The study of natural phenomena on the basis of an 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 that requires 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 on the turn you just need to grab the railing (changing the direction of movement), or stop (changing the speed value) 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
Dynamics is called upon to answer the sacramental question of why the physical body moves in one way or another or is at rest.
Consider the state of rest. Based on the concept of the relativity of motion, we can conclude: there are no and cannot be absolutely motionless bodies. Anyan object, being motionless with respect to one reference body, moves relative to another. For example, a book lying on a table is motionless relative to the table, but if we consider its position in relation to a passing person, we draw a natural conclusion: the book is moving.
Therefore, the laws of motion of bodies are considered in inertial frames of reference. What is it?
Inertial frame of reference is called, in which the body is at rest or performs uniform and rectilinear motion, provided there is no influence of other objects or objects on it.
In the above example, the frame of reference associated with the table can be called inertial. A person moving uniformly and in a straight line can serve as a frame of reference for the ISO. If its movement 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 cannot serve as a reference body for IFR, as it rotates uniformly around its own axis. Bodies on the surface have centripetal acceleration.
What is momentum?
The phenomenon of inertia is directly related to ISO. Remember what happens if a moving car stops abruptly? Passengers are in danger as they continue on their journey. It can be stopped by a seat in front or seat belts. This process is explained by the inertia of the passenger. Is that right?
Inertia is a phenomenon that presupposes the preservationconstant speed of the body in the absence of influence of other bodies on it. The passenger is under the influence of belts or seats. The phenomenon of inertia 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 makes it possible to lower the bar if we shake the thermometer.
Measure of inertia is called the mass of the body. When interacting, the speed changes faster for bodies with less 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: speed changes, significant deformation occurs. It turns out that the inertia of a concrete wall significantly exceeds the inertia of a car.
Is it possible to meet the phenomenon of inertia in nature? The condition under which the body is without interconnection 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.
Basic quantities
Studying dynamics at the experimental level involves experimenting with measurements of physical quantities. Most interesting:
- acceleration as a measure of the speed of change in the speed of bodies; designate it with the letter a, measure in m/s2;
- mass as a measure of inertia; marked with the letter m, measured in kg;
- force as a measure of the mutual action of bodies; most often denoted by the letter F, measured in N (newtons).
The relationship between these quantitiesset out in three patterns, derived 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 manage them. It is the concepts of "acceleration", "force", "mass" that Newton's laws connect with 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 orbiting the Earth is only affected by gravity.
Resultant
The action of several forces can be replaced by one force.
The geometric sum of forces acting on a body is called the resultant.
We are talking about a 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 fairly massive wardrobe, you can invite friends. Together we achieve the desired result. But you can only invite 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 Newton's laws with 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 uniformly and rectilinearly orrests if no forces act on it, or this action is compensated.
It can be argued that the resultant in this case is equal to 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 force of attraction is compensated by the reaction force of the support, and the thrust force of the engine is equal in absolute value to the force of resistance to movement.
The chandelier rests on the ceiling, as the force of gravity is compensated by the tension of its fixtures.
Only those forces that are applied to one body can be compensated.
Newton's second law
Let's move on. The reasons that cause a 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 a body is defined as the product of the body's mass and the acceleration acquired under the action of the forces.
2 Newton's law (formula: F=ma), unfortunately, does not establish causal relationships between the basic concepts of kinematics and dynamics. He cannot pinpoint exactly what is causing the bodies to accelerate.
Let's formulate it differently: the acceleration received by the body is directly proportional to the resultant forces and inversely proportional to the mass of the body.
Thus, it can be established that the change in speed occurs only depending on the force applied to it and the mass of the body.
2 Newton's law, the formula of which may be as follows: a=F/m, is considered fundamental in vector form, since it makes it possibleestablish connections between 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 movement of the car is possible if the traction force of the engines exceeds the force of resistance to movement. As the thrust increases, so does the acceleration. Trucks are equipped with high-power engines, because their mass is much higher than the mass of a passenger car.
Fireballs designed for high-speed racing are lightened in such a way that the minimum necessary parts are attached to them, and engine power is increased to the limits 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.
The law of interaction
Newton's laws, based on the forces of nature, state 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 is also stretched under the action of the ball.
The formulation of the third regularity completes Newton's laws. In short, it sounds like this: action equals reaction. What does this 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.
Enforcement of laws
The famous "Horse and Cart" problem can be confusing. The horse harnessed to the said wagon moves itfrom place. In accordance with Newton's third law, these two objects act on each other with equal forces, but in practice a horse can move a cart, which does not fit into the foundations of the pattern.
The solution is found if we take into account that this system of bodies is not closed. The road has its effect on both bodies. The static 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 position changes, then the horse under no circumstances will move it from its place. His hooves will slip on the road and there will be no movement.
In childhood, sledding each other, everyone could come across such an example. If two or three children sit on the sled, then the efforts of one child are clearly not enough to move them.
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 above. An object moves towards the earth under the influence of the same force as the Earth moves towards 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 assert that the acceleration of an object is as many times greater than the acceleration of the Earth. We are observing a change in the speed of the body, the Earth does not move from its orbit.
Limits of applicability
Modern physics does not deny Newton's laws, but only establishes the limits of their applicability. Until the beginning of the 20th century, physicists had no doubt that these laws explained all natural phenomena.
1, 2, 3 lawNewton fully reveals the causes of the behavior of macroscopic bodies. The movement of objects with negligible speeds is fully described by these postulates.
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, the laws change their form in non-inertial FRs. For their application, the concept of inertial force is introduced.
Newton's laws can explain the movement of astronomical bodies, the rules for their location and interaction. The law of universal gravitation is introduced for this purpose. It is impossible to see the result of the attraction of small bodies, because the force is scanty.
Mutual attraction
There is a legend according to which Mr. Newton, who was sitting in the garden and watching the fall of apples, had a brilliant idea: to explain the movement of objects near the surface of the Earth and the movement of space bodies on the basis of mutual attraction. It's not that far from the truth. Observations and accurate calculation concerned not only the fall of apples, but also the movement of the moon. The laws of this movement 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 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 the bodies, proportional to the masses of the bodies andinversely proportional to the square of the distance between the centers of the bodies.
Mathematical notation: F=GMm/r2, where F is the force of attraction, M, m are the masses of the interacting bodies, r is the distance between them. The proportionality coefficient (G=6.62 x 10-11 Nm2/kg2) is called the gravitational constant.
Physical meaning: this constant is equal to the force of attraction between two bodies of 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 attraction is so huge that it completely determines their movement.
It is Newton's law of gravity that states that to launch rockets, you need fuel that can create such jet thrust to overcome the influence of the Earth. The speed required for this is the first escape velocity, which is 8 km/s.
Modern rocket technology makes it possible to launch unmanned stations as artificial satellites of the Sun to other planets to explore. The speed developed by such a device is the second space velocity, equal to 11 km / s.
Algorithm for applying laws
Solving problems of dynamics is subject to a certain sequence of actions:
- Analyze the task, identify data, type of movement.
- Draw a drawing indicating all the forces acting on the body and the direction of acceleration (if any). Select coordinate system.
- Write first or second laws, depending on availabilitybody acceleration, 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).
- Rewrite the equation in projections on the selected coordinate axes.
- If the resulting system of equations is not enough, then write down others: definitions of forces, equations of kinematics, etc.
- Solve the system of equations for the desired value.
- Perform a dimensional check to determine if the resulting formula is correct.
- Calculate.
Usually these steps are enough to solve any standard problem.
