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

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To determine the speed required for a coaster to create a normal force of 2mg at the top of a 12-meter radius loop, the calculations involve centripetal force and gravitational force. The initial attempt resulted in a negative square root, indicating an error in the sign of acceleration. By recognizing that the coaster's acceleration is directed downward, the issue was resolved, leading to the correct speed of 19 m/s. Understanding the direction of forces is crucial in solving such physics problems. This highlights the importance of correctly interpreting acceleration in dynamics.
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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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