QUESTION 2 [10 marks]

Question

These forces are not drawn to scale.
Figure 4: Diagram showing vectors acting on a point.
9

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.
TOTAL:

Answer 1

10 marks

Answer:
Question 2.1: Forces P, Q, and R are considered vectors because they have magnitude and direction, and they follow the rules of vector addition and subtraction.

Question 2.2: To calculate Fx, we need to find the sum of all the horizontal components.
Fx = Px + Qx + Rx
Fx = 5 + (-2) + (-4)
Fx = -1

Magnitude of Fx = |Fx| = 1
Direction of Fx is to the left (negative direction).

Question 2.3: To calculate Fy, we need to find the sum of all the vertical components.
Fy = Py + Qy + Ry
Fy = 4 + (-3) + 6
Fy = 7

Magnitude of Fy = |Fy| = 7
Direction of Fy is upwards.

Question 2.4: To calculate the magnitude of the resultant force FR, we can use Pythagoras theorem.
FR = sqrt((Fx)^2 + (Fy)^2)
FR = sqrt((-1)^2 + 7^2)
FR = sqrt(1 + 49)
FR = sqrt(50)
FR = 5√2

Magnitude of the resultant force FR = 5√2

Question 2.5: To calculate the direction of the resultant force in reference to the x-axis, we can use trigonometry.
tanθ = Fy / Fx
tanθ = 7 / -1
θ = tan^(-1)(-7)
θ ≈ -81.87°

Therefore, the direction of the resultant force FR in reference to the x-axis is approximately 81.87° below the negative x-axis.