hanical Design$2$

estion $(1)$

helical compression spring is wound with a $4mm$ diameter music wire with squared and ound ends. The spring has $10$ total coils, an outside diameter of $34mm$ and a free length height$)$ of $80mm.$ Use $G=79\mathrm{.}3$GPa,$S_{se}=310$MPa,$A=2170,m=0\mathrm{.}146,S_{yt}=0\mathrm{.}75S_{ut},S_{sy}=\mathrm{.}577S_{yt},$ the number of inactive coils is $2.$ Determine:

a$)$ The spring modulus $($stiffness$).$

b$)$ The force needed to compress the spring to solid height and the resulting shear stress and if the spring is solid$-$safe or not.

c$)$ The fatigue factor of safety if the spring is subjected to a periodic force ranging between a minimum of $50N$ and a maximum of $250N.$