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What happens to acceleration when a rollercoaster goes through a loop?

The roller coaster train reaches its maximum speed and maximum centripetal acceleration at the bottom of the loop, which can be obtained from energy considerations. In this way, the maximum centripetal acceleration is found to be 5g (upwards) at the bottom of a circular loop, if it is g downwards in the highest point.



When a rollercoaster enters a vertical loop, it experiences a dramatic increase in centripetal acceleration, which keeps the train on the track. As you enter the bottom of the loop, gravity and centripetal force work together, often making you feel "pushed" into your seat with a force of 3.0g to 5.0g. As the train climbs toward the top of the loop, its velocity decreases, and at the very apex, the "g-force" drops significantly. In many modern "clothoid" (teardrop-shaped) loops, designers aim for about 1.0g to 1.5g at the top, which provides a sensation of "weightlessness" while still ensuring enough force exists to keep the wheels in contact with the rails. The change in the radius of the loop is the secret to safety; a perfect circle would require dangerously high entry speeds to clear the top, but the teardrop shape allows for a more controlled, comfortable, and thrilling transition of forces throughout the entire 360-degree rotation.

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For a roller coaster, gravity pulls down on the cars and its riders with a constant force, whether they move uphill, downhill, or through a loop. The rigid steel tracks, together with gravity, provide the centripetal force needed to keep the cars on the arching path as they move through the loop.

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Rollercoaster trains have no engine or no power source of their own. Instead, they rely on a supply of potential energy that is converted to kinetic energy. Traditionally, a rollercoaster relies on gravitational potential energy – the energy it possesses due to its height.

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Basic mathematical subjects such as calculus help determine the height needed to allow the car to get up the next hill, the maximum speed, and the angles of ascent and descent. These calculations also help make sure that the roller coaster is safe. No doubt about it--math keeps you on track.

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