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 11-{ m m}-high hill, then descends 20 m to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.5 m and that a loaded car will have a maximum mass of 420 kg. For safety reasons, the spring constant should be 12 % 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 340 kg car if the spring is compressed the full amount?

Explanation / Answer

The compression in the spring, x = 2.5 m The height of the hill, h = 11 m The mass of car, m = 420 kg So the energy required to go the top, E = mgh = 420*9.8*11 = 45276 J The energy of spring = mgh + 12% of mgh (1/2)kx^2 = 45276 + 5433.12 = 50709.12 K = 16226.p N/m b) Car is given  50709.12 J. It loses some going up the hill then gains more coming down the other side.
It gains an extra mg?h = 340 . 9.8 . 7 = 23324 J

Total KE is 50709.12 + 23324 = 74033.12 J

0.5 . m . v^2 = 74033.12 v = 20.8 m/s v = 20.8 m/s

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