Why cant the second hill of a roller coaster be taller than the first?

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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(d) Due to frictional lost, the mechanical energy of the coaster has decreased, so the second hill has to be lower 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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Each gain in height corresponds to the loss of speed as kinetic energy (due to speed) is transformed into potential energy (due to height). Each loss in height corresponds to a gain of speed as potential energy (due to height) is transformed into kinetic energy (due to speed).

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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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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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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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In most roller coasters, the hills decrease in height as the train moves along the track. This is necessary because the total energy reservoir built up in the lift hill is gradually lost to friction between the train and the track, as well as between the train and the air.

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Every roller coaster begins with a very high hill. The higher the hill, the greater the potential or stored energy of the roller coaster car. When the car reaches the bottom of the hill, the potential energy has been completely converted into kinetic energy which is the energy of motion.

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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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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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Mass does not make a roller coaster go faster but it does make it harder to slow down. This is why amusement parks test roller coasters with dummies filled with water. The water dummies increase the mass of the train making it harder for the resistance forces to slow it down so it's less likely to get stuck.

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It is impossible for the back of the train to exceed the speed of the front, because all of the cars are connected. However, the back may feel faster than the front at some points, due to the front pulling it. If the front is already going down a drop, than it is going to whip the back over the crest faster.

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The potential energy of the roller coaster when it is at the top of a hill is converted into kinetic energy as the roller coaster speeds down the hill. As the roller coaster goes up another hill, it slows down. The kinetic energy is converted into potential energy.

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In roller coasters, the two forms of energy that are most important are gravitational potential energy and kinetic energy. Gravitational potential energy is the energy that an object has because of its height and is equal to the object's mass multiplied by its height multiplied by the gravitational constant (PE = mgh).

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