# Zero Resultant

## Couples

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

$C = Fd$

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

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## 015 Solving for a force and its angle and angle of two forces with given resultant

**Problem 015**

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

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

## 014 Solving for force with given resultant

**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.

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