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Dragon's Descent" is an amusement park ride that lifts riders up a tower about 100m off the ground at constant speed, lets the riders contemplate their future for a few seconds before the ride platform is in freefall, for two seconds. A piston driven breaking system (giant spring) slows the riders to a stop in the next three seconds. There is no friction with the Tower or drag on the riders. The air in the piston gets hot upon compression. The riders and platform on another ride have a mass of 1000kg. Use conservation of energy to find the spring constant of the piston if they fall 64m, 40m of which the piston is pushing up on the platform, with 50% losses to heat the air in the piston. There will be additional bonus points for getting the answer correct.

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