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 9.40 N and is directed at an angle of = 61.0 above the negative x axis in the second quadrant. F 2 has a magnitude of 7.00 N and is directed at an angle of = 54.0 below the negative x axis in the third quadrant.

1.:

What is the x component Fx of the resultant force?

Express your answer in newtons.

Part B

What is the y component Fy of the resultant force?

Express your answer in newtons.

Part C

What is the magnitude F of the resultant force?

Express your answer in newtons.

Part 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.

Express your answer in degrees.

Explanation / Answer

Because it makes the computations much simpler, convert both angles to be measured counterclockwise from the positive x axis:
= 180° - 61° = 119°
= 180 + 54 = 234°
Fx = (9.40)cos(119°) + (7)cos(234°)
Fx -8.67N
Fy = (9.40)sin(119°) + (7)sin(234°)
Fy 2.55 N
|F| = {-8.67² + 2.55²}
|F| = 9.04 N
Because Fy > 0 and Fx < 0 we compensate the inverse tangent function for the second quadrant:

= 180° + tan^-1(Fy/Fx)
= 180° + tan^-1(2.55/-8.67)
= 163.61°
This is standard form measured counterclockwise from the positive x axis
= 16.39° clockwise from the negative x axis

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