Newton's original expression in Mathematical Principles of Natural Philosophy;
For a particle with momentum, under the action of external force, the rate of change of momentum with time is proportional to the external force acting on the particle, and the direction of the external force is the same; Expressed by formula:.
Common expressions:
The acceleration of an object is directly proportional to the applied force and inversely proportional to its mass (directly proportional to the reciprocal of its mass). The direction of acceleration is the same as that of external force. Newton's second law of motion can be expressed in proportion, that is, or; It can also be expressed by an equation, that is, ∑F=kma, where k is the proportional coefficient; Only when f is Newton, m is kilogram and a is m/s? When it is a unit, ∑F=ma holds.
Characteristics of law
Newton's second law of motion has five characteristics:
Instantaneity: Newton's second law of motion is the instantaneous effect of force. Acceleration and force produce, change and disappear at the same time.
Vector: it is a vector expression, and the directions of acceleration and resultant force are always the same.
Independence: an object is subjected to several external forces, and the acceleration generated by one external force is only related to this external force and has nothing to do with other forces. The vector sum of acceleration produced by each force is equal to the acceleration produced by the resultant force, and the resultant force acceleration is related to the resultant force.
Causality: Force is the cause of acceleration, and acceleration is the function of force. Therefore, force is the reason to change the motion state of an object.
Equivalence inequality: although it is not a force, it reflects the change of the state of the object; Although it is only a method to measure the mass of an object, m has nothing to do with the presence or absence.
experimental verification
Newton's second law of motion experiment is a very basic and necessary confirmatory experiment in physics, which involves the basic ways and methods to test a physical law or law, so there are often special requirements for its experimental accuracy.
The verification experiment of Newton's second law of motion is to measure the acceleration of a moving system under different actions and test whether they conform to the above relationship.
Using modern experimental teaching facilities to improve and supplement the original experimental means can better reflect the scientific literacy and attitude of physics.
Main experimental verification methods of Newton's second law of motion
Explanation of experimental verification method
Verification by point timer method: When studying the relationship between the acceleration of the system and the mass and tension of the system, the point timer is fixed at one end of the board, the weight and the car are fixed at both ends of the thin wire with bolts, and the thin wire passes through the pulley. Using the weight of the heavy object as the pulling force, the trolley dragging the paper tape moves on the plane, and then the trolley, the heavy object on it and the hook code bolted at the other end of the line form a moving system. Every experiment must indicate the tension and the quality of the system on the paper tape. In order to counteract friction, the following two methods are usually adopted: oblique sliding method and horizontal pulling method.
Inclined sliding method and horizontal pulling method
Verification on the air-cushion guide rail: After the air-cushion guide rail is leveled (because the guide rail has a certain bend, there is resistance between the slider and the guide rail, and leveling is generally measured by the equal speed of the slider when it passes through two photoelectric doors), the viscous damping constant b is measured. In order to correct the speed loss caused by viscous frictional resistance, the measurement of viscous damping constant must be solved. There are two main methods: inclined guide rail method and vibration method.
Verification by nonlinear regression method: the main factor affecting the measurement of verification law on air cushion guide rail is air resistance, and the influence can be reduced to a negligible level through correction. But the commonly used linear regression method is not enough to explain the whole regression equation; There are also some problems in binary linear regression method. This rule is verified by nonlinear regression method. Firstly, the dynamic model of particle motion is linearized, and the linear estimation of model parameters is obtained, which is used as the initial value of nonlinear model, and the nonlinear regression analysis of dynamic model is carried out. The nonlinear regression method verifies the correctness of the law, improves the traditional experimental method of verifying the law, and has certain application and popularization value.