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 16 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 430 kg . For safety reasons, the spring constant should be 14 % larger than the minimum needed for the car to just make it over the top.

A)

What spring constant should you specify?

Express your answer to two significant figures and include the appropriate units.

B)

What is the maximum speed of a 330 kg car if the spring is compressed the full amount?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

given

height of hill, h = 13 m

depth of lowest point = d = 16 m from th etop point

a. spring compression, x = 2.2m

spring constant = k

mass, m = 430 kg

hence

mgh = 0.5kx^2

k = 2mgh/x^2 = 22660.289256198 N/m

using 14% larger value of k

k = 25832.7297520 N/m

b. maximum speed of the car = v

0.5mv^2 = mgd + (0.5kx^2 - mgh)

0.5mv^2 = mg(d - h) + 0.5kx^2

v = 18.69835286 m/s

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