Problem#$5(30$ points$)$

A Helical Compression Spring is made out of music wire. The wire gauge is no$.18.$ The inner coil diameter is $0\mathrm{.}5^(\text{'}\text{'}).$

The ends are squared and is compressed between two flat plates. The number of acual runs $($N$\_($a$))$ is $12\mathrm{.}5$ turns.

$1-$Estimate the deflection for $10$ lbf $.$

$2-$What is the factor of safety for the induced stress in part a$.$

$2-$Estimate the maximum and minimum shear stress on the spring coil cross section for the force in part a$.$

$3-$What is the solid length of the spring