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 mb = 6.2 kg and the sign has a mass of ms = 17.2 kg. The length of the beam is L = 2.52 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 wire? 2What is the net force the hinge exerts on the beam?

3.The maximum tension the wire can have without breaking is T = 861 N.What is the maximum mass sign that can be hung from the beam?

Explanation / Answer

1.

balancing moment about hinge point ,

Tsin33.8 x 2L/3 = 6.2gcos33.8 x L/2 + 17.2gcos33.8 x L

T = 165.72 x 3/2sin33.8 = 446.86 N

2.

balancing forces in x

T = Hx

Hx = 446.86 N

balancing forces in y

mg + Mg = Hy

Hy = 23.4*9.8 = 229.32 N

net hinge force = sqrt ( Hy^2 + Hx^2) = 502.2 N

3

.Tsin33.8 x 2L/3 = 6.2gcos33.8 x L/2 + mgcos33.8 x L

here T is 861 N , so we have to find out m

861sin33.8 x 2L/3 = 6.2gcos33.8 x L/2 + mgcos33.8 x L

319.31 = 25.27 + 8.15m

m = 36.08 kg

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