The magnitude of the acceleration of an object is directly proportional to the force acting on the object and inversely proportional to the mass of the object, and the direction of the acceleration is the same as that of the resultant force. From the physical point of view, Newton's second law of motion can also be expressed as "the rate of momentum change with time is proportional to the sum of external forces", that is, the first derivative of momentum with time is equal to the sum of external forces. Newton's second law shows that at macro low speed, the proportional expressions are: a∝F/m, f ∝ ma; The mathematical expression can be written as F=kma, where k is a proportional coefficient and a constant. However, since the force was not designated as the unit of force at that time, the selection of the proportional coefficient k was arbitrary. If k= 1, there will be F=ma, which is the mathematical expression of Newton's second law we are familiar with today.

The content of Newton's second law

The acceleration of an object is proportional to the acting force and inversely proportional to the mass of the object.

In the international unit, the unit of force is Newton, and the symbol N is defined according to Newton's second law: an object with a mass of 1kg is generated1m/s 2; The force of acceleration is called1n. That is, 1n = 1 kg m/s 2.

Newton's second law formula

F =ma (unit: n (cattle) or kg m/s 2) N=(kg×m)/(s×s)

(when all units adopt the international system of units, k = 1 and f = KMA means F=ma).

explain

(1) Newton's second law is the instantaneous law of force. Force and acceleration occur at the same time, change at the same time and disappear at the same time.

⑵F=ma is a vector equation, and the positive direction should be specified when applying it. All forces or accelerations in the same direction as the positive direction should be positive, and vice versa. In general, the direction of acceleration is positive.

⑶ According to the principle of independent action of force, when Newton's second law is used to deal with the motion of an object in a plane, the force acting on the object can be decomposed orthogonally, and the component form of Newton's second law can be applied in two mutually perpendicular directions: Fx=max and Fy=may.

Six properties of Newton's second law:

(1) Causality: Force is the cause of acceleration. If there is no force, there is no acceleration.

⑵ Vectorality: both force and acceleration are vectors, and the direction of the acceleration of an object is determined by the direction of the combined external force on the object. In the mathematical expression ∑F= ma of Newton's second law, the equal sign not only means that the values on the left and right sides are equal, but also means that the direction of acceleration of an object is the same as that of the external force.

According to the vector of force, the force can be synthesized or decomposed by orthogonal decomposition method.

⑶ Instantaneity: When the external force on an object (with a certain mass) changes suddenly, the magnitude or direction of acceleration determined by the force also changes suddenly; When the external force is zero, the acceleration is also zero, and the acceleration and the external force are in one-to-one correspondence. Newton's second law is the law of instantaneous correspondence, which shows the instantaneous effect of force.

⑷ Relativity: There is a coordinate system in nature. In this coordinate system, when an object is not stressed, it will maintain a uniform linear motion or a static state. This coordinate system is called inertial reference system. Both the ground and objects moving in a straight line at rest or at a constant speed relative to the ground can be regarded as inertial reference frames, and Newton's law only holds in inertial reference frames.

5. Independence: The accelerations generated by various forces on the object do not interfere with each other, while the actual acceleration of the object is the vector sum of the accelerations generated by various forces. The relationship between the component force and the component acceleration in all directions also follows Newton's second law.

[6] Identity: A and F correspond to a certain state of the same object.