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gravitational potential energyA = kinetic energyB + gravitational potential energyB or mghA= mvB2 + mghB as seen in the equation above. The value of 30 m/s is reasonable for motion of a roller-coaster.
The underlying principle of all roller coasters is the law of conservation of energy, which describes how energy can neither be lost nor created; energy is only transferred from one form to another.
What does it take? Roller coaster engineering falls under the domain of the mechanical engineer. Mechanical engineers apply the principles of engineering, physics, and material science for the design, analysis, manufacturing, and maintenance of mechanical systems.
To accurately model every component of roller coaster design, a branch of math called calculus is needed. Calculus is used to create and analyze curves, loops, and twists along the roller coaster track. It helps with slope calculations and finds the maximum and minimum points along the track.
Calculus is a crucial part of the designing of roller coasters. It is used to notify engineers of speeds, velocities, etc. at many different points along the track. This information is used to make sure that all passengers are safe when they ride, and make the coasters enjoyable.
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An example of a polynomial function that represents a basic rollercoaster would be f(x)= -0.000833(x3 + 12x2 -580x -1200). The graphs shows two basic loops that are formed from the function and how it would mirror a ride.
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When building a roller coaster, designers and engineers consider factors like the intended rider, preferred material, cart type, and track layout. As a result, we end up with designs that vary from a thematic coaster like Space Mountain to a thrill ride like the Superman Ride of Steel.

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