How to prove Newton s first and second laws by rational reasoning

The basis of Newton's first and second laws was experimentation, and the physical theories of that era were not yet mature. And the general theory of relativity explains these two laws. But how did general relativity be based on Newton's laws?

Why do you say that? The general theory of relativity was developed on the basis of the special theory of relativity. It completely discarded Newton's view of time and space, and was not based on this law at all.

The law of inertia can be derived from Aninstein's field equations, and its physical source is the action of all other matter on the object under study, and inertia is the interaction! Although I don't have a very deep understanding of this, this is exactly the idea of general relativity, and it is also the idea that Mach once put forward.

Deriving the form of any force according to the most basic principles was the direction of Einstein's efforts in the second half of his life, but it failed. When talking about the inability to understand quantum theory, even he himself said, when will new ideas appear? What a blessing it would be if anyone could live to that time.

I think the root of your problem is why I'm looking out in this universe.

In analytical mechanics, through generalized coordinates, using the Lagrangian equations, the virtual work principle, and the Hamiltonian regular equations, those physical formulas can be derived almost from a purely mathematical point of view, and I think these are the basis for turning over analytical mechanics.

Newton's second law of motion states that the acceleration of an object is proportional to the net force experienced by the object and inversely proportional to the mass of the objectWhereas, the direction of the acceleration of the object is the same as that of the net force.

From the point of view of physics, Newton's second law of motion can also be expressed as the rate of change of momentum of an object with time is proportional to the sum of the external forces exerted on itThat is, the first derivative of momentum to time is equal to the sum of external forces.

where the net force (resultant) f and acceleration a are vectors (vectors) and masses m are pure (scalars).

The impulse theorem is derived from Newton's second theorem. But I think this formula is obtained through experiments, first to study the relationship between force and acceleration by determining mass, and then to study the relationship between acceleration and mass by determining force, so as to conclude that f is proportional to a, and a is inversely proportional to m.

It seems that there is no derivation formula.

According to the functional relationship between them, it is obtained: f am, and by adding the appropriate coefficient k between them, we get f=ma, k=1 because when the mass and acceleration of the object are 1, the force on the object is 1n, therefore, k=1

This formula is derived using the impulse theorem: the accumulation of the combined external force on the object in time is the increment of the impulse of the object.

Impulse formula: ft = ep

The impulse of the object: ep=mv

ft=△ep=mv-mv0=m(v-v0)

Your return is truly satisfying, and at the same time allows yourself to discover a fatal mistake in my own problem. It's a pity. That's when I wrote Newton's binomial theorem as Newton's second law in physics, but I still appreciate your wonderful return, after all, math and physics are very closely related.

The impulse theorem is derived from Newton's second theorem. First, the relationship between force and acceleration is studied by determining the mass, and then the relationship between acceleration and mass is studied by determining the force, so as to conclude that f is proportional to a and a is inversely proportional to m

f am, add the appropriate coefficient k between them, and the reason is that when the mass and acceleration of the object are both 1, the force on the object is 1n, therefore, the derivation of the formula k=1 uses the impulse theorem: the accumulation of the combined external force on the object in time is the incremental impulse of the object: ft = ep The impulse of the object:

ep=mv ft=△ep=mv-mv0=m(v-v0) ∴f/m=(v-v0)/t ∵(v-v0)/t=a ∴ f=ma

Newton's first law (law of inertia) reads: 1. The tangent object will maintain its original state of motion without external force, that is, a state of stationary or linear motion.

According to this law, assuming that no external force is applied or the sum of the applied external forces is zero, then the object in motion always remains in a state of uniform linear motion, and the object at rest always remains at rest. The property exhibited by an object that maintains a constant state of motion is called inertia.

Newton's first law is not an experimental law, it is based on a large number of experiments and scientific reasoning, Newton's first law describes the situation: a state of an object without being acted on by an external force, and the situation without any external force does not exist, if you want to understand, go to the compulsory 1 Newton's first law of physics, there is Galileo's experiment.

Newton's first law was elevated from experimental summaries, and this axiomatic law cannot be proved.

The main experimental methods of secondary school physics are:

1) Equivalence (substitution);

2) Establish an ideal model method;

3) control variable method;

4) Experimental reasoning;

5) conversion method;

5) Analogy, etc.

That's the experiment that Galileo did, where the same trolley slid down from a standstill at the same position on the same inclined plane (this is to ensure that the trolley has the same speed every time it reaches the horizontal plane, taking care to ensure a single variable). For the first time, a towel was laid on the horizontal plane, and the trolley slid on the towel for a short distance before stopping (as shown in Figure A); the second time, a smoother cotton cloth is spread on the horizontal surface, and the trolley glides on the cotton cloth for a longer distance (as shown in Figure B); The third time is a smooth plank, and the car glides the farthest distance (Figure C). Newton's first law of motion.

