2.A car rolls on the frictionless track as shown below. The car is not attached to the track. a) Find an expression for the normal force at the top of

the hill, as a function of the velocity and the radius R1. b) Find an expression for the normal force at the top of the loop, as a function of the velocity and the radius R2. (The car will be upside down) c) If R1=R2=6.0 m, graph the normal force as a function of velocity at the top of the hill and the loop.OK to use Desmos. Describe in words how the normal force changes with velocity for each case. d) If R1=R2=6.0 m, what is the range of velocities for which the car will remain in contact with the track while going over the hill? What is the range of velocities for which the car will remain in contact with the track while going around the loop?