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-high hill, then descends 15m to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.2m and that a loaded car will have a maximum mass of 440kg . For safety reasons, the spring constant should be 11% larger than the minimum needed for the car to just make it over the top

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

Explanation / Answer

at highest point ,

By conservation of energy

(1/2)KX2=mgh

(1/2)*K*2,22=440*9.8*11

K=19600 N/m

Given

Ko=1.12*19600=21952 N/m

at lowest point of cliff i,e h=11-15=-4 m

By conservation of energy

(1/2)KoX2=mgh+(1/2)mV2

(1/2)*21952*2.22=360*9.8*(-4)+(1/2)*360*V2

V=19.33 m/s

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