3-32 Deterire the agnitutde and diretiun angle 9 ufforce Fa so that the particle shawm in Fig. P1-12 is in oqui-Jibrium.к -м33= 80 NFie. P3-12

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Step 1

Given:

The magnitude and direction angle $θ$ of force $F_{4}$ is determined below.

Step 2

The figure which represents all the forces is given below,

Step 3

On applying equations of equilibrium for the system in the y-direction,

$\sum_{} F_{y} = 0$

$F_{1} \sin (30^{\circ} + 33^{\circ}) + F_{2} \sin 30^{\circ} - F_{3} \sin 60^{\circ} + F_{4} \sin θ = 0$

$F_{4} \sin θ = - 500 \times \sin 63^{\circ} - 750 \times \sin 30^{\circ} + 1000 \times \sin 60^{\circ}$

$F_{4} \sin θ = 45.522 \dots \dots (1)$

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