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转动物体处于平衡状态时,它所受的合力矩应等于零。据此,可判断一些情况下静摩擦力的方向。例一根质量为m的均匀木棒斜靠在一个内表面为球面的碗内,处于静止状态,○为球心。判断碗对木棒静摩擦力的方向。如图一,若先不考虑摩擦,木棒当受重力mg、碗底和碗边的支持力N_1和N_2。重力作用线与碗边支持力的作用线交于P。由于木棒处于静止状态,所以对任意的假定轴,其合力矩必为零。对轴P,只有N_1对木棒产生一个顺时针方向的力矩,所以碗底和碗边对木棒应有如图的静摩擦力f_1和f_2(产生逆时针方向力矩)。改变木棒在碗中的位置,它所受的静摩擦力方向也要变化。实际上,其中存在一个临界情况。如图二,N_1、N_2、mg作用线交于一点P(P必和碗在同一球面上),若碗球面
When the rotating object is in equilibrium, the resultant moment it receives should be equal to zero. Based on this, the direction of static friction can be determined in some cases. For example, a uniform wooden rod with a mass of m leans against a bowl with a spherical inner surface and is in a stationary state. ○ is a sphere center. Determine the direction of the bowl’s static friction on the stick. As shown in Figure 1, if the friction is not considered first, the sticks will be supported by the force of gravity mg, bowl bottom and bowl edge N_1 and N_2. The line of action of the force of gravity and the supporting force of the bowl edge is intersected by P. Because the stick is at rest, the resultant torque must be zero for any assumed axis. For the axis P, only N_1 produces a clockwise torque on the stick, so the bowl bottom and the bowl edge should have static frictional forces f_1 and f_2 (produced counterclockwise moments) for the stick. Changing the position of the stick in the bowl also changes the direction of static friction. In fact, there is a critical situation. In Figure 2, the N_1, N_2, and mg lines of action intersect at a point P (P must be on the same sphere as the bowl) if the bowl sphere