Zero Resultant

Couple is a system of forces whose magnitude of the resultant is zero and yet has a moment sum. Geometrically, couple is composed of two equal forces that are parallel to each other and acting in opposite direction. The magnitude of the couple is given by
 

 
Where $F$ are the two forces and $d$ is the moment arm, or the perpendicular distance between the forces.
 

Problem 015
Forces F, P, and T are concurrent and acting in the direction as shown in Fig. P-015.

1. Find the value of F and α if T = 450 N, P = 250 N, β = 30°, and the resultant is 300 N acting up along the y-axis.
2. Find the value of F and α if T = 450 N, P = 250 N, β = 30° and the resultant is zero.
3. Find the value of α and β if T = 450 N, P = 250 N, F = 350 N, and the resultant is zero.

Problem 014
From Fig. P-014, P is directed at an angle α from x-axis and the 200 N force is acting at a slope of 5 vertical to 12 horizontal.

1. Find P and α if the resultant is 500 N to the right along the x-axis.
2. Find P and α if the resultant is 500 N upward to the right with a slope of 3 horizontal to 4 vertical.
3. Find P and α if the resultant is zero.