$7)$ A crate is pulled up a ramp a distance of $30$ m with a force of $\backslash ($ f$=[8\backslash$overrightarrow$\{00\},500]\backslash ).$ The crate ends up $2$ m higher above the ground than where it started.

a$)$ Find the force applied on the crate that moves the crate up the ramp and the force that is perpendicular to the ramp that lifts the crate up off the ramp.

b$)$ Find the work done moving the crate up the ramp and the work done lifting the crate $2$ m above the ground.