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--high hill, then descends 17 to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.3 and that a loaded car will have a maximum mass of 450 . For safety reasons, the spring constant should be 14 larger than the minimum needed for the car to just make it over the top.

What is the maximum speed of a 360 car if the spring is compressed the full amount?

Explanation / Answer

the change in the potential energy of the car as itdecends from the height h to h' will be                          U = mg(h-h') the change in the potentil energy = kinetic energyof the car            U = mv^2 / 2 if the spring absorbs all this kinetic energy bycompressing to a length of 2.2 m then                      mv^2 /2 = kx^2 / 2          m = mass ofthe coster          k = forceconstatn          x =compressed length          v =velocityof the coster     from the above relation we cna sovle forthe force constant and for m = 340 kg the velocity of the car                     v = (kx^2 / m) .

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