A flagpole is to be installed on the front of an office building as shown below. The pole

itself weighs 150 N and is 2 meters long. The support wire is attached at a 60º angle at
a point 0.5 meters from the building.

A. Find the value of the tension in the support cable.

B. Find the magnitude and direction of the net force exerted on the pole by the
attachment fixture on the building.

To find the value of the tension in the support cable (A), we can use trigonometry. Here's how you can do it step by step:

Step 1: Draw a diagram to visualize the situation. In this case, draw a triangle representing the flagpole, with the weight of the pole acting downwards and the tension in the support cable acting upwards.

Step 2: Label the given information on the diagram. We know that the weight of the pole is 150 N, and the support cable is attached at a 60º angle.

Step 3: Break down the weight of the pole into its vertical and horizontal components. The vertical component is equal to the weight of the pole, which is 150 N. The horizontal component is zero since there is no horizontal force acting on the pole.

Step 4: Use trigonometry to find the tension in the support cable. Since the angle between the support cable and the vertical component of the weight is 60º, we can use the sine function to determine the tension.

Tension / vertical component = sin(angle)
Tension / 150 N = sin(60º)

Step 5: Solve for the tension in the support cable. Multiply both sides of the equation by 150 N.

Tension = 150 N * sin(60º)
Tension = 129.9 N (approximately)

Therefore, the tension in the support cable is approximately 129.9 N.

To find the magnitude and direction of the net force exerted on the pole by the attachment fixture on the building (B), we can analyze the forces acting on the pole at the attachment point. Here's how you can do it:

Step 1: Identify the forces acting on the pole at the attachment point. There are two forces involved: the horizontal component of the tension in the support cable and the horizontal component of the weight of the pole.

Step 2: Determine the horizontal component of the tension. Since the support cable is attached at a 60º angle, the horizontal component of the tension can be found using the cosine function.

Horizontal component of tension = Tension * cos(angle)
Horizontal component of tension = 129.9 N * cos(60º)

Step 3: Determine the horizontal component of the weight of the pole. Since there is no horizontal force acting on the pole, the horizontal component of the weight is zero.

Step 4: Calculate the net force exerted on the pole by adding the horizontal components of the tension and weight.

Net force = Horizontal component of tension + Horizontal component of weight
Net force = 129.9 N * cos(60º) + 0

Step 5: Solve for the magnitude of the net force.

Net force = 129.9 N * cos(60º)
Net force = 64.95 N (approximately)

The magnitude of the net force exerted on the pole by the attachment fixture on the building is approximately 64.95 N. Since the horizontal component of the weight is zero, the direction of the net force is the same as the direction of the horizontal component of the tension, which depends on the angle between the support cable and the vertical component of the weight.