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## Homework Statement

Consider a frictionless roller coaster. The acceleration due to gravity is 9.8 ms

^{-2}. Passenger cars start at point A with zero initial speed, accelerate as they go down to a point B, swing around the vertical circular loop B-C-B of radius 15m, then go on towards further adventures. When a car goes through the top of the loop, point C, the passengers feel weightless. What is the height of the starting point A above the loops bottom, point B?

## Homework Equations

U

_{gi}+KE

_{i}=U

_{gf}+KE

_{f}

mgh

_{i}+.5mv

_{i}

^{2}=mgh

_{f}+.5mv

^{2}

_{f}

v[tex]\geq[/tex][tex]\sqrt{gr}[/tex]

## The Attempt at a Solution

Since the cart is at the top of the track and has zero initial speed the initial K.E. is cancelled out. Also since the final location of the cart is the refrence point, the U

_{gf}will be cancelled out, so I am left with the following relationship:

mgh=.5mv

^{2}

V= 12.1244 m/s

h=[tex]\frac{v

^{2}}{2g}[/tex]

=7.5m

This answer is clearly incorrect because the radius of the loop alone is 15m. Any clues as to where I am missing the mark? Thanks in advance.

Joe