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题一个力F=10N,分解成两个分力F1和F2,已知F1的方向与F成30°角,而分力F2的大小为6N.求: (1)分力F1的大小为多少? (2)分力F2的方向如何? 解法1三角形法则 合力与其分力可以构成一个矢量三角形,利用边角关系,可以分析各分力的变化情况. 从图1可知,当分力F1由零逐渐增加时,分力F2先减少后增加,显然当分力F2与分力F1相互垂直时,分力F2为最小值.即F2|min=Fsinθ. 以这个最小值为临界值,对题目进行分析,有如下三种情况:
A force of F=10N is decomposed into two components F1 and F2. The direction of F1 is known to be 30° with F, and the magnitude of component F2 is 6N. Find: (1) What is the size of force F1? (2) What is the direction of component force F2? Solution 1 Triangle rule The resultant force and its component forces can form a vector triangle. Using edge relationships, it is possible to analyze the variation of each component force. From Figure 1, it can be seen that when the force component F1 changes from zero to zero When increasing, the component force F2 decreases first and then increases. Obviously, when the component force F2 and the component force F1 are perpendicular to each other, the component force F2 is the minimum value, that is, F2|min=Fsinθ. This minimum value is used as the critical value to analyze the problem. There are three situations: