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

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 A degree , the length of the beam is L = 3.75 m, the coefficient of static friction between the wall and the beam is ?s = 0.480, 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. PICTURE ATTACHED:

Explanation / Answer

2w = Tsin 30 + coeff of friction x N

Tcos 30 = N

hence,

2w = T/2 + 0.48xTx30.5 /2 eq 1

Torque balance about point on the wall

2wx + w x 3.75/2 = T/2 x 3.75 eq2

=>T/2 = 2wx/3.75 +w/2

substituting in eq 1

2w = (2wX/3.75+w/2) (1+0.48x1.732)

=> 2= (2x/3+0.5)(1.83)

=> x = 0.89m

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