Engineering Statics

A-3


Two forces, P and Q, are applied as shown at point A on the eye hook. Knowing that force P is 50 pounds and force Q is 35 pounds, 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 15.95 lb., and a y component of -77.1 lb.
The magnitude of the resultant can be determined using the Pythagorean Theorem.
Completing calculation, we find the magnitude of the resultant is 78.7 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 -78.3°.