Answer:
408N at 89.89°
Explanation:
This problem requires that we resolve the force vectors into
x- and y
-componentsOnce this is done, we can add the components easily, as the one 2-dimensional problem will be two 1-dimensional problems.
Finally, we will convert the resultant force into standard form and find the equilibrant.
Resolve into components:
F1x =F1cos 180°= 232(−1)=−232N
F1y=F1sin180°=0N
F2x=F2cos(−140°)=194(−0.766)=−148.6N
F1y=F1sin(−140°)=232(−0.643)=−149.17N
Note the change of the angle used to give the direction of
F2. Standard angles (rotation from thex
-axis; counterclockwise is +) should be used to avoid sign errors in the results.
Now, we add the components:
Fx=F1x+F2x=−380.6N
Fy=F1y+F1y=−148.17N
Technically, this is the resultant force. However, it should be changed back into standard form. Here's how:
F=√(Fx)2(Fy)2=√(−380.6)^2(−148.17)^2=408N
θ=tan−1(−148.17−380.6)
=89.89°
