Statics (4) Decomposition of a force along the coordinate axes If the three perpendicular components of a force along the coordinate axes are FF,and F then F=F+F+F Fr F due to F=Xi, F,=Yj, F=Zk O We get F=Xi+Yj+Zk ∴F=√X2+Y2+2 Z2 X Y COSC=-. COS F Cosy
11 (4) Decomposition of a force along the coordinate axes: If the three perpendicular components of a force along the coordinate axes are then: Fx Fy Fz , and F =Fx +Fy +Fz 2 2 2 F= X +Y +Z F Z F Y F X cos= ,cos = ,cosg = F Xi F Yj F Zk due to x = , y = , z = We get F =Xi +Yj+Zk Fx Fy Fz
学 4、力沿坐标轴分解: 若以F,F,F表示力沿直角 坐标轴的正交分量,则: f=F+F+F Fx 而: 所以:F=X++Zk ∴F=√X2+Y2+2 Z2 X Y COSC=-. COS F Cosy 12
12 4、力沿坐标轴分解： 若以 表示力沿直角 坐标轴的正交分量，则： Fx Fy Fz , , F =Fx +Fy +Fz 2 2 2 F= X +Y +Z F Z F Y F X cos= ,cos = ,cosg = F Xi F Yj F Zk x = , y = , z = 而： 所以： F =Xi +Yj+Zk Fx Fy Fz
Statics 2. The composition of a concurrent force system in space ()The graphical method: It is same as in the case of the composition of a coplanar system of concurrent forces. It can be solved by the force polygon. R=F+F2+B3+…+Fn=∑F The resultant force is equal to the geometrical sum of the components (2)The analytical method: Because F=Xi+Y j+Z, k, substitute it into the equation above We get R=∑X1+∑1j+∑Zk Rx=∑X ∑ X, is the projection of the resultant force onto the尽,=∑Y axis x. hence R=∑Z 13
13 (1) The graphical method: It is same as in the case of the composition of a coplanar system of concurrent forces. It can be solved by the force polygon. The resultant force is equal to the geometrical sum of the components. R=F1 +F2 +F3 ++Fn =F i (2)The analytical method: Because , substitute it into the equation above We get is the projection of the resultant force onto the axis x, hence F X i Y j Z k i = i + i + i R X i Y j Z k = i + i + i Xi Rx =Xi Ry =Yi Rz =Zi 2. The composition of a concurrent force system in space:
学 空间汇交力系的合成 1、几何法:与平面汇交力系的合成方法相同,也可用力多 边形方法求合力。 R=F1+F2+F3+……+Fn=∑F; 即:合力等于各分力的矢量和 2、解析法: 由于F=X+Yj+zk代入上式 合力R=∑X;i+∑Hj+∑Zk Rx=∑x 由∑X,为合力在轴的投影,{R R=∑Z
14 1、几何法：与平面汇交力系的合成方法相同，也可用力多 边形方法求合力。 即：合力等于各分力的矢量和 R=F1 +F2 +F3 ++Fn =F i 2、解析法： 由于 代入上式 合力 由 为合力在x轴的投影， ∴ F X i Y j Z k i = i + i + i R X i Y j Z k = i + i + i Xi Rx =Xi Ry =Yi Rz =Zi 二、空间汇交力系的合成：
Statics (3)The law of projection of the resultant force: The projection of the resultant force of a force system in space onto an axis is equal to the algebraic sum of the projections of the component forces onto the same axis The resultant force is given by R=√R2+R2+R2=∑x)+C∑y)+(∑ R R R COSa=- cOS B COSy= R R R 15
15 (3) The law of projection of the resultant force: The projection of the resultant force of a force system in space onto an axis is equal to the algebraic sum of the projections of the component forces onto the same axis. The resultant force is given by = + + = + + 2 2 2 2 2 2 R R R R ( X) ( Y) ( Z) x y z R R R R R Rx y z cos= ,cos == ,cosg =