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一些读物在谈隔离法时,往往指出加速度不同的物体不能作整体隔离。这一说法,笔者认为没有根据。请看下面的推导:设质点系有n个质点。对任一质点州m_i可写出它的动力学方程F_i+f_i=m_ia_i。F_i表示它所受系统外力的合力;f_i表示它所受系统内力的合力。对系统内每一个质点均可写出相同形式的方程。我们将方程两边分别求和,便可得sum from i=1 to n F_i+sum from i f_i=1 to n=sum from i=1 to n m_ia_i。注意,这里sum from i=1 to n F_i和sum from i=1 to n f_i均是矢量和而不是合力,因为这些力并不作用在同一质点上。对于内力,容易得知它们的矢量和必为零,即
Some books, when talking about isolation methods, often point out that objects with different accelerations cannot be isolated as a whole. This statement, the author thinks there is no basis. See the following derivation: Let the mass point be n particles. The kinetic equation F_i+f_i=m_ia_i can be written for any material state m_i. F_i denotes the resultant force of the external force of the system it receives; f_i denotes the resultant force of the internal force of the system it receives. The same form of equation can be written for each mass point in the system. We sum the two sides of the equation to obtain sum from i=1 to n F_i+sum from i f_i=1 to n=sum from i=1 to n m_ia_i. Note that here sum from i=1 to n F_i and sum from i=1 to n f_i are vector sums instead of resultant forces because these forces do not act on the same mass point. For internal forces, it is easy to know that their vector sum must be zero, ie