牛顿第二运动定律

2023-03-09 16:12 作者:Everybody26 0人读过 | 我要投稿

今天就是给各位介绍一下牛顿第二运动定律鸭～

但在此之前，我需要给各位说说：Mass&Weight（质量和重量）

This intuitive notion of the mass of an object is not very precise because the concept “quantity of matter” is not very well defined. More precisely, we can say that mass is a measure of the inertia of an object. The more mass an object has, the greater the force needed to give it a particular acceleration. It is harder to start it moving from rest, or to stop it when it is moving, or to change its velocity sideways out of a straight-line path.

给各位举个🌰：A truck has much more inertia than a baseball moving at the same speed, and a much greater force is needed to change the truck’s velocity at the same rate as the ball’s. The truck therefore has much more mass.

Mass is a property of an object itself (a measure of an object’s inertia, or its “quantity of matter”). Weight, on the other hand, is a force, the pull of gravity acting on an object.

再举个🌰哈：

Suppose we take an object to the Moon. The object will weigh only about one-sixth（六分之一）as much as it did on Earth, since the force of gravity is weaker. But its mass will be the same. It will have the same amount of matter as on Earth, and will have just as much inertia—in the absence of friction, it will be just as hard to start it moving on the Moon as on Earth, or to stop it once it is moving.

都到这里了，是时候请出今天的主角了：牛顿第二运动定律！！！

The greater the mass, the less the acceleration for the same net force. The mathematical relation, as Newton argued, is that the acceleration of an object is inversely proportional to its mass. These relationships are found to hold in general and can be summarized as follows:

The acceleration of an object is directly proportional to the net force acting on it, and is inversely proportional to the object’s mass. The direction of the acceleration is in the direction of the net force acting on the object.

「是不是突然有一股懵直冲天灵盖？我也是（笑）」

那我们先翻译成人话：物体加速度的大小跟作用力成正比，跟物体的质量成反比，且与物体质量的倒数成正比；加速度的方向跟作用力的方向相同。

我的个人理解（有误请谅解）：拉一个东西用的力越大，移动的加速度更快（成正比）；物体越重则移动它所需的力就越大（成正比）；我把物体往左拉它就会向左加速。

Newton’s second law can be written as an equation:

where a stands for acceleration, m for the mass, and F for the net force on the object. The symbol ∑（Greek “sigma”) stands for “sum of”; F stands for force, so ∑F means the vector sum of all forces acting on the object, which we define as the net force.

We rearrange this equation to obtain the familiar statement of Newton’s second law:

Newton’s second law relates the description of motion to the cause of motion, force. It is one of the most fundamental relationships in physics. From Newton’s second law we can make a more precise definition of force as an action capable of accelerating an object.

Every force F is a vector, with magnitude and direction. Equation 4–1 is a vector equation valid in any inertial reference frame. It can be written in component form in rectangular coordinates as：