a)What is the x component F x of the resultant force? b)What is the y component

Question

a)What is the x component Fx of the resultant force?

b)What is the y component Fy of the resultant force?

c)What is the magnitude F of the resultant force?

d)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.

Two forces, and act at a point, as shown in the picture. (Figure 1) has a magnitude of 9.00N and is directed at an angle of alpha = 58.0 degree above the negative x axis in the second quadrant. has a magnitude of 6.60N and is directed at an angle of beta = 52.3 degree below the negative x axis in the third quadrant.

Explanation / Answer

Fnet = F1 + F2

a)

Fnet (x) = F1 (x) + F2 (x)

= F1 * cos(alpha) + F2 * cos(beta)

= 9 * cos(58) + 6.6 * cos(52.3)

= 8.805 N -ve x-axis

b)

Fnet (y) = F1 (y) + F2 (y)

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

= 9 * sin(58) - 6.6 * sin(52.3)

= 2.41 N +ve y-axis

c)

|Fnet| = sqrt(2.41^2 + 8.805^2) = 9.1288 N

d)

Fnet (y) = 0

F1 * sin(alpha) = F2 * sin(y)

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