A special electronic sensor is embedded in the seat of a car that takes riders a

Question

A special electronic sensor is embedded in the seat of a car that takes riders around a circular loop-the-loop 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 19 m. Sitting on the seat before the ride starts, a rider is level and stationary, and the electronic sensor reads 760 N. At the top of the loop, the rider is upside-down and moving, and the sensor reads 390 N. What is the speed of the rider at the top of the loop?

Explanation / Answer

When the rider is at the top of the loop, the centripetal force is directed toward the center (as always) which is downward relative to the rider. Take down as positive, and the forces acting on the rider are the normal force (-n, upward) and the weight of the rider (w, downward). From Newton's 2nd law: ?F(c) = ma(c) = w - n Centripetal acceleration, a(c) = v

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