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The Physics Behind a Roller Coaster:


The Physics of a Roller Coaster:


The making of these fun rides involves an extensive understanding of the complex physics behind them. There are many variations on roller coaster design. But needless to say, they all involve going around loops, bends, and twists at high speed.
There are no motors used to power the ride. All movement is due to gravity. The ride starts by descending down a steep hill, converting the stored gravitational potential energy into kinetic energy, by gaining speed. It is impossible for a roller coaster to return to its original height because a small amount of the energy is lost due to friction. The roller coaster returns to its original position using a motorized lift system.


Assuming no friction is lost when the center of mass of the roller coaster falls a vertical height h (from the initial hill) it will have a kinetic energy equal to the gravitational potential energy stored in the height h.

This can be expressed mathematically as follows.

Let W be the gravitational potential energy at the top of the hill.

Then,

equation for gravitational potential energy of roller coaster at height h
where m is the mass of the roller coaster, and g is the acceleration due to gravity, which equals 9.8 m/s2 on earth's surface.

The kinetic energy of the roller coaster is:

equation for kinetic energy of roller coaster

where v is the speed of the roller coaster.

If we assume no friction losses, then energy is conserved. Therefore,

conservation of energy for roller coaster

Thus,

conservation of energy for roller coaster 2

mass cancels out, and

velocity of roller coaster
The results allow us to approximate the speed of the roller coaster knowing only the vertical height h that it fell (on any part of the track). Of course, due to friction lost the speed will be a little less than predicted.

Acceleration is important in roller coaster physics. The main type of acceleration on a roller coaster is centripetal acceleration. Centripetal Acceleration can produce strong g-forces, which can either push you into your seat or make you feel like you're going to fly out of it.

Centripetal acceleration occurs mainly when the roller coaster is traveling at high speed around a loop, as illustrated in the figure below.


where R is the radius of the loop.

The centripetal acceleration experienced by the riders going around the loop is:

centripetal acceleration experienced by the riders on a roller coaster going around a loop

Centripetal acceleration can also occur when the riders twist around a track, as illustrated in the figure below.

The acceleration experienced by the riders can be as high as 3-6 g (which is 3-6 times the force of gravity)

In conclusion, the physics of roller coaster, in general, is a combination of potential energy converted into kinetic energy (high speed), and using this speed to create centripetal acceleration around different portions of the track.

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