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 kg and the sign has a mass of m_s 16.1 kg. The length of the beam is L = 2.74 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 = 30.1 degree. What is the tension in the wire? N Submit What is the net force the hinge exerts on the beam? N Submit The maximum tension the wire can have without breaking is T = 945 N. What is the maximum mass sign that can be hung from the beam? kg Submit 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

Here ,

1) let the tension in the string is T

balancing the torque about the pivot point

T * sin(30.1 degree) * 2L/3 - L * 16.1 * 9.8 - 6 * 9.8 * L/2 =0

solving for T

T = 384 N

the tension in the string is 384 N

2)

for the net hinge force

Fnet = 384 * cos(30.1) i + ((16.1 + 6) * 9.8 - 384 * sin(30.1))

Fnet = 332.2 i + 24 j = sqrt(332.2^2 + 24^2)

Fnet = 333.1 N

3)

let the maxium mass is m

balancing the torque about the pivot point

945 * sin(30.1 degree) * 2L/3 - L * m * 9.8 - 6 * 9.8 * L/2 =0

solving for m

m = 29.23 Kg

the maximum mass is 29.23 Kg

4)

for a heavier sign

the correct options are :

option 2 , option 3

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