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

k= 27000 N/m

( I tried 18.37 but the answer was wrong )

Explanation / Answer

let the spring constant needed is k

Now,

using conservation of energy

for roller coaster to reach the top of 11 m hill

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

0.5 * k * 2^2 = 450 * 9.8 * 11

k = 24255 N/m

Now , as the spring constant should be 13 % higher

spring constant = 24255 * 113/100

spring constant = 27408 N/m

the spring constant of the spring is 27408 N/m

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

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