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 12-m-high hill, then descends 15 m to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.2 m and that a loaded car will have a maximum mass of 450 kg . For safety reasons, the spring constant should be 10 % larger than the minimum needed for the car to just make it over the top.

What spring constant should you specify?

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

Explanation / Answer

the initial elastic potential energy trnsfered into gravitational potential energy

mgh = 1/2 kx^2

k = 2 mgh/ x^2 = 2 (450 kg)(9.8)(12)/(2.2)^2

=21867.76 N/m

(b)

from the conservation of energy

1/2 kx^2 = mgh + 1/2 mv^2

kx^2 = 2mgh + mv^2

v = root kx^2/m - 2gh

= root 21867.76 N/m(2.2)^2/320 - 2 (9.8) ( -12)

=23.78m/s

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