Figure $6$ shows a roller$-$coaster car released from rest from height $h.$ The car then slides freely down a frictionless track which includes a circular loop of radius $R$ as shown in the figure.

$($a$)$ Find the required height $h$ of the release point in terms of $R$ such that the car barely makes it around the loop

$($b$)$ Show that when the rethe normal force on the car at the bottom of the loop exceeds that of the top of the loop by six times the car's weight.