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									PHYSICS OF ROLLERCOASTERS


        Nathaniel McClain II
             PHY 3091
      Florida State University
PHYSICS OF ROLLERCOASTERS

             • Allen, John (b. May 21,
               1907, Philadelphia, Pa.,
               U.S.--d. Aug. 17, 1979,
               Philadelphia), American
               designer of roller coasters
               who ignited the coaster
               boom of the 1970s
               following the mid-century
               decline in amusement
               parks.
   PHYSICS OF ROLLERCOASTERS
       POTENTIAL ENERGY
• Stored energy that depends            • Potential energy is a property of a
  upon the relative position of             system and not of an individual body
                                            or particle. It depends only on its
  various parts of a system. A              initial and final configurations; it is
  train of cars on a gravity-               independent of the path the object
  powered roller coaster has                travels. The value of potential energy
  more potential energy raised              is arbitrary and relative to the choice
                                            of reference point. Gravitational
  above the ground at the top of            potential energy near the Earth's
  a hill than it has after falling to       surface may be computed by
  the earth along the hill's                multiplying the weight of an object by
  inclined track. In the elevated           its distance above the reference point.
  position it is capable of doing       •   Potential energy may be converted
                                            into energy of motion, called kinetic
  more work. By extension, the              energy. Traditionally potential energy
  higher the lift hill, the greater         is included with kinetic energy as a
  the potential energy.                     form of mechanical energy so that the
                                            total energy in gravitational systems
                                            can be calculated as a constant.
PHYSICS OF ROLLERCOASTERS
    POTENTIAL ENERGY

             • AT THIS POINT IN THE RIDE .
               . . at the top of the lift hill, the
               potential energy of the
               gravity-powered coaster is at
               its greatest, because the
               coaster is at its highest
               elevation. Beyond this point,
               as gravitation gives the car
               velocity, the potential energy
               is transferred into kinetic
               energy. The coaster does,
               however, regain some
               potential energy each time it
               climbs another hill or ramp on
               the rest of the ride.
    PHYSICS OF ROLLERCOASTERS
             GRAVITY
• In mechanics, the universal force
   of attraction that affects all
   matter. It is the weakest of the
   four basic physical forces, but, on
   the scale of everyday objects near
   the Earth, it is the dominant one.
   The fall of bodies released from a
   height to the surface of the Earth
   and the weight of resting bodies
   at or near the surface are the
   most familiar manifestations of
   gravitation. Gravity is the
   traditional source of power for
   roller coasters, accelerating the
   cars through all the twists and
   turns of the ride, from the lift hill
   through to the brake run.
     PHYSICS OF ROLLERCOASTERS
              VELOCITY
• Quantity that designates how fast and         •   Roller coaster rides incur many changes in
    in what direction a point is moving.            speed and direction, or velocity, and the
    Because it has direction as well as             rate of this change is acceleration. It is not
                                                    true, as often thought, that the speed of a
    magnitude, velocity is known as a               car at the bottom of a hill is equal to its
    vector quantity and cannot be                   initial velocity plus its drop velocity; actually
    specified completely by a number, as            the greater the drop height, the less initial
    can be done with time or length, which          velocity influences final velocity. Along the
    are scalar quantities.                          same lines, speed is not directly proportional
                                                    to the drop height but to the square root of
•   A point always moves in a direction             the drop height. Doubling the speed of a
    that is tangent to its path; for a              coaster ride requires quadrupling the height
    circular path, for example, its direction       of the hill.
    at any instant is perpendicular to a line   •   AT THIS POINT IN THE RIDE . . . the track
    from the point to the center of the             curves back upward and the speed drops as
    circle (a radius). The magnitude of the         the roller coaster climbs the second hill.
    velocity (i.e., the speed) is the time          Owing to the change in velocity, the riders
    rate at which the point is moving along         experience upward centripetal
    its path.                                       acceleration in the form of positive g-
                                                    forces. This compression makes them feel
                                                    heavier than normal. On the climb the
                                                    coaster regains some potential energy
                                                    that it had lost to kinetic energy on the
                                                    previous descent.
PHYSICS OF ROLLERCOASTERS
      ACCELERATION
             • Time rate at which a velocity is
                 changing. Because velocity has both
                 magnitude and direction, it is called a
                 vector quantity; acceleration is also a
                 vector quantity and must account for
                 changes in both the magnitude and
                 direction of a velocity.
             •   If the velocity of a roller coaster
                 moving on a straight path is increasing
                 (i.e., if the speed, which is the
                 magnitude of the velocity, is
                 increasing), the acceleration vector will
                 have the same direction as the velocity
                 vector. If the velocity is decreasing
                 (that is, the coaster is decelerating),
                 the acceleration vector will point in the
                 opposite direction. So, whether the
                 coaster is increasing speed down a hill
                 or decreasing speed up a hill, it is
                 regarded as acceleration in the
                 mathematical sense.
   PHYSICS OF ROLLERCOASTERS
         ACCELERATION
• Changes in acceleration greatly contribute to the thrill of
  a roller coaster ride. A rider may feel greater sensations
  in a low-speed coaster with sharp acceleration changes
  than on a faster coaster with a smoother ride. Pure
  speed is often not as recognizable as the surge of
  acceleration during a coaster ride.
• A common fallacy is that acceleration increases along
  with the weight of the riders and the car, when actually
  the acceleration of a coaster in free-fall is independent
  of its mass. Acceleration does increase, however, with a
  steeper angle of descent.
   PHYSICS OF ROLLERCOASTERS
         ACCELERATION
• AT THIS POINT IN THE RIDE .
  . . at the bottom of the second
  hill, the coaster, in theory,
  reaches an instant of zero
  acceleration, at the point
  where its speed is greatest,
  relative to anywhere else on
  that hill. Zero acceleration also
  occurs for an instant at the top
  of a hill, where in turn the
  speed is at its lowest level. At
  the bottom of the dip, the
  riders experience compression,
  or acceleration stress,
  owing to forces greater than
  their usual weight.
   PHYSICS OF ROLLERCOASTERS
            FRICTION
• Force that resists the sliding or rolling of one
  solid object over another. Frictional forces, such
  as the traction needed to walk without slipping,
  may be beneficial; but they also present a great
  measure of opposition to motion. Friction, along
  with air resistance, or wind drag, are dissipative
  forces that are neglected in idealized discussions
  of fundamental mechanics, in which gravitation
  is the only force considered.
PHYSICS OF ROLLERCOASTERS
   PHYSICS OF ROLLERCOASTERS
      ACCELERATION STRESS
• Physiological changes
  that occur in the human
  body in motion as a result
  of rapid increase of
  speed. Rapid acceleration
  and surges in
  acceleration are felt more
  critically than are gradual
  shifts.
   PHYSICS OF ROLLERCOASTERS
       CENTRIFUGAL FORCE
• Quantity, peculiar to a
  particle moving on a
  circular path, that has the
  same magnitude and
  dimensions as the force
  that keeps the particle on
  its circular path (the
  centripetal force) but
  points in the opposite
  direction.
     PHYSICS OF ROLLERCOASTERS
         KINETIC ENERGY
• Form of energy that an object or a particle has
  by reason of its motion. If work, which transfers
  energy, is done on a roller coaster by applying a
  net force, such as gravity, the coaster speeds up
  and thereby gains kinetic energy. Kinetic energy
  is a property of a moving object and depends
  not only on its motion but also on its mass. The
  kind of motion may be translation (or motion
  along a path from one place to another),
  rotation about an axis, vibration, or any
  combination of these.

								
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