You are designing a roller coaster. The first goal is to have the passenger cars

Question

You are designing a roller coaster. The first goal is to have the passenger cars traveling at 120 miles per hour at the bottom of the first fall. The second goal is to have the cars come into the boarding platform at 7 m/s.
a) the friction between the wheels and the track wastes 7% of the total energy during the first fall. To achieve the high speed goal (120 mph) how high must the crest of the first hill be?
b) the remainder of the roller coaster path wastes another 85% of the original total energy. to achieve the end speed goal (7 m/s) how high must the crest of the first hill be
c) what should the height of the first hill be? Explain briefly.

Explanation / Answer

120 mph = 53.64 m/sec now lets use conservation of energy with some adjustments to the friction losses: mv^2/2=mgh*0.93 (because 7% are gone) --> h=v^2/2g0.93=157.87 m b) same manner but waste of energy will be 92% v=7 m/sec mv^2/2=mgh*0.08 --> h=v^2/2g0.08=31.25 m

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