Prior to being placed in its hole, a 5700-N, 9.0-m-long, uniform utility pole makes some nonzero angle with the vertical. A vertical cable attached 2.0 m below its upper encl holds it in place while its lower end rests on the ground. (a) Find the tension in the cable and the magnitude and direction of the force exerted by the ground on the pole. (b) Why don’t we need to know the angle the pole makes with the vertical, as long as it is not zero?
Solution 85P Introduction We have to calculate the tension of the rope and then we have to calculate the force exerted by ground on the pole. Finally we have discuss why the angle of the pole does not required to do this calculations. Step 1 Following diagram is the free body diagram of the situation Since the pole is not rotating now, the moment about the point B will be zero. Now the moment about point B is = r 1cos r T2cos = 0 r1w (4.5 m)(5700 N) T = r2 = (7.0 m) = 3664 N So the tension of the rope is ground. Now no horizontal force is acting on the pole. Also since the pole is not moving, the sum of vertical forces will also be zero. Hence we have F = F + v w = 0 F =vw T = 5700 N 3664 N = 2036 N Hence the vertical component of force exerted by ground is 2036 N. Since there is no horizontal force, the total force exerted by ground is 2036 N and it is vertically upward.