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## Homework Statement

A roller coaster at the nearby amusement park Physics Hill, has a large circular loop where cars travel at the top of the loop at 25.0 m/s causing the riders to enjoy an acceleration of 3g. Assuming the height of this loop is the same as the diameter, how high is the loop?

## Homework Equations

g = 9.8 m/s^2

v^2/r = a

_{centripetal}

## The Attempt at a Solution

I figured at the top of the loop the acceleration acting on the car is all downward. There is already 1g of acceleration on the car so the centripetal acceleration plus the existing 1g needs to equal the 3g's of acceleration the riders are experiencing. However my answer for the radius seems unrealistic.

v^2/r + g = 3g

v^2/r = 2g

25^2/r = 19.6

r = 31.89m

d = 63.78m