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对于动量守恒定律的一般表达式,其中的速度是矢量,一定要用即时速度。但对于系统在某一方向动量守恒时,其表达式可采用标量式,这时的速度我们往往可以用平均速度来代换,从而使解题过程大为简化。在物体做匀变速直线运动的情况下,我们不难证明,物体系动量守恒的标量式中的速度V,完全可以用平均速度V来代替。现证明如下: 现在以两个物体组成的物体系为例。如果甲、乙两物体的质量分别为m_1、m_2,在碰撞前它们的速度分别为V_1、V_2,碰撞后为V_1′,V_2′,则动量守恒定律可写成如下数学表达式 m_1V_1+m_2V_2=m_1V_1′+m_2V_2′(1) 因为两物体做匀变速直线运动,所以甲物体在速度由V_1变化到V_1′这段时间内的平均速度
For the general expression of the law of conservation of momentum, where the speed is a vector, we must use the instant speed. However, when the momentum of the system is conserved in a certain direction, its expression can be scalar. At this time, we can often substitute the average speed, so that the problem-solving process is greatly simplified. In the case of a uniform linear motion of an object, it is not difficult to prove that the velocity V in the scalar equation where the momentum system of the object system is conserved can be completely replaced by the average velocity V. The proof is as follows: Now take the system composed of two objects as an example. If the masses of A and B are m_1 and m_2 respectively, their velocity is V_1 and V_2 before the collision, and V_1′ and V_2′ after the collision, the law of conservation of momentum can be written as the following mathematical expression m_1V_1+m_2V_2=m_1V_1 ’+m_2V_2’ (1) Since the two objects perform a linear motion at a constant speed, the average speed of the armour object during the time when the speed changes from V_1 to V_1’