A coil spring with plain ends that are ground is to operate with a load that fluctuates between $45$

and $90$ lb $,$ during which the deflection is to vary by $\frac{1}{2}in.$ Because of space limitations$,$ a mean

coil diameter of $2$ in $.$ has been selected. Steel spring wire corresponding to the shot$-$peened

wire in Figure $12\mathrm{.}16$ is to be used. The beneficial effect of the specified presetting is not to be

taken into account in the calculations. It is considered to provide a sufficient safety factor to

allow for the possibility of higher stresses, should the spring ever close solid. Choose an

appropriate clash allowance, and determine appropriate values for

r $N,d,$ anws $L_f.($See Figure P$12\mathrm{.}6.)$