Determining β in the L-Shaped Rod Problem

[aaronfue]

Homework Statement

The position of the L-shaped rod shown is controlled by a cable attached at point B. Determine the angle, β, in terms of θ.

The Attempt at a Solution

From the FBD attached, I was able to get:

β = tan^-1($\frac{0.24sinθ - EF}{0.24cosθ+0.32}$)

How can I determine what EF is? Is it possible to get an actual number? FG = 0.160

 

[Simon Bridge]

Is the beta angle supposed to be the angle the cable BE makes to the vertical?

Then I think there is something not quite right about your diagram ...
F is vertically above the pivot of the beam and level with the top of the pulley?
It is 160mm horizontally from F to the center of the pulley.

It looks like you'll need the diameter of the pulley.

 

[nvn]

FG = 0.160.

aaronfue: FG is not 160 mm. FG is simply AB*sin(theta), whereas EF = 160 mm.

Here are my current thoughts. Theta can be any value; it is given. Given theta, then I think beta can be any value, depending on the pulley radius. You are given the pulley axle horizontal location, which is EF = 160 mm.

But are you given the pulley radius? If not, I am currently thinking beta will also be a function of pulley radius, r.