A roller coaster car of mass is launched by a compressed spring of spring constant. Assume that there is no friction or air drag. Starting from rest, the coaster is pushed by the compressed spring, climbs up and then down a hill of height 3.5R, and then goes around the inside of a loop of radius R. R = 20 meters, k = 700 N/m, m = 1000 kg a.) What is the minimum distance the spring must be compressed for the coaster to make it over the hill? b.) In the case of the coaster just making it over the first hill, what will be the normal force of the track on the coaster when it reaches the top of the loop? (Use conservation of mechanical energy to determine the speed at the top of the loop and the free body diagram method to determine the normal force.)