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 20 m to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.0 m and that a loaded car will have a maximum mass of 450 kg . For safety reasons, the spring constant should be 13 % larger than the minimum needed for the car to just make it over the top.

a) What spring constant should you specify?

b) What is the maximum speed of a 320 kg car if the spring is compressed the full amount?

Explanation / Answer

PE at the top of the hill

PE = m g h = 450 kg * 9.8 m/s2 * 11 m = 48510 J

PE of fully compressed spring

PE = (1/2) k * x2

48510 J = (1/2) k' 22

k' = 24255 N/m

k = 1.13 * (24255)

k = 27408 N/m = 2.74 * 104 N/m

--------------------------------------------------

ME = PEgrav + PEspring

= 48510 J + 1.13 (48510) = 103326 J

At the bottom of the 20 m slope

KE = (1/2) m v2

103326 J = (1/2) (320 kg) v2

v = 25.4 m/s

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