Question $3(15)$

Genco$-$Crush labs uses a conventional ball mill crusher to reduce bituminous coals lumps that are needed for boiler feed. The feed of $220kg$ of coal with a compressive strength of $22\mathrm{.}5M\frac{N}{m^2}.$ The feed size is $50mm$ and the total energy required was $17\mathrm{.}0k\frac{J}{k}g.$ The screen analysis of product is provided below:

$\backslash$table$[[$Size of aperture $(mm),6\mathrm{.}0,4\mathrm{.}0,2\mathrm{.}0,0\mathrm{.}75,0\mathrm{.}50,0\mathrm{.}25,0\mathrm{.}125],[$Amount of product $(kg),0,59,42,53,20,40,6\mathrm{.}0]]$

Calculate the power $(kW)$ that would be needed to crush $1k\frac{g}{s}$ of coal $($same material$)$ of compressive strength $45M\frac{N}{m^2}$ from a feed of $45mm$ to product of $0\mathrm{.}5mm$ average size? Apply Kick's Law.

Hint: compute mean length diameter $($mass$)!$

Hint: equate energy to power using mass!