These forces are not drawn to scale.

Question

Figure 4: Diagram showing vectors acting on a point.
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Question 2.1 [2 marks]
Why are forces P, Q and R considered vectors?
Question 2.2 [2 marks]
Calculate Fx the resultant of all the horizontal/parallel components acting on point O. Give the magnitude and direction.
Question 2.3 [2 marks]
Calculate Fy the resultant of all the vertical/perpendicular components acting on point O. Give the magnitude and direction.
Question 2.4 [2 marks]
Hence, calculate the magnitude of the resultant force (FR) acting at this point. Question 2.5 [2 marks]
Calculate the direction of the resultant force in reference to the x-axis.

Answer 1

Answer:

2.1 Forces P, Q, and R are considered vectors because they have both magnitude (size) and direction. In this case, they are represented by arrows on the diagram.

2.2 To calculate the horizontal component Fx:
Fx = P + Qcos(30°) - R = 200 + 150cos(30°) - 100 = 337.32 N

Magnitude of Fx = |Fx| = 337.32 N
Direction of Fx = arctan(150sin(30°) / (200 + 150cos(30°))) = 26.57°

2.3 To calculate the vertical component Fy:
Fy = Qsin(30°) + R = 150sin(30°) + 100 = 175 N

Magnitude of Fy = |Fy| = 175 N
Direction of Fy = 90°

2.4 To calculate the magnitude of the resultant force FR:
FR = sqrt(Fx^2 + Fy^2) = sqrt((337.32)^2 + (175)^2) = 381.16 N

2.5 To calculate the direction of the resultant force in reference to the x-axis:
Direction of FR = arctan(175 / 337.32) = 26.57°

Therefore, the magnitude of the resultant force acting at point O is 381.16 N, and its direction is 26.57° above the x-axis.