A uniform rigid pole of length L = 2.83 m and mass M = 8.01 kg is to be supporte

Question

A uniform rigid pole of length L = 2.83 m and mass M = 8.01 kg is to be supported from a vertical wall in a horizontal position, as shown in the figure. The pole is not attached directly to the wall, so the coefficient of static friction, ?s, between the wall and the pole provides the only vertical force on one end of the pole. The other end of the pole is supported by a light rope that is attached to the wall at a point a distance D = 1.29 m directly above the point where the pole contacts the wall. Determine the minimum value of ?s that will keep the pole horizontal and not allow its end to slide down the wall.

A uniform rigid pole of length L = 2.83 m and mass M = 8.01 kg is to be supported from a vertical wall in a horizontal position, as shown in the figure. The pole is not attached directly to the wall, so the coefficient of static friction, ?s, between the wall and the pole provides the only vertical force on one end of the pole. The other end of the pole is supported by a light rope that is attached to the wall at a point a distance D = 1.29 m directly above the point where the pole contacts the wall. Determine the minimum value of ?s that will keep the pole horizontal and not allow its end to slide down the wall.

Explanation / Answer

Let the tension in the rope=T

horizontal eq ---- N(normal reaction)=Tcos

vertical eq---- Mg = N+ Tsin

=tan-1(1.29/2.83)

= 24.50o

balancing moments about the point of contact with the wall,

MgL/2 = T sin * L

Mg = 2Tsin

T = 94.65 N

Normal reaction =Tcos = 94.65*cos 24.5

= 86.13 N

= (Mg - Tsin )/N = 0.456 Ans.

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