You have been hired to design a spring-launched roller coaster thatwill carry tw

Question

You have been hired to design a spring-launched roller coaster thatwill carry two passengers per car. The car goes up a 10-m highhill, then descends 15m to the track's lowest point. You'vedetermined that the spring can be compressed a maximum o 2.0m andthat a loaded car will have a maximum mass of 400kg. For safetyreasons, the spring constant should be 10% larger than the minimumneeded for the car to just make it over the top.
a) what spring constant (k) should you specify ?

b) What is the maximum speed of a 350 kg car if the spring iscompressed the full amount.

Explanation / Answer

For this problem, the spring should be strong enough to getthe car jsust over the top so: mgh = (1/2)kx^2 (400)*(9.8)*(10) = (0.5)*(k)*(2.0^2) k = 39200/2.645 k = 19600 N/m -- -- Increase by 10%, so: k = 19600 * 1.10 = 21560 N/m = 21.6 N/m---->specified spring constant -- -- Maximum speed of a 350 kg car will be at the bottom of theroller coaster: (1/2)mv^2 + mg(Y1-Y2) = (1/2)kx^2
(0.5)*(350)*(v^2) + (350)(9.8)(10-15) =(0.5)*(21560)*(2.0^2) v^2 = 344.4
v = 18.56 m/s

This should be better

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