Final Answer:
The magnitude of the force for each of the supported pins at a and b can be calculated using the equations of static equilibrium.
Step-by-step explanation:
First, we need to identify the forces acting on each pin. At point a, there are two forces acting: the force due to the weight of the object (W) and the force due to the support (F). At point b, there is only one force acting, which is the force due to the support (F).
We can start by calculating the force due to the weight of the object at point a. The weight of the object is given as 50 N, and the distance from the center of gravity to point a is 0.4 m. Therefore, the force due to the weight of the object at point a is:
F_wa = W * g * sin(θ) = 50 N * 9.8 m/s² * sin(θ)
where θ is the angle between the line of action of the force and the horizontal direction.
Next, we can calculate the force due to the support at point a. The force due to the support is given as F = 75 N, and the distance from the point of application of the force to point a is 0.4 m. Therefore, the force due to the support at point a is:
F_fa = F * cos(θ) = 75 N * cos(θ)
Now, we can calculate the magnitude of the force for each of the supported pins at points a and b. At point a, the magnitude of the force due to the weight of the object is:
|F_wa| = sqrt(F_wa²) = sqrt(50 N * 9.8 m/s² * sin(θ)²)
And the magnitude of the force due to the support at point a is:
|F_fa| = sqrt(F_fa²) = sqrt(75 N * cos(θ)²)
At point b, there is only one force acting, which is the force due to the support. The magnitude of this force is:
|F_fb| = sqrt(F_fb²) = sqrt(75 N * cos(θ)²)
Finally, we can calculate the magnitude of the force for each of the supported pins at points a and b by adding the magnitudes of the forces acting at those points:
|F_a| = |F_wa| + |F_fa| = sqrt(50 N * 9.8 m/s² * sin(θ)²) + sqrt(75 N * cos(θ)²)
|F_b| = |F_fb| = sqrt(75 N * cos(θ)²)
Therefore, the magnitude of the force for each of the supported pins at points a and b is given by the equations above.