DataAnalysis

Data and Calculations:
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Graph 1: Altitude(m) vs Time (sec) ** Altitude was based off of sea level, so in order to find the exact results subtraction was necessary 90' ~ 27.43m **
 * Graph 2: x Acceleration (m/s²)

**Graph 3: y Acceleration (m/s²)**

**Graph 4: z Acceleration (m/s²)**



__**Calculations:**__

PE + KE = PE + KE ← Law of Conservation of Energy

mgy = 1/2mv2

Mass cancels out

90 feet = 27.43 meters, 51 mph = 22.8 m/s

(9.8) 27.43m = ½ 22.82

268.81 J = 259.92 J


 * 8.89 Joules** of energy lost to friction.

__**Relativity****:**__

Though Hershey claims that the velocity at which each cart travels is about 51 miles per hour (22.8m/s), Newton’s theory of relativity begs to differ. Of course, whether or not that statement is true depends on the frame of reference. From a “rest” point of view, both carts are in fact moving at about 22.8 meters per second at their top speed, proving that Hershey Park is true to its word. However, when a rider is looking from one cart to the other, the velocity of the other cart ranges from 0, when the carts are parallel to each other and moving in the same direction, to 45.6 meters per second, when the carts are moving in opposite directions. Because the carts are not moving at a speed that is close to the speed of light, their vectors can simply be added or subtracted, depending on the direction that one is moving relative to the other. Knowing that both carts move at the same speed relative to a ground watcher, the maximum speed that one can be moving relative to the other is exactly double the speed of one of them, while the minimum is 0. __**Centripetal Force:**__

Most of the time on the ride, the cart is moving in an up and down, wavelike motion, but in order to keep the ride confined to a specific space, and to provide added fun for riders, there are several turns in the ride, and one that almost makes a full circle. During these turns, there is not only a downward acceleration due to gravity, but also an acceleration pointing to the center of the circle making up the turn, called centripetal acceleration. The normal force of the track on the cart creates this acceleration. Without the track, the cart would move in a straight line and would fly into the air, but lucky for all Hershey park attendees, the track keeps the cart from doing such.