Question

A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mb = 6.7 kg and the sign has a mass of ms = 17.4 kg. The length of the beam is L = 2.83 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 θ = 34.5°.

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 = 946 N. What is the maximum mass sign that can be hung from the beam?

Answer 1

image with reference angles for ease in understanding

Where:
beam weight
weight of the sign
tension
horzontal force component of the hinge
  vertical component of the force of the hinge

1)What is the tension in the wire?

the hinge is taken as origin

The torque of a force is given by

  is the distance from the origin to the point of application of force
  is the force applied
  angle between, projection of r and F

torque beam weight

the negative is because tries, turn clockwise the beam

torque sign weight

the negative is because tries, turn clockwise the beam

torque of the tension

the net moment on the beam is

replacing

, and

expression to the tension

2)What is the net force the hinge exerts on the beam?

summations of horizontal forces

sum of vertical forces

magnitude of the forces of the hinges

3)The maximum tension the wire can have without breaking is T = 946 N. What is the maximum mass sign that can be hung from the beam?

you can use the following equation

for tension

for beam

for sign

replacing

expression for the mass

the maximum mass sign that can be hung from the beam is