91Ó°ÊÓ

$$\begin{gathered} a=5.0\text{cm} \\ b=15.0\text{cm} \\ W=900\text{N} \end{gathered}$$

By applying equilibrium conditions, you can write the equations for force and torque in terms of unknown forces and distances. Then by solving these two equations, you can get the value of unknown forces. The direction of force can be determined by checking the sign of value of forces. The equations used are given below.

Static Equilibrium conditions:

$$\begin{gathered} ∑F_x=0 \\ ∑F_y=0 \\ ∑\mathrm{τ}=0 \end{gathered}$$

Applying static equilibrium conditions to FBD:

$$\begin{gathered} ∑{\mathrm{F}}_{\mathrm{y}}=0 \\ {\mathrm{F}}_{\mathrm{A}}+{\mathrm{F}}_{\mathrm{B}}+\mathrm{W}=0······\left(1\right) \\ ∑\mathrm{τ}=0 \end{gathered}$$

Using point B as a pivot point,

$\left(W×b\right)-(F_A×a)=0······\left(2\right)$

From equation (2):

$\left(900×15\right)--\left(F_A×5\right)=0$

Hence,

$$\begin{gathered} F_A=2700\text{N} \\ =2.7×{10}^3\text{N} \end{gathered}$$

The magnitude of force at point A is$F_A=2.7×{10}^3\text{N}$ .

The positive sign indicates that the force at point A is directed upward

Plugging in the value of in equation (1):

$2700+F_B+900=0$

Hence,

$F_B=-3600\text{N}$

The magnitude of force at point B is $F_B=3.6×{10}^3\text{N}$.

The negative sign indicates that the force at point B is directed downwards.