$(10$ pts $)$ A spring has natural length $0\mathrm{.}5$ m $.$ A force of $200$ N is required to hold the spring stretched to a length of $0\mathrm{.}7$ m $.$ How much work $($in Joules$)$ is needed to stretch the spring from $0\mathrm{.}7$ m to $1\mathrm{.}0$ m $?$