A roller-coaster car shown in Figure P8.72 is released from rest from a height h and then mows freely with negligible friction. The roller-coaster track includes a circular loop of radius R in a senical plane. (a) First suppose theca: barely makes in around the loop: at the top of the loop. the riders are upside down and feel weightless. Find the required height h
of the release point above the bottom of the loop in terns d R (b) Now assume the release point is at or above the minimum required height. Show that the normal force on the car at the bottom of the loop exceeds the nor-mal force at the top of the loop by six times the
cars weight. The normal force un each rider follows the same rule. Such a large normal forte is dangerous and very uncomfortable for the riders. Roller coasters are therefore not built with circular loops in vertical planes. Figure P6.17 (page 170) shows an actual design.
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