Finding the Optimal Speed for a Coaster Loop: Solving for Centripital Forces

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SUMMARY

The discussion focuses on calculating the speed required for a roller coaster to maintain a normal force of 2mg at the top of a clothoid loop with a radius of 12 meters. The correct speed determined is 19 m/s. The initial attempt led to a negative square root, indicating an error in the sign of the acceleration. The resolution involved recognizing that the coaster's acceleration is directed downward, which clarified the calculations.

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  • Ability to manipulate algebraic expressions involving square roots
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Homework Statement


1. a) Determine the speed required by a coaster that would cause a rider to experience a normal force of 2mg at the top of a clothoid loop where the radius is 12meters.


Homework Equations





The Attempt at a Solution



http://i160.photobucket.com/albums/t161/mike_302/physicsq.jpg

That is my attempt at aa solution. Now, the only problem is that I get a square root negative... Obviously imaginary. Can't do it. But if I made the number positive, I get the right value of 19m/s for speed.

Somewhere/somehow, I need to cancel out the negative in there. Can someone explain how?

Thanks!
 
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Hint: In which direction is the coaster's acceleration? Is that positive or negative?
 
oh! okay. so acceleration is down. GOT IT! WOW! HUGE thanks!
 

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