One end of a uniform 3.20 -m-long rod of weight w is supported by a cable at an

Question

One end of a uniform 3.20-m-long rod of weight w is supported by a cable at an angle of ? = 37

One end of a uniform 3.20-m-long rod of weight w is supported by a cable at an angle of ? = 37 degree with the rod. The other end rests against a wall, where it is held by friction (see figure). The coefficient of static friction between the wall and the rod is ?s = 0.520. Determine the minimum distance x from point A at which an additional weight w (the same as the weight of the rod) can be hung without causing the rod to slip at point A.

Explanation / Answer

f = 0.520Tcos37
in vertical,
Tsin37 + f = 2w
Tsin37 + 0.520Tcos37    = 2w
T = 1.97w
balancing moment about wall point,
wx + w(3.2/2)   = 3.2Tsin37
wx + 1.6w = 3.79w
x = 2.19 m

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