A roller coaster at the Six Flags Great America amusement parkin Gurnee, Illinois, incorporates some clever design technology andsome basic physics. Each vertical loop, instead of being circular,is shaped like a teardrop (Fig. P6.20). The cars ride on the insideof the loop at the top, and the speeds are high enough to ensurethat the cars remain on the track. The biggest loop is 40.0 m high,with a maximum speed of 31.0 m/s (nearly 70 mph) at the bottom.Suppose the speed at the top is 14.0m/s and the corresponding centripetal acceleration is2g.
(a) What is the radius of the arc of the teardrop at thetop?
(b) If the total mass of a car plus the riders is M,what force does the rail exert on the car at the top?
(c) Suppose the roller coaster had a circular loop of radius10.0 m. If the cars have the samespeed, 14.0 m/s at the top, what isthe centripetal acceleration at the top?