A uniform beam of mass m = 1kg is inclined at an angle theta = 60 degree to the

Question

A uniform beam of mass m = 1kg is inclined at an angle theta = 60 degree to the horizontal. Its upper end is tied to a wail by a rope and the lower end rests on a rough floor (see figure below). The block M is supported a cable attached to the upper end of the beam. If the coefficient of static friction between beam and floor mu s = 0.4: Find the maximum mass M that can be suspended from the top before the beam slips. Determine the magnitude of the force exerted by the floor on the beam Determine the magnitude of the force exerted by the beam on the rope at P

Explanation / Answer

i) balancing the forces in the horizontal direction
mew*Mg*cos = T

but the tension is caused due to the weights of both the rod and the mass M

thus T = (M+m)g

thus mew*Mg*cos = (M+m)g

solve and get the value of M

ii) since the rod is at rest thus the net vertical force is also zero

thus (M+m)g = N (N being the contact force applied by the floor on the rod

iii) the force applied by the rod on the rope would be = mg

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