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Objective: To identify whether positive, negative, or zero work is being done, to identify the force that is doing the work, and to describe the energy transformation associated with such work.

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Roller Coaster Loops

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Investigate the effect of heights and radius of circular loops on the speeds and number of Gs.

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Investigate coaster design considerations that effect the safety and the thrill of the ride.

Explore data associated with roller coaster loops and the rider’s experience.

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Compare and contrast circular loops with clothoid loops.

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Investigate the effect of heights and radius of clothoid loops on the speeds and number of Gs.

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Roller Coaster Loops Today’s coasters provide riders with weightless sensations and abnormally large G forces. Weightless sensations occur when the seat pushes on riders with a force that is less than their weight. Large G forces occur when the seat pushes with a force much greater than their weight. The number of Gs (Gs) is the ratio of this seat force to the rider's weight. The coaster loop provides much of this thrill. The earliest designs included circular loops as shown in Figure 1. Table 1 depicts the estimated speed (v) and the Gs for a rider starting from a 60-meter high drop. Because of the inherent dangers of circular loops and of the advent of tubular steel coasters, non-circular loops became popular in coaster designs. The teardrop-shaped loop with its continuously-changing radius, shown in Figure 2, is termed a clothoid loop. Table 2 shows the effect of the radii (R) at the top and bottom of a loop upon the rider experience.

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Each Science Reasoning task is based on a passage or story that presents data and information or describes an experiment or phenomenon. Students must combine an understanding of science content and science reasoning skills (science practices) to answer questions about the passage or story. Tap anywhere to view the passage.

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Stopping Distance One aspect of safe driving involves the ability to stop a car readily. This ability depends upon the driver's alertness and readiness to stop, the conditions of the road, the speed of the car, and the braking characteristics of the car. The actual distance it takes to stop a car consists of two parts - the reaction distance and braking distance. When a driver sees an event in his/her field of view that might warrant braking (for example, a dog running into the street), a collection of actions must be taken before the braking actually begins. First the driver must identify the event and decide if braking is necessary. Then the driver must lift his/her foot off the gas pedal and move it to the brake pedal. And finally, the driver must press the brake down its full distance in order to obtain maximum braking acceleration. The time to do all this is known as the reaction time. The distance traveled during this time is known as the reaction distance. Once the brakes are applied, the car begins to slow to a stop. The distance traveled by the car during this time is known as the braking distance. The braking distance is dependent upon the original speed of the car, the road conditions, and characteristics of the car such as its profile area, mass and tire conditions. Figure 1 shows the stopping distance for a Toyota Prius on dry pavement resulting from a 0.75-second reaction time. The reaction time of the driver is highly dependent upon the alertness of the driver. Small changes in reaction time can have a large effect upon the total stopping distance. Table 1 shows the reaction distance, braking distance, and total stopping distance for a Toyota Prius with an original speed of 50.0 mi/hr and varying reaction times.

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