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Does the roller coaster ever get higher than the first hill?

The first hill of a roller coaster is always the highest point of the roller coaster because friction and drag immediately begin robbing the car of energy. At the top of the first hill, a car's energy is almost entirely gravitational potential energy (because its velocity is zero or almost zero).



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This places some limits on the design. For example, the coaster car can't go through a loop or over a hill that is taller than the initial hill because going higher would require more energy than it has available. If the track is too long, friction might eventually cause the coaster car to come to a complete stop.

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Absent other energy sources, like linear electric motors or kick wheels, the roller coaster gets all its energy from the chain that drags it up the initial hill. By the second hill, some energy has been lost to friction and there isn't enough to get over a hill that's higher than the first one.

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I the height of the second hill is higher than the first one, then it needs additional energy to climb the second hill. The coaster keeps on losing energy from air resistance and rolling friction between the rails and the coaster wheels and will eventually come to rest.

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Once you start cruising down that first hill, gravity takes over and all the built-up potential energy changes to kinetic energy. Gravity applies a constant downward force on the cars.

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The oldest operating roller coaster is Leap-The-Dips at Lakemont Park in Pennsylvania, a side friction roller coaster built in 1902.

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Almost all roller coaster designers build a track that brings you back down. At the top of the first and tallest hill, your potential energy is at its highest it will ever be on this ride. As you begin to descend, your potential energy decreases until it's all gone at the bottom of the hill.

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The purpose of the coaster's initial ascent is to build up a sort of reservoir of potential energy. The concept of potential energy, often referred to as energy of position, is very simple: As the coaster gets higher in the air, gravity can pull it down a greater distance. You experience this phenomenon all the time.

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Roller coasters almost always begin with an initial vertical drop. A motor hauls the cars to the top of a high hill and from that point on gravity is doing all the work. Typical vertical drops might range in height from 50 - 80 meters.

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We see that velocity of the roller coaster is independent of its mass and is solely dependent on local g and initial h . Therefore, for an ideal roller coaster an empty roller coaster or a full roller coaster will take the same amount of time for a single trip.

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It suggests that the chances of being killed on a rollercoaster are just one in 170 million, while the injury odds are approximately one in 15.5 million.

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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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At the bottom of the loop, gravity and the change in direction of the passenger's inertia from a downward vertical direction to one that is horizontal push the passenger into the seat, causing the passenger to once again feel very heavy.

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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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Are you daring - or, perhaps, crazy - enough to ride the Loop the Loop? The first looping roller coaster was Lina Beecher's infamous Flip Flap Railway, installed at Sea Lion Park. Riding the Flip Flap Railway was a bit of a death wish because it used a perfectly circular loop.

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