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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?

https://brainmass.com/physics/acceleration/magnitude-and-direction-of-the-total-force-exerted-on-a-roller-coaster-car-by-the-track-9782

#### Solution Preview

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 ...

#### Solution Summary

The solution shows good explanations and calculations to arrive at the answer.

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