Engineering Statics

A-9


Knowing the tension in the cable, BC, is 625N, determine the resultant of the three forces exerted at point B of beam AB.

whereWhen a force is defined by geometry rather than a trigonometric angle, we know that the x and y components of the force are proportional to the distances in the x and y direction.
The force generated by the cable is shown in green.
The resultant of the two forces can be divided into components in the i and j directions. 
Note that trigonometry is used for the 320 N force and the 450 N force is in the negative y direction only. 
The x components are added together to get the resultant's 
x component in the i direction.
Similarly the y components are added together to get the resultant in the j direction.
This gives us the resultant in vector form.
The magnitude of resultant can be determined by taking the square root of the sum of the components squared.
Performing the arithmetic gives us the magnitude of the resultant.
The angle that the resultant makes with the positive x axis can be found by taking the inverse tangent of the y component divided by the x component of the resultant.
Note that since the x and y components are both negative, the angle is in the third quadrant.
Doing the work on the calculator gives an answer of 46.8°,
while the actual answer is 46.8° + 180°, or 226.8°.