Roller coasters actually incorporate the simple physics that I have just learnt this year. The cars on the roller coaster move not by self-powering. Instead, the roller coaster is pulled up with a chain or cable along the lift hill only to the first peak of the coaster track, which is the tallest hill of the ride. The law of the conversion of energy then comes into the picture; energy can neither be destroyed nor created, thus the loss in potential energy = the gain in kinetic energy.
As the roller coaster rise up the lift hill, it gains potential energy. The formula for potential energy is given by PE = mgh, where m is mass, g is acceleration due to gravity and h is the height above ground. Thus, the roller coaster will have the highest potential energy at the highest peak.
The potential energy accumulated by the rise in height is transferred to kinetic energy as the cars race down the first downward slope. The formula for kinetic energy is given by KE = 1/2mv2. Thus, the roller coaster has the highest speed and kinetic energy at the lowest peak, when most of the potential energy has been converted to kinetic energy.
Kinetic energy can then be converted back into potential energy as the train moves up again to the second peak. This hill is necessarily lower, as some mechanical energy would be lost to friction. Through this, roller coasters are able to complete the rest of the ride without any mechanical assistance.
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