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 13-m-high hill, then descends 18m 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 450kg . 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 spring constant should you specify?

What is the maximum speed of a 340kg car if the spring is compressed the full amount?

Explanation / Answer

Considering the no losses, (ideal condition)

Energy in the spring should be suffucient to take roller coaster to top

0.5*k*x^2 = m*g*h

0.5*k*2.2^2 = 450*9.81*13

k = 23714.25 N/m

Applying safety condition = 1.14*23714.25 = 27034.25 N/m

Energy stored gets converted to kinetic energy

0.5*27034.25*2.2^2 = 0.5*350*v^2

v = 19.335 m/sec

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.