Dynamics of uniform circular motion

[bulbasaur88]

A special electronic sensor is embedded in the seat of a car that takes riders around a circular loop-the-loop ride at an amusement park. The sensor measures the magnitude of the normal force that the seat exerts on a rider. The loop-the-loop ride is in the vertical plane and its radius is 21 m. Sitting on the seat before the ride starts, a rider is level and stationary, and the electronic sensor reads 770 N. At the top of the loop the rider is upside down and moving, and the sensor reads 350 N. What is the speed of the rider at the top of the loop?

I think this problem is a great problem for centripetal acceleration in vertical circular motion; however, I cannot check to see if I understand the concept behind the problem because there is no answer provided. Could someone please let me know if at least my set-up is correct?

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Given
R = 21 meters
W = 770 N
m = 770/9.8 kg
F_N = 350 N at the top

At the top:
F_c = mg + F_{N =} mv² / R
R[F_N + mg] = mv²

Plug-n-Chug to solve for V
V = 17.3 m/s

 

[Hootenanny]

I haven't checked the numbers, but your set up looks fine to me

 

[bulbasaur88]

FANTASTIC THANK YOU