*Video of a moving Roller Coaster*

Conservation of Energy [ Moving Roller Coaster ]

http://www.youtube.com/watch?v=j3eqpYgyVJw&feature=related

Done by:

Mariam ALKhouri 

11.57 

*PHOTOS*

*Clothoid Loop*

 

Roller coasters today employ clothoid loops rather than the circular loops of earlier roller coasters.  This is because circular loops require greater entry speeds to complete the loop.  The greater entry speeds subject passengers to greater centripetal acceleration through the lower half of the loop, therefore greater G’s.  If the radius is reduced at the top of the loop, the centripetal acceleration is increased sufficiently to keep the passengers and the train from slowing too much as they move through the loop.  A large radius is kept through the bottom half of the loop, thereby reducing the centripetal acceleration and the G’s acting on the passengers.

*G-Forces*

G-forces are used for explaining the relative effects of centripetal acceleration that a rider feels while on a roller coaster.  Consequently, the greater the centripetal acceleration, the greater the G-forces felt by the passengers.  A force of 1 G is the usual force of the Earth’s gravitational pull that a person feels when they are at rest on the Earth’s surface; in other words, it can be described as a person’s normal weight.  When a person feels weightless, as in free fall or in space, they are experiencing 0 G’s.  When the roller coaster train is going down a hill, the passengers usually undergo somewhere between 0 and 1 G.  However, if the top of the hill is curved more narrowly than a parabola, the passengers will experience negative G’s as they rise above the seat and get pushed down by the lap bar.  This is because gravity and the passengers’ inertia would have them fall in a parabolic arc.  G-forces greater than 1 can be felt at the bottom of hills as the train changes direction.  In this case the train is pushing up on the passengers with more than the force of gravity because it is changing their direction of movement from down to up.  G-forces that are felt when changing direction horizontally are called lateral G’s.  Lateral G’s can be converted into normal G-forces by banking turns.

*Centripetal Acceleration*

Curves are an essential part of a roller coaster, and centripetal acceleration is part of moving in a circular path.  Therefore, centripetal acceleration is also an essential part of a roller coaster. 

Centripetal acceleration points toward the center of the circular path of the train, but is felt by passengers as a force pushing them to the outer edge of the circular path.  This feeling is often described as centrifugal force, although there is no actual force pushing or pulling passengers away from the circle.  The “centrifugal force” is actually your body’s inertia, or its resistance to the train’s change in direction: your body wants to continue in a straight line and attempts to do so as the train turns.  Luckily, your body is strapped into the roller coaster train, otherwise your body would continue in the straight path that the train was following before it entered the curve.

The equation for centripetal acceleration is:

a_r =  v² / r

Where a_r is centripetal acceleration, v is velocity in meters per second, and r is the radius of the circle in meters.  This means that the higher the train’s velocity, the greater the centripetal acceleration.  This also means that the smaller the curve of the path being traveled, the greater the centripetal acceleration.  Because of this, many high-speed roller coasters use banked turns rather than the flat ones that are safe for slower speeds. Banking the turns in a roller coaster gives you the feeling of being pushed into your seat rather than being thrown to the side of the car.

*Friction*

 

For a non-idealized roller coaster system, not all of the energy is conserved.  Friction is the main cause of energy leaks in the system and the reason why mechanical energy is not fully conserved for a real roller coaster.  This is because friction is a nonconservative force. Nonconservative forces are forces that cause a change in total mechanical energy.  Friction opposes motion by working in the opposite direction.  The friction between the train and its tracks as well as between the train and the air take energy out of the system, slowing the train and creating both heat and sound.  This effect is most noticeable at the end of the ride as all remaining kinetic energy is taken out of the system though brakes.  Because of the energy leaks due to friction, each successive hill or loop on a roller coaster must be shorter than all the hills or loops previous to it, otherwise the train will not have enough energy to make it all the way over.