BK$80$A$4000$ Engineering Mechanics I a$)$ The pictured aerial platform has a motor which is capable of generating a moment $M$ of max $30$

kNm at point A $.$ The boom of the platform weighs $4000$ N $.$ How large of a burden W can the platform lift

up from the ground, if in the beginning the angle $$ is $30$ degrees? $($Illustration on the left below.$)$

b$)$ Acrobat $A$ is able to exert a moment of max $350$ Nm on the pole. If the female acrobat $G$ weighs $50$

kg $,$ what is the maximum angle $$ to which acrobat A can allow to pole to turn without things getting out

of hand? $($Illustration on the right below.$)$

Replace the distributed load by an equivalent resultant force and specify its location measured from

point $0.$

Exercise $1$

Calculate the resultant force.

Calculate the resultant moment exerted on point $O.$ The given dimensions are meters.

The pin bracket shown on the right is loaded by three

bars which exert the following forces to the pin $($and

therefore to the bracket$).$

a$)$ Determine the magnitude of force $F$ so that the

resultant force is as small as possible.

b$)$ What is the magnitude $($and direction$)$ of this

resultant force?

give me formal solutions step by step.