Suppose we want to make a spring scale for measuring mass. We want each $1\mathrm{.}0$ cm change in length to correspond to a mass difference of $100$ g$.$ Recall that the force of gravity is given by

Fg $=$ mg$,$

where

g $=9\mathrm{.}8$ m$/$s$2.$

$($a$)$ What should be the value of the spring constant?

N$/$m

$($b$)$ How much work is done by a $9$ kg mass in stretching the spring?

J