4. A flagpole is mounted from the side of my house, held by flagpole mount- ing

Question

4. A flagpole is mounted from the side of my house, held by flagpole mount- ing bracket, inclined at an angle of 35 degrees above the horizontal, as shown in the photo. The pole is 10 feet long, and weighs 2 lbs. A 5 lbs weight is tied to the end (not shown). To support this, the mounting bracket must exert a net force together with a torque (a moment or couple) on the end of the pole. (a) What is the net force, and what is the couple? The sleeve of the mounting bracket is 2 inches long. It is a bit loose, so the pole comes in contact with the sleeve at the bottom on one end, and at the top on the other end, as shown in the exaggerated figure below. What is the force (that comprises the couple) at these two points?

Explanation / Answer

Torque due to weight of pole about bracket = (Mp g) (L/2) cos(theta)
                                                                 = (2 g )(10/2) cos 35 ( anticlockwise)
                                                                 = 8.19 g
Torque due to weight tied to end of pole = MgL cos theta = 40.96g (anticlockwise)
Torque due to bracket is equal and opposite to the torque of weights = 49.15g clockwise
                                                                                                       =1582.5

Force of bracket is equal to total weight of pole + mass tied = (2=5)g = 225.4

Torque exreted by bracket is also = Force * distance between the points where force acts
                               1582.2 = F *(2/12)
                                  F = 9493.2 lbf

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