Engineering Statics

A-10


Determine the tension required in cable AB, knowing that the resultant of the three forces exerted at point B of boom BC must the directed along BC. Determine the magnitude of the resultant.

thus The resultant of the two forces can be divided into components 
in the i and j directions.
Addition/subtraction indicates that the component along the j' direction is 0.
The tension T can be solved for from the j' direction, placing the T sin(65°+35°) or T sin(100°) on the left side of the equation.
Performing the arithmetic gives us the value of T=95 lb.
Substituting into the i' component of the equation yields a vector resultant of -89.9 in the i' direction. 
Since the i' direction is along the boom, the negative sign indicates that the boom is in compression.
The magnitude of the resultant is 89.9 lb.