Unit1GeneralEquilibrium__ConditionsofASystem..doc

General Equilibrium Conditions of A System 力系的一般平衡条件 In this section, we shall consider the conditions that the forces and couples acting upon a body must satisfy in order to be in equilibrium. 在这一部分，我们将研究为了使一个物体保持平衡，作用在其上的力和力偶所必须满足的条件。 According to Newton’s first law, the sum of the forces exerted on a body at rest must be zero. Notice, however, that this law says nothing about the moment, or rotational effects, of the forces. Clearly, the total moment must also be zero, else the body would rotate. 根据牛顿第一定律，施加在一个静止物体上的力系的合力一定为零。然而，请注意这个定律对力矩或力系的转动效应只字未提。显然，合力矩也一定为零，否则物体将会转动。 The fundamental problem here is that Newton’s first law (and second law), as originally stated, applies only for very small bodies, or particles, with negligible dimensions and nonzero mass. However, it can be extended to bodies of finite size as follows. 这里的基本问题是原先叙述的牛顿第一定律（和第二定律）只适用于非常小的物体，或者尺寸可以忽略的非零质量的粒子。然而，它可以扩展到如下所述的有限尺寸的物体。 Consider a system consisting of two particles, and let and be the forces due to the interaction between them (Fig .1.1). These forces are called internal forces, since they are due to interactions between bodies within the system. Assuming that the internal forces obey Newton’s third law, we have .Suppose that there are also forces, such as and , exerted on the particles due to interactions with bodies outside the system. Such forces are called external forces. Clearly, and the forces acting upon a particular particle must have the same point of application because a particle has negligible dimensions. 考虑一个由两个质点组成的系统，假设 和为它们之间的相互作用力(图.1.1)。这些力称为内力，因为它们是由于系统内部的物体之间的相互作用而产生的。假定内力服从牛顿第三定律，我们有。假如还有质点与系统外物体之间的相互作用力施加在质点上，如 和,这些力称为外力。显然，作用在一个特定粒子上的力一定有相同的应用，因为粒子的尺寸可以忽略。 We shall say that the system is in equilibrium if each particle within it is in equilibrium. In this case, by Newton’s first law, the sum of the forces acting upon each particle must be zero. For particle A we have 如果系统内的每一个质点处于平衡，我们就可以说系统是平衡的。在本例中，依据牛顿第一定律，作用在每个质点上的力的合力一定为零。对质点A我们有： and for pa