A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of

Question

A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mp-6.9 kg and the sign has a mass of m,-15.7 kg. The length of the beam is L = 2.65 m. The sign is attached at the very end of the beam, but the horizontal wire holding up the beam is attached 2/3 of the way to the end of the beam. The angle the wire makes with the beam is -33.8 1) What is the tension in the wirei? N Submit 2) What is the net force the hinge exerts on the beam? N Submit 3) The maximum tension the wire can have without breaking is T -783 N. What is the maximum mass sign that can be hung from the beam? kg Submit

Explanation / Answer

1] Balancing torque about hinge

msg*L cos theta + mbg*L/2* cos theta = T* sin theta *2L/3

T = [15.7*9.8* cos 33.8 degree + 6.9*9.8* cos 33.8 degree]*3/(2 sin 33.8 degree)

= 496.26 N

2] Net force at hinge = -496.26 i + (15.7*9.8+6.9*9.8) j = -496.26i + 221.48j

= sqrt(496.26^2+221.48^2)

= 543 N

3] msg*L cos theta + mbg*L/2* cos theta = T* sin theta *2L/3

ms = [T sin theta *2/3 - mbg cos theta/2 ]/(g cos theta)

= [783* sin 33.8 degree *2/3 - 6.9*9.8 cos 33.8 degree/2]/[9.8 cos 33.8 degree]

= 32.2 kg answer

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