Calculating Forces and Tension on a Hinged Beam

[ctwokay]

Homework Statement

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 = 16.8 kg. The length of the beam is L = 2.43 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 = 32.9°.

Q1: What is the net force the hinge exerts on the beam?
Q2:The maximum tension the wire can have without breaking is T = 921 N.
What is the maximum mass sign that can be hung from the beam?

Homework Equations

τ=0 as it is static
F=0 as it is not moving

The Attempt at a Solution

For the first question, I form τ=0 where I have 3 torque, τ of tension, τ of beam and do I include τ of the sign?
And sum of forces is 0, so I have forces on hinge of x is Fh,x-Tcosθ=0, component of y is Fh,y-mbg-msg-Tsinθ=0
mbg is mass of beam, msg is mass of the sign.
Is there somewhere I did it wrong?

Second question I use r*T=(mb*horizontal distance from the hinge+m*horizontal distance from the hinge)*9.81
Is this correct?

 

[anathema]

Hello,

For the first question, you are correct in setting up the equations for torque and sum of forces. However, you do not need to include the torque of the sign as it is not causing any rotation. The torque of the beam and the tension in the wire are the only two torques acting on the beam. Additionally, your equations for the sum of forces on the hinge are correct.

For the second question, your equation for torque is correct. However, you can simplify it by using the fact that the torque of the beam and the torque of the sign must be equal. This means that the mass of the sign multiplied by its horizontal distance from the hinge must equal the mass of the beam multiplied by its horizontal distance from the hinge. So, you can set up the equation as msg*(2/3)*L = mb*(1/3)*L. This will allow you to solve for the maximum mass of the sign that can be hung from the beam.