A cable that weighs $5\frac{N}{m}$ is used to go up $50N$ of ore from the bottom of a well $100$ meters lower.

$($i$)$ Suppose that at some point, $x$ meters of cable have been brought to the surface. So the work to get back up $x$ more meters

is about $w(x)x.$ What is $w(x)?$

$w(x)=$

$$

Express your answer with a formula.

$($ii$)$ What is$,$ in Joules, the work required to bring the ore to the surface? Round the answer to$3$significant figures.