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 2.6 m and that a loaded car will have a maximum mass of 400 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.

(B) what is the maximum speed of a 360 kg car if the spring is compressed the full amount?________m/s

Explanation / Answer

Energy from the spring = Energy absorbed by roller coaster to be able to make it to the top of a 10-meter hill

Energy from spring = (1/2)(k)x^2

where

k = spring constant
x = maximum length where spring can be compressed = 2 m (given)

For the roller coaster to make it to the top of the 10-m hill, its energy must be

Potential energy = mgh

where

m = 400 kg (given)
g = acceleration due to gravity = 9.8 m/sec^2 (constant)
h = 12 m (given)

Therefore,

(1/2)(k)(2.6)^2 = (400)(9.8)(12)

k = 400(9.8)(12)/2

k = 23520 N/m

<< What spring constant should you specify? >>

Since it is required that the spring constant must be 10% larger than the minimum required, then

k = 1.1*23520

k = 25872 N/m

<< What is the maximum speed of a 360 kg car if the spring is compressed the full amount? >>

Again, applying the law of conservation of energy,

(1/2)(25872)(2.6)^2 = (1/2)(360)(V^2)

where

V = maximum velocity of 360-kg car

Solving for "V",

V = 22.04m/sec.

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