A roller-coaster car is released from rest at the top of the rise and then moves
ID: 2218814 • Letter: A
Question
A roller-coaster car is released from rest at the top of the rise and then moves freely with negligible friction. The roller coaster shown in the figure below has a circular loop of the radius R in a vertical plane.(a) suppose first that the car barely makes it around the loop: at the top of the loop the riders are upside down and feel weightless. Find the required height of the release point above the bottom of the loop in terms of R. (b) Now assume that 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 normal force at the top of the loop by six times the weight of the car. The normal force on each rider is follows the same rule. Such a large normal force is dangerous and very uncomfortable for the riders. Roller coasters are therefore not built with circular loops in vertical planes.Explanation / Answer
A roller coaster car is released from rest at the top of the first rise and then moves freely with negligible friction. The roller
coaster shown in Fig. P7.62 has a circular loop of radius R in the vertical plane. (a) First, suppose the car barely makes it around the
loop; at the top of the loop the riders are upside down and feel weightless. Find the required height of the release point above the bottom
of the loop, in terms of R. (b) Now assume that 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 normal force at the top by six times the weight of the car. The normal force on each rider
follows the same rule. Such a large normal force is dangerous and very uncomfortable for the riders. Roller coasters are therefore not
build with circular loops in vertical planes. Figure P5.24 and the photograph on page 134 show two actual designs.
(b) If the release comes from a higher point, there will be some normal force at the top NT and at the bottom NB. Summing forces at
both points
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