机械工程导论第四章105-120页翻译.doc

EXAMPLE 4.2 The control lever rotates when the 10-lb and 25 lb forces act on it as show in Figure 4.8(a). Determine the magnitude and direction of the resultant by using the vector polygon approach. SOLUTION The two forces are combined in a sketch using the head-to-tail rule. In Figure 4.8(b), the 25-lb force is sketched first and the 10=1b force is added at the angle of 500 from vertical. The resultant R extends from the tail of the 25-1b force vector (which is labeled as the start point) to the head of the 10-lb force vector (labeled as the endpoint). The three vectors form a side-angle-side triangle. Applying the law of cosines from Appendix B, we solve for the side length R through from which R＝33.29 lb. The angle θ at which R acts is similarly determined by applying the law of sines The resultant acts at the angle θ＝11.13o shown in Figure 4.8(b). 控制杆转动的时候，10磅和25磅的力作用于它如图4.8所示（一）。利用矢量多边形的方法确定的合力的大小和方向。解决方案这两个力结合在一个素描用头去尾规则。图4.8（b），25磅的力画第一和10 = 1b力在垂直500°增加。所得到的R的25-1b力向量的尾部延伸（这是标示为出发点）到10磅的力向量的头（标记为端点）。三个向量形成一个边角边三角形。应用从附录B余弦定理，我们解决的边长r通过从R＝33.29磅。在R的行为是通过施加正弦定理同样确定角θ在角θ＝11.13o如图4.8所示的所得的行为（B）。MOMENT OF A FORCE When you are trying to loosen; a frozen bolt, the bolt is more easily turned when a wrench with a long handle is used. The tendency of a force.(in this case, applied to the handles end) to make an object rotate is called a moment. The magnitude of a moment depends both on the force that is applied and on the lever arm that separates the force from a pivot point. Perpendicular Lever Arm The magnitude of a moment is found from its definition (4.8) where Mo is the moment of the force about point O , F is the magnitude of the force, and d is the perpendicular lever arm distance from the forces line of action to point O. The term torque can also be used to describe the effect of a force acting over a lever arm, but mechanical engineers generally reserve torque to describe moments that cause rotation of a shaft in a m