Question

QUESTION 3 Determine the total of the x-components of the three individual forces (F) 120 N 150 N 30° 80 N 40° 35°

Answer 1

The x component of the 80 N force which is applied at an angle of with respect to x axis in the postive x-direction (toward right) is
$F_{x,80}= F_{80}\cdot cos \ \theta = 80\cdot cos \ 40^{\circ}= 61.3 N$
Similarly, The x-component of 120 N force which is applied at an angle of $(40^{\circ}+30^{\circ})= 70^{\circ}$ with respect to x axis in the positive x-direction (rightward) is
$F_{x,120}= F_{120}\cdot cos \ \theta = 120\cdot cos \ 70^{\circ}= 41 N$
In the same way, The x-component of 150 N force which is applied at an angle of $35^{\circ}$ with respect to negative is
$F_{x,150}= F_{150}\cdot cos \ \theta = 150\cdot cos \ (180^{\circ}-35^{\circ})=150\cdot cos\ 145^{\circ} =-122.8 N$
The minus sign is for opposite direction with positive x axis or with the directions of $F_{x,80}$ and $F_{x,120}$ ..
Therefore the resultant force at the positive x direction is
The above value carries a minus sign so that the resultant force is 20.57 N at the negative x axis of toward left according to the diagram.