The figure below shows a roller$-$coaster car on a track. The car is fully loaded with passengers and has a total mass of $460$ kg $.$ At point A $,$ the car is at the lowest point in a circular arc of radius $r_1=12\mathrm{.}6m.$ At point $B,$ the car is at the highest point of a circular arc of radius $r_2=14\mathrm{.}3m.$

$($a$)$ If the car has a speed of $21\mathrm{.}0\frac{m}{s}$ at point A $,$ what is the magnitude of the force $($in N $)$ of the track on the car at this point?

$$

N

$($b$)$ What is the maximum speed $($in $\frac{m}{s})$ the car can have at point B in order for the car to maintain contact with the track at all times $($that is$,$ so that it does not "jump" off the track$)?$

$\frac{m}{s}$