A Roller Coaster Traveling With an Initial Speed of 15

Contents

## Roller Coaster Physics

Source: http://www.flickr.com/photos/jekert/3089042791

One can all-time proceeds an appreciation of roller coaster physics past riding on a roller coaster and experiencing the thrill of the ride. There are many variations on roller coaster design. But needless to say, they all involve going around loops, bends, and twists at loftier speed.

The typical roller coaster works by gravity. In that location are no motors used to ability it during the ride. Starting from balance, it simply descends down a steep colina, and converts the (stored) gravitational potential energy into kinetic free energy, by gaining speed. A small corporeality of the energy is lost due to friction, which is why it’s impossible for a roller coaster to return to its original height after the ride is over.

The roller coaster uses a motorized lift system to return to its original position at the top of the initial hill, ready for the next ride.

The figure below illustrates the concept.

Source: http://en.wikipedia.org/wiki/Flying_roller_coaster. Author: http://en.wikipedia.org/wiki/File:GL-X-Flight.jpg

Bold no friction losses, when the center of mass of the roller coaster falls a vertical height

*h*

(from the initial colina) it will take a kinetic energy equal to the gravitational potential energy stored in the pinnacle

*h*.

This tin can exist expressed mathematically as follows.

Permit

*W*

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

Then,

where

*m*

is the mass of the roller coaster, and

*yard*

is the acceleration due to gravity, which equals 9.eight yard/due south^{2}

on globe’due south surface.

The kinetic energy of the roller coaster is:

where

*v*

is the speed of the roller coaster.

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

Thus,

mass cancels out, and

This outcome is nice considering it allows usa to gauge the speed of the roller coaster knowing only the vertical height

*h*

that it barbarous (on any function of the track). Of grade, due to friction losses the speed will exist a bit less than this, but information technology is very useful nonetheless.

Some other important aspect of roller coaster physics is the dispatch the riders experience. The main type of acceleration on a roller coaster is

*centripetal acceleration*. This blazon of acceleration tin produce strong

*g-forces*, which can either push yous into your seat or make you feel like you’re going to fly out of it.

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

Source: http://www.flickr.com/photos/joeshlabotnik/2479908266

where

*R*

is the radius of the loop.

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

Centripetal acceleration tin too occur when the riders twist around a track, as illustrated in the effigy below.

Source: http://en.wikipedia.org/wiki/Roller_coaster_elements. Author: http://en.wikipedia.org/wiki/User:BrandonR

The centripetal acceleration experienced by the riders twisting around the track is:

where

*westward*

is the rate of twist (in radians/2nd) of the riders as they move along the track, and

*R*

is the radius of the twist at the location of the passenger.

The acceleration experienced past riders on roller coasters tin can be quite high, as much equally iii-6

*1000*

(which is 3-half dozen times the force of gravity).

In summary, the physics of roller coasters (in general) is a combination of gravitational potential free energy converted into kinetic energy (high speed), and using this speed to create centripetal dispatch around unlike portions of the rail.

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### A Roller Coaster Traveling With an Initial Speed of 15

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