One end of a uniform 4.30 -m-long rod of weight F g is supported by a cable at a

Question

One end of a uniform 4.30-m-long rod of weight Fg is supported by a cable at an angle of ? = 37

One end of a uniform 4.30-m-long rod of weight Fg is supported by a cable at an angle of ? = 37 degree with the rod. The other end rests against the wall, where it is held by friction as shown in the figure below. The coefficient of static friction between the wall and the rod is ?s = 0.455. Determine the minimum distance x from point A at which an additional object, also with the same weight Fg, can be hung without causing the rod to slip at point A.

Explanation / Answer

taking moment of all the forces about A ..

T*sin 37 * 4.3 = Fg*4.3/2 + Fg*x

so.. T = Fg*(2.15+x) / 2.5878046

normal reaction at A = Tcos 37 = 0.308615 * Fg*(2.15+x)

vertical force at A = 2*Fg - T*sin 37 = 2Fg - 0.2325581* Fg*(2.15+x)

2Fg - 0.2325581* Fg*(2.15+x) = 0.455* 0.308615 * Fg*(2.15+x)
so... 2.15 + x = 5.362247645
so.. x = 3.21225 m

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