A 9.00 m uniform beam is hinged to a vertical wall and held horizontally by a 5.

Question

A 9.00 m uniform beam is hinged to a vertical wall and held horizontally by a 5.00 m cable attached to the wall 4.00 m above the hinge, as shown in the figure below (Figure 1) . The metal of this cable has a test strength of 1.20 kN, which means that it will break if the tension in it exceeds that amount.

A-What is the heaviest beam that the cable can support with the given configuration?

B-Find the horizontal component of the force the hinge exerts on the beam.

C-Find the vertical component of the force the hinge exerts on the beam.

Explanation / Answer

net torque about contact point is zero. T*cosalpha*3=mg*4.5 where cos alpha=4/5. so T*4*3/5=mg*4.5 Let T=1.2 so m=0.065(kg). -------------- N=T*sin alpha=T*3/5=0.72(N) --------- N'=mg-T* cos alpha=0.065*9.8-1.2*4/5=-0.32(N)

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