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
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