The spring constant for a helical coil spring, $k,$ theoretically follows the form shown where d $($lower case$)$ is the wire diameter, D $($UPPER CASE$)$ is the mean diameter of the coil, na is the number of active coils and $G$ is a material property called the shear modulus.

Assume the following AVERAGE

measurements:

Wire diameter $d=1500$ microns

Modulus $G=56k\frac{N}{s}q.mm.$

Out side diameter O$D=31mm$

Active coils na $=60$

Also assume that all the measurements

have an uncertainty of $2\mathrm{.}6\%$ of the average.

Use the

High$-$Low method to determine $($a$)k$ and $($b$)$ delta$-$k$,$ the uncertainty in $k$ in $\frac{N}{m}.$