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 m_b = 6.3 kg and the sign has a mass of m_s = 17.8 kg. The length of the beam is L = 2.66 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 theta = 30.7degree. 1) What is the tension in the wire? 2) What is the net force the hinge exerts on the beam? 3) The maximum tension the wire can have without breaking is T = 1075 N. What is the maximum mass sign that can be hung from the beam? 4) What else could be done in order to be able to hold a heavier sign? while still keeping it horizontal, attach the wire to the end of the beam keeping the wire attached at the same location on the beam, make the wire perpendicular to the beam attach the sign on the beam closer to the wall shorten the length of the wire attaching the box to the beam

Explanation / Answer

Balancing torque about hinge,

T*2.66*2/3* sin 30.7 degree = 6.3*9.8*2.66*0.5*cos 30.7 degree + 17.8*9.8*2.66*cos 30.7 degree = 47.917*9.8

T = 47.917 *9.8/ (2.66*2/3* sin 30.7 degree)

= 518.67 N

Force exerted by hinge = 518.7 i + (6.3+17.8)*9.8 j = 518.7 i + 236.2 j

= sqrt(518.7^2+ 236.2^2)

= 570 N

For maximum mass, balancing torque about hinge,

1075*2.66*2/3* sin 30.7 degree = 6.3*9.8*2.66*0.5*cos 30.7 degree + M*9.8*2.66*cos 30.7 degree

(1075*2.66*2/3* sin 30.7 degree - 6.3*9.8*2.66*0.5*cos 30.7 degree )/(9.8*2.66*cos 30.7 degree ) = M

= 40.271 kg

To hold larger mass, attach the wire at the end of beam,

make wire perpendicular to beam

attach the sign on the beam closer to wall

first three options are correct

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