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Magnitude and direction of the total force exerted on a roller coaster car by the track

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A roller coaster car of mass 320 kilograms(including passengers) travels around a horizontal curve of radius 35 meters. Its speed is 16 meters per second. What is the magnitude and direction of the total force exerted on the car by the track?

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If you think of the track as a circle, and the roller coaster as a ball travelling around the center of the circle, then you can find the centripetal acceleration of the rollercoaster, which is equal to v^2/r, or 7.3 m/s^2.

This acceleration is always heading away from the center of the circle, meaning the coaster car is exerting Fcentripetal = Fa = 320 * 7.3 = 2.34 kN of force on the tracks. Equivalently, the tracks must exert the same magnitude of ...

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