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, F1 and F2, act at a point, as shown in the picture. (Fiqure 1) F1 has a magnitude of 8.80 N and is directed at an angle of -65.0° above the negative x axis in the second quadrant. F2 has a magnitude of 5.40 N and is directed at an angle of = 53.3° below the negative x axis in the third quadrant. Figure 1of 1

Explanation / Answer

given,

F1 magnitude = 8.80N

F1 angle(alpha) = 65 degrees

F2 magnitude = 5.40N

F2 angle(beta) = 53.3 degrees

A)

We take x-directiion as negative because both forces are same,

Fx = -cos(alpha)F1 + (-cos(beta)F2)
    = -cos(65)*8.80 + (-cos(53.3)*5.40)

    = -3.719 -3.227

    = -6.946 N

====================================

B)

from the figure we take F1 as positive and F2 as negative

Fy = sin(alpha)F1 – sin(beta)F2
     = sin((65)*8.80 - sin(53.3)*5.40

     = 7.976 - 4.33

     = 3.646 N

====================================

C)

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

   =sqrt(-6.946^2 + 3.646^2)

=sqrt(61.54)

= 7.85 N

================================

D)

Y = tan^-1(Fy / Fx)

   = tan^-1(3.646 / -6.946)

   =tan^-1(-0.525)

   = 27.7 degrees (degrees are measured from ( -ve ) x-axis in clockwise direction)

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