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

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 9.20 N and is directed at an angle of ? = 56.0 ? above the negative x axis in the second quadrant. F? 2 has a magnitude of 6.00 N and is directed at an angle of ? = 53.8 ? below the negative x axis in the third quadrant.

What is the x component Fx of the resultant force?

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. Answer in degrees.

Explanation / Answer

Resultant force in X direction,

Fx = -F1*cos(alpha) -F2*cos((beta)

=-9.2*cos(56) -6*cos(53.8)

=-8.688 N

Resultant force in Y direction,

Fy = F1*sin(alpha) -F2*csin((beta)

=9.2*sin(56) -6*sin(53.8)

=2.785 Angle to +x axis,

Theta = tan-1(Fy/Fx) = tan-1(2.785/-8.688)

=-17.77 degrees

Angle to the -x direction = 17.77(clockwise)

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