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Old Jul 25th 2017, 12:11 PM   #1
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Roller Coaster Physics: From a dumb graduate student who forgot all his education

Out of curiosity and not out of any desire to test this, would you be able to stay on a roller coaster without any restraints going around a loop? (e.g. if you came to a loop without a seatbelt, would you fall out and die)
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Old Jul 25th 2017, 02:38 PM   #2
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A roller coaster on a properly designed loop will generate centripetal forces that will keep you planted in your seat even while upside down. To get technical: if the radial acceleration is greater than acceleration due to gravity then you will not fall out:

$\displaystyle \frac {v^2} R \ge g $

where v = the coaster velocity at the top of the loop in m/s, g = acceleration due to gravity = 9.8 m/s^2, and R is the radius of the loop in meters. So as long as the velocity of the coaster at the top of the loop is greater than $\displaystyle \sqrt {gR} $ you'll be fine.

Last edited by ChipB; Jul 25th 2017 at 02:41 PM.
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