# A uniform 8 m 1500 kg beam is hinged to a wall and supported by a thin cable attached 2 m from the free end of the beam as shown in the figure. The beam is supported at an angle of 30 degrees above the horizontal.

a) free diagram
b) find the tension in the cable
c) how hard does the beam push inward on the wall?

## 2 answers

1. Without the diagram, it is not clear at what angle the cable makes with the vertical.

Draw the free diagram.

The hinge at the wall means that there will be a horizontal and a vertical force to achieve equilibrium, meaning
ΣFx=0
ΣFy=0, and
Σmoments=0

The "uniform beam" means that the weight is distributed uniformly along the beam, or its centre of mass is at mid-length.

You will have three unknowns, namely Rx and Ry at the hinge, and T for the tension of the cable.

Set-up the 3 equilibrium equations and solve for the unknowns, and hence the solution to (b) and (c).

2. Tension= 13203.5
beam pushes at magnitude 13002.91N
My sig figs maybe be slightly off

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