When a lift is descending with acceleration ams$-2,$ the tension in the lift cable is $11625$ N$.$ The total mass of the lift and its contents is $1250$ kg$.$

$($a$)$ Find the value of a$.$

$($b$)$ A crate on the floor of the lift has a mass of $200$ kg$.$ Find the magnitude of the reaction of the floor on the crate.