, if the speed of the body does not change, the second, if there is acceleration).
- Rewrite the equation in projections onto the selected coordinate axes.
- If the obtained system of equations is not enough, then write down others: definitions of forces, kinematics equations, etc.
- Solve a system of equations for the desired quantity.
- Perform a dimensional check to determine the correctness of the resulting formula.
- Calculate.
Usually these actions are quite enough to solve any standard task.