24. Considera roller coaster like Kingda Ka at Six Flags Great Adventure at Jack

Question

24. Considera roller coaster like Kingda Ka at Six Flags Great Adventure at Jackson, New Jersey. This coaster starts from a position A, at h 0 m, and then speeds up to VA = 120 m/s, Find (a) the speed of Kingda Ka when it reaches the top of the track at position B, where the height is h8 130 m, and (b) the speed of the roller coaster when it turns around at the very top, and falls back to the ground, at approximately hc = 10, since the roller is sitting above the initial ground it started. (c) Make a qualitative sketch of the coaster from positions A - C, explain what is happening in each position, and does this make any sense to the real life coaster, yes or no?

Explanation / Answer

a] by energy conservation,

mghB + 0.5mvB^2 = 0.5mvA^2

vB = sqrt(vA^2- 2ghB) = sqrt(120^2-2*9.8*130) = 108.87 m/s

b] vC = sqrt(120^2-2*9.8*10) = 119.18 m/s

c] At A it had only Kinetic energy. As it goes to top , KE decreases and PE increases. After turning from the top, its KE starts increasing PE decreases.

Yes, it make sense to anextent, but in real life coaster there is friction also and motor too.

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