Galileo believed that it was the resistance of the plane to the trolley that caused the trolley to stop, and the smoother the plane, the farther the trolley would slide. Shows that the lower the resistance, the farther the trolley will slide Galileo scientifically imagined that if a very smooth plane could be found with zero resistance, the trolley would not slow down and would continue to travel at a constant speed.

This is an ideal experiment, that is, it is assumed that it cannot really happen in reality, and here it should be a method of combining the establishment of an ideal model and experimental reasoning.

Ideal experiment method, also known as imagination innovation method, thought experiment method, reasoning method.

It is a method of researching problems through generalization, abstraction, and reasoning on the basis of experiments. In order to solve some difficult problems in scientific theories, scientists use the original theoretical knowledge (such as principles, theorems, laws, etc.) as the "materials" of thought experiments, put forward the idea of solving these problems as the goal of ideal experiments, and give the conditions required for the "interaction" of these experimental "materials" in their imagination, and then "process" the "materials" of these thought experiments according to strict logical thinking operation methods. As a result, a series of new principles and laws reflecting the objective laws of matter are derived, so that scientific problems can be solved and the development of science can be promoted.

Newton's first law was established on the basis of scientific experiments, through the analysis of experimental data, and further through reasoning (in fact, objects that are not subject to friction do not exist at all), so the experiment mainly used experimental reasoning to form Newton's first law The reflection law of light, the law of electric current in parallel circuits, and Ohm's law experiments are all conclusions drawn directly through real experimental data, and the conclusion formation method is different from Newton's first law, so a, c, and d cannot be selected

The experiment of the vacuum cannot transmit sound is based on the real experiment, and the conclusion is formed through further reasoning (pumping gas outward, but less and less, it is impossible to pump into a vacuum), and the experiment uses the experimental reasoning method, and its formation principle is the same as Newton's first law, so option b is correct

Therefore, choose B

I don't agree with the guys upstairs. I think the answer should be a.

Let's start with the experimental process of Newton's first law.

I remember that the book said that if you slide a piece of wood off an inclined plane and then slide it on a horizontal plane, it will slide a little on the flat ground and then stop; If you slide down at the same height, change the horizontal plane to a smoother material, and it will slide farther; If you change to a smoother material, it will slide farther. The next thing is not the actual experiment, but our reasoning. If the horizontal plane is ideally perfectly smooth, the block will not stop and move at infinity, and we will get the result of Newton's first law.

So, this kind of experiment is the actual situation experiment, and the central idea is to reduce the actual situation to the more and more ideal (but never to the absolute ideal) reasoning to the unrealistic ideal situation, which is the central idea.

The landlord looks at the four options of A, B, C, D, A is very similar, we pump air in a container, the less air in it, the weaker the sound we hear, but we can never pump absolutely no air in it, but we can reason and guess that if there is really no air at all, it is really impossible to hear the sound at all, so we conclude that the sound cannot be transmitted in a vacuum. This is also the method of practical and ideal induction.

b, c, and d have little to do with this kind of thinking, and b just look at the effect, without this assertion of what would happen in an ideal situation; c is a means of describing physical quantities, which is completely artificially defined by such a thing as magnetic inductance lines (belonging to artificial definitions, although they do not exist originally, and they are also at the ideological level, but this is fundamentally different from Newton's first law, which does not go through the gradual process of actually becoming ideal and inducting a complete ideal); D is entirely a matter of measuring force, and has nothing to do with whether the situation is ideal or not.

c The interaction between the magnetic pole and the magnetic pole, the magnetic field and the current, and the current and the current all occur through the magnetic field, and the electric field and the magnetic field are both objectively existing substances.

Magnetic lines are imaginary lines, similar to electric field lines.

cDescribe the magnetic field with magnetic inductance lines.

None of them can be directly verified.

A x does not equal four makes sense.

c Magnetic fields do exist, and we all have experience with them, but how to describe them? There are only magnetic inductance lines, magnetic inductance lines do not exist, they are imagined by people, abstract, so choose C

Support the second theory: Newton's first law is derived by experiment + reasoning, and cannot be verified by experiments in the laboratory. Because, it is premised on the absence of force, which is almost impossible in the whole universe at present.

The same is true for item b, pure vacuum is almost non-existent, for example, as we do the vacuum bell experiment, as more and more gas is pumped out (close to vacuum), you will find that the sound becomes weaker and weaker, and the positive air cannot transmit sound. That is, it is also experiment + reasoning.

I think it's all right, but with a different emphasis.

The first emphasis is on "a large number of experiments", which is indeed Ohm's law, because at that time the technology could not come up with an exact formula, and could only be inferred from experimental data, and this answer was actually not so reasonable.

The latter question emphasizes the process of "rational reasoning", and it cannot be said that it is Ohm's law, because it is not rational reasoning at all, but only the law obtained from a large amount of data. It is reasonable reasoning that a vacuum cannot transmit sound, because a medium is required for sound propagation.

B, it should be B, this is a scientific reasoning experiment, based on hypothesis.