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

[mike_302]

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!

 

[Doc Al]

Hint: In which direction is the coaster's acceleration? Is that positive or negative?

 

[mike_302]

oh! okay. so acceleration is down. GOT IT! WOW! HUGE thanks!