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
upon the relative position of
various parts of a system. A
train of cars on a gravitypowered roller coaster has
more potential energy raised
above the ground at the top of
a hill than it has after falling to
the earth along the hill's
inclined track. In the elevated
position it is capable of doing
more work. By extension, the
higher the lift hill, the greater
the potential energy.
• Potential energy is a property of a
•
system and not of an individual body
or particle. It depends only on its
initial and final configurations; it is
independent of the path the object
travels. The value of potential energy
is arbitrary and relative to the choice
of reference point. Gravitational
potential energy near the Earth's
surface may be computed by
multiplying the weight of an object by
its distance above the reference point.
Potential energy may be converted
into energy of motion, called kinetic
energy. Traditionally potential energy is
included with kinetic energy as a 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
•
in what direction a point is moving.
Because it has direction as well as
magnitude, velocity is known as a
vector quantity and cannot be
specified completely by a number, as
can be done with time or length, which
are scalar quantities.
A point always moves in a direction
that is tangent to its path; for a
circular path, for example, its direction
at any instant is perpendicular to a line
from the point to the center of the
circle (a radius). The magnitude of the
velocity (i.e., the speed) is the time
rate at which the point is moving along
its path.
•
•
Roller coaster rides incur many changes in
speed and direction, or velocity, and the rate
of this change is acceleration. It is not true,
as often thought