Problem $5(4$ points$)$: A static service music wire helical compression spring is needed to support a maximum operating load of $20-$lbf$,$ with deflection

at this load equal to $1\mathrm{.}75$ in $.$ The solid height of the spring cannot exceed $1\mathrm{.}5$ inch. The free length must not exceed $4$ in$.$ The static factor of safety

must equal or exceed $1\mathrm{.}2.$ For robust linearity, use clash clearance $($allowance$)$ of $15\%.$ Further, the following design requirements must be met: the

spring must operate over a $0\mathrm{.}75$ in rod. A $0\mathrm{.}050-$in diametral clearance allowance should be adequate to avoid interference between the rod and the

spring due to out$-$of$-$round coils. Start with a wire diameter of $0\mathrm{.}075$ in $.$ Obtain the quantities listed below and see if these come within the design

requirements.

Mean diameter, spring index, spring rate $($using force$/$deflection$),$ number of active coils $($use the spring rate equation from Lec. $3$ to find

this after finding spring rate first$),$ solid length, free length, load at solid length, and static factor of safety against yield. You may end up

iterating on the wire diameter to get reasonable answers.