Problem $3\mathrm{.}26$

The pulley shown is frictionless and all weights are negligible.

$($a$)$ Show that $=.$

$($b$)$ By drawing an FBD of the pulley and writing and solving equilibrium equations, determine the force $F$ in terms of the force $T$ and

angle $.$ Plot the ratio $\frac{F}{T}$ versus $$ for $090.$

$($c$)$ Imagine a structure has this pulley and cable arrangement, and you carefully measure $$ and $$ and find they are not equal. Explain

possible circumstances that might cause this to occur.

Figure P$3\mathrm{.}26$