$[-/10$ Points$]$ SCALCET$96\mathrm{.}4\mathrm{.}009.$EP$.$

According to Hooke's Law, the force required to hold the spring stretched $xm$ beyond its natural length is given by $f(x)=kx,$ where $k$ is the spring constant.

Suppose that $5$ J of work is needed to stretch a spring from its natural length of $32$ cm to a length of $49$ cm $.$

Find the exact value of $k,$ in $\frac{N}{m}.$

$k=\frac{N}{m}$

$($a$)$ How much work $($in J$)$ is needed to stretch the spring from $37$ cm to $41$ cm $?($Round your answer to two decimal places.$)$

$$ J

$($b$)$ How far beyond its natural length $($in cm $)$ will a force of $40$ N keep the spring stretched? $($Round your answer one decimal place.$)$

$$ cm$[-/10$ Points$]$ SCALCET$96\mathrm{.}4\mathrm{.}009.$EP$.$

According to Hooke's Law, the force required to hold the spring stretched $xm$ beyond its natural length is given by $f(x)=kx,$ where $k$ is the spring constant.

Suppose that $5$ J of work is needed to stretch a spring from its natural length of $32$ cm to a length of $49$ cm $.$

Find the exact value of $k,$ in $\frac{N}{m}.$

$k=\frac{N}{m}$

$($a$)$ How much work $($in J$)$ is needed to stretch the spring from $37$ cm to $41$ cm $?($Round your answer to two decimal places.$)$

$$ J

$($b$)$ How far beyond its natural length $($in cm $)$ will a force of $40$ N keep the spring stretched? $($Round your answer one decimal place.$)$

$$ cm