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 10m high hill, then descends 20m to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.3m and that a loaded car will have a maximum mass of 420kg . 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 350kg car if the spring is compressed the full amount?

Explanation / Answer

1) Set 0 potential at the bottom of the 10 m hill PE at the top of the hill: PE(grav.) = mgh = (400 kg)(9.8 m/s^2)(10 m) = 39200 J PE of fully compressed spring: PE(spring) = (1/2)kx^2 39200 J = (1/2)k'(2.1 m)^2 k' = 17778 N/m k = 1.15(17778 N/m) = 20444 N/m 2) Set 0 potential at the bottom of the 20 m slope Initially: ME = PE(grav) + PE(spring) = 39200 J + 1.15(39200 J) = 84280 J At the bottom of the 20-m slope: ME = KE KE = (1/2)mv^2 84280 J = (1/2)(350 kg)v^2 v = 21.9 m/s

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