1.) You are designing a roller coaster for a new amusement park on the Moon. You
ID: 1473010 • Letter: 1
Question
1.) You are designing a roller coaster for a new amusement park on the Moon. You envision a loop with a radius of 60 meters in your track. (a) What minimum speed at the top will a car have to possess in order to successfully negotiate the loop? The gravitational acceleration on the Moon is 1.6 m/s2. (b) What speed at the top of the loop would a car need to have if the same roller coaster was built on Earth?
1.) You are designing a roller coaster for a new amusement park on the Moon. You envision a loop with a radius of 60 meters in your track. (a) What minimum speed at the top will a car have to possess in order to successfully negotiate the loop? The gravitational acceleration on the Moon is 1.6 m/s2. (b) What speed at the top of the loop would a car need to have if the same roller coaster was built on Earth?
2.) Find the minimum speed of a roller coaster at the top of a vertical loop for the roller coaster to successfully negotiate the loop. The radius of the loop is 22 mExplanation / Answer
(a)
In this case the centrifugal force must be equal to weight. Mathematically, it can be expressed asm
m v2 /R = m g
Rearrange for v
v = gR = (1.6 x 60 ) = 9.7979 m/s
Round off the result to 3 significant digits
Minimum speed , v = 9.80 m/s
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(b)
On Earth:
The speed is
v = r g
v = ( 9.8 ) ( 60 ) = 588
On Earth, the speed = 24.248 m/s
Round off the result to 3 significant digits
v = 24.2 m/s
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Velocity:
v = rg = ( 22 m ) ( 9. 8) = 14.7 m/s
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