Engineering Statics

A-2


Two forces are applied at point A of the beam shown.
Determine the magnitude and direction of the resultant.

The first thing we do is identify the x and y axes, 
creating a diagram of the forces with a frame of reference.
The resultant of the two forces can be divided into components in the i and j directions.
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's y component in the j direction.
This gives us an x component of -10.88 lb, and a y component of -4.168 lb.
The magnitude of the resultant can be determined using the Pythagorean Theorem.
Completing calculation, we find the magnitude of the resultant is 11.65 lb.
The angle the resultant makes with the x-axis can be determined by taking the arctangent of the y component of the resultant divided by the x component.
The angle the resultant makes with the x-axis is 20.96°.