After its release at the top of the first rise, a roller-coaster car moves freel

Question

After its release at the top of the first rise, a roller-coaster car moves freely with negligible friction, The roller coaster shown in Figure P8.26 has a circular loop of radius 20.2 m The car barely makes it around the loop. At the top of the loop, the riders are upside down and feel weightless. Figure P8.26 (a) Find the speed of the roller coaster car at the top of the loop (position 3). _______ m/s (b) Find the speed of the roller coaster car at position 1. m/s (c) Find the speed of the roller coaster car at position 2. _______ m/s (d) Find the difference in height between positions 1 and 4 if the speed at position 4 is 9.10 m/s. _______ m

Explanation / Answer

a) g = v^2/r

v = sqrt(g*r)

= sqrt(9.8*20.2)

= 14.07 m/s

b) v = sqrt(5*g*r)

= sqrt(5*9.8*20.2)

= 31.46 m/s

c) v = sqrt(3*g*r)

= sqrt(3*9.8*20.2)

= 24.37 m/s

d) v2^2 - v1^2 = 2*g*h

h = (v2^2-v1^2)/(2*g)

= (31.46^2-9.1^2)/(2*9.8)

= 46.27 m

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