A $41\mathrm{.}0$ kg box initially at rest is pushed $5\mathrm{.}30$ m along a rough, horizontal floor with a constant applied horizontal force of $130$ N$.$ If the coefficient of friction between box and floor is $0\mathrm{.}300,$ find the following.

$($a$)$ the work done by the applied force

J

$($b$)$ the increase in internal energy in the box$-$floor system due to friction

J

$($c$)$ the work done by the normal force

J

$($d$)$ the work done by the gravitational force

J

$($e$)$ the change in kinetic energy of the box

J

$($f$)$ the final speed of the box

m$/$s