On a blanked race track, the smallest circular path on whichcars can move has a

Question

On a blanked race track, the smallest circular path on whichcars can move has a radius of 112m, while the largest has a radiusof 165m, as the drawing illustrates. The height of the outer wallis 18m. find: a) the smallest & b) the largest speed at which cars can move on this trackwithout relying on friction Book answers: a) 19 m/s and b) 23 m/s thanks! On a blanked race track, the smallest circular path on whichcars can move has a radius of 112m, while the largest has a radiusof 165m, as the drawing illustrates. The height of the outer wallis 18m. find: a) the smallest & b) the largest speed at which cars can move on this trackwithout relying on friction Book answers: a) 19 m/s and b) 23 m/s thanks!

Explanation / Answer

    From the figure,                            horizontal distance between outer and innerwalls, d = 165 - 112 = 53 m                                                                height of outer wall, h = 18 m        tan = 18 / 53 (a)     r = 112 m     smallest speed, V = ( r g tan ) = ( 112 * 9.8 * 18 / 53 ) = 19.3 m/s (b)     r = 165 m     smallest speed, V = ( r g tan ) = ( 165 * 9.8 * 18 / 53 ) = 23.4 m/s

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