You have been hired to design a spring-launched roller coaster that will carry t

Question

You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 13-m-high hill, then descends 18 m to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.1 m and that a loaded car will have a maximum mass of 450 kg . For safety reasons, the spring constant should be 10 % larger than the minimum needed for the car to just make it over the top. What spring constant should you specify? What is the maximum speed of a 370 kg car if the spring is compressed the full amount?

Explanation / Answer

car comes from 18m height to bottom.

then Gravitational PE will convert into spring PE.

m gh = k x^2 / 2

450 x 9.8 x 18 = k (2.1^2) / 2

k = 36000 N/m

Spring constant will be 10% larger then k = 1.10 x 36000 =39600 N/m .........Ans

Spring is compressed to 2.1m then

stored spring PE = k x^2 /2 = 39600 x 2.1^2 / 2 = 87318 J

87318 = 370v^2 /2

v = 21.73 m/s

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