Two forces, F 1 and F 2, act at a point, as shown in the picture. (Figure 1) F 1

Question

  Two forces, F 1 and F 2, act at a point, as shown in the picture. (Figure 1) F 1 has a magnitude of 8.60 Nand is directed at an angle of = 64.0 above the negative x axis in the second quadrant. F 2 has a magnitude of 6.60 N and is directed at an angle of = 53.9 below the negative x axis in the third quadrant. What is the y component Fy of the resultant force? What is the magnitude F of the resultant force? What is the angle that the resultant force forms with the negative x axis? In this problem, assume that positive angles are measured clockwise from the negative x axis.

Explanation / Answer

1) F1x = -8.6*cos(64) = -3.76
F2x = -6.6*cos(53.9) = -3.88

Fx = F1x + F2x

=  -3.76+ -3.88 = -7.64

2) F1y = 8.6*sin(64) = 7.72
F2y = -6.6*sin(53.9) = -5.33

Fy = F1y + F2y

=  7.72+ (-5.33) = 2.39

3) |F| = sqrt(Fx^2 + Fy^2)

= sqrt ( -7.64+ 2.39) = 3.16

4) alpha-gamma = atan (Fy/Fx) = -0.31

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