A roller-coaster car shown in Figure P8.72 is releasedfrom rest from a height h and then

Chapter 8, Problem 72

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A roller-coaster car shown in Figure P8.72 is releasedfrom rest from a height h and then moves freely withnegligible friction. The roller-coaster track includes acircular loop of radius R in a vertical plane. (a) Firstsuppose the car barely makes it around the loop; at thetop of the loop, the riders are upside down and feelweightless. Find the required height h of the releasepoint above the bottom of the loop in terms of R.(b) Now assume the release point is at or above theminimum required height. Show that the normal forceon the car at the bottom of the loop exceeds the normalforce at the top of the loop by six times the carsweight. The normal force on each rider follows thesame rule. Such a large normal force is dangerousand very uncomfortable for the riders. Roller coastersare therefore not built with circular loops in verticalplanes. Figure P6.17 (page 170) shows an actual design.