Engineering Statics

A-6


A hook retains two cables supporting staging. Knowing that P is 65 N and a is 55°, determine the magnitude of the resulatant.

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 -82.3 N, and a y component of -21.69 N.
The magnitude of the resultant can be determined using the Pythagorean Theorem.
Completing calculation, we find the magnitude of the resultant is 85.1 N.
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 14.7°.