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As shown in the figure below, a uniform beam is supported by a cable at one end

ID: 2144950 • Letter: A

Question

As shown in the figure below, a uniform beam is supported by a cable at one end and the force of friction at the other end. The cable makes an angle of ? = 30

As shown in the figure below, a uniform beam is supported by a cable at one end and the force of friction at the other end. The cable makes an angle of ? = 30 degree , the length of the beam is L = 4.25 m, the coefficient of static friction between the wall and the beam is ?s = 0.500, and the weight of the beam is represented by w. Determine the minimum distance x from point A at which an additional weight 2w (twice the weight of the rod) can be hung without causing the rod to slip at point A.

Explanation / Answer

vertical forces balance: T sin30 + f = w + 2w

horizontal forces balance: T cos30 = n

torques balance: torque from tension = torque from weight of beam + additional weight

T L sin30 = 2w * x + w * L/2

T * 0.5 + u (T * 0.8660) = 3w (and) T * 0.5 = 2 w x / 4.25 + w * 0.5

0.5 T + 0.500 * 0.8660 T = 3w (and) T = 0.941 wx + w

T = 3.215 w and T = (0.941 x + 1 )w

3.215 w = (0.941 x + 1 )w

3.215 = 0.941 x + 1

x = 2.35 m