学 §2-2平面汇交力系合成与平衡的解析法 力在坐标轴上的投影 X=F=F coSa Y Fr Y-F,=F Sina=F cosB F +F x F Y F CoOsa= F coSB fF 16
16 F F F X x cos= = F F F Y y cos = = 2 2 F = Fx +Fy §2-2 平面汇交力系合成与平衡的解析法 一、力在坐标轴上的投影 X=Fx=F·cos ： Y=Fy=F·sin=F ·cos
Statics Ⅱ The law of projection of a resultant force From the diagram the projections of all forces on the x and y axes are Y4 R R2=X1+k2-X4=∑X 3 R R=1+2+y3+4=∑ YY F 十 4 R2=∑XR,=∑Y The law of projection of a resultant force: The projection of the resultant force on an axis is equal to the algebraic sum of the projections of all forces on the same axis 7
17 Ⅱ The law of projection of a resultant force From the diagram the projections of all forces on the x and y Axes are: Rx =X1 +X2 −X4 =X Ry =−Y1 +Y2 +Y3 +Y4 =Y Rx =X Ry =Y The law of projection of a resultant force: The projection of the resultant force on an axis is equal to the algebraic sum of the projections of all forces on the same axis. 即：
学 二、合力投影定理 由图可看出,各分力在x轴和在y 轴投影的和分别为 4 R2=X1+k2-X4=∑X 3 R R=1+2+y3+4=∑ F2 R2=∑XR,=∑Y X2 合力投影定理:合力在任一轴上的投影,等于各分力在同一 轴上投影的代数和。 18
18 二、合力投影定理 由图可看出，各分力在x轴和在y 轴投影的和分别为： Rx =X1 +X2 −X4 =X Ry =−Y1 +Y2 +Y3 +Y4 =Y Rx =X Ry =Y 合力投影定理：合力在任一轴上的投影，等于各分力在同一 轴上投影的代数和。 即：
Statics The magnitude of the resultant force: R=R+R= ∑x x2+∑y Its direction: R R∑ tgBR /.:0=/=tg ∑X Its point of application: The point of intersection of all forces II The analytical method of composition and the equilibrium See above for a coplanar system of concurrent forces to be in equilibrium it is necessary and sufficient that the resultant of these orces Is zero R=0=R2+R2=0 R.=>X=0 This is the necessary and sufficient condition Ry-2=0 of equilibrium, called balanced equations
19 The magnitude of the resultant force: Its direction: Its point of application: x y R R tg = − − = = X Y R R x y 1 1 ∴ tg tg The point of intersection of all forces. Ⅲ The analytical method of composition and the equilibrium See above, for a coplanar system of concurrent forces to be in equilibrium it is necessary and sufficient that the resultant of these forces is zero. = = = = 0 0 R Y R X y x This is the necessary and sufficient condition of equilibrium, called balanced equations. 0 0 2 2 R = = Rx + Ry = = + = + 2 2 2 2 R R R x y x y
学 合力的大小R=R2+R2=∑x2+∑y2 R R ∑Y 方向:1g=R 8=tgR=tg>x 作用点:为该力系的汇交点 三、平面汇交力系合成与平衡的解析法 从前述可知:平面汇交力系平衡的必要与充分条件是该力系 的合力为零。即: R=0=√R2+R2=0 R=∑X=0 为平衡的充要条件,也叫平衡方程 R=∑Y=0 20
20 合力的大小： 方向： 作用点： x y R R tg = − − = = X Y R R x y 1 1 ∴ tg tg 为该力系的汇交点 三、平面汇交力系合成与平衡的解析法 从前述可知：平面汇交力系平衡的必要与充分条件是该力系 的合力为零。 即： = = = = 0 0 R Y R X y x 为平衡的充要条件，也叫平衡方程 0 0 2 2 R = = Rx + Ry = = + = + 2 2 2 2 R R R x y x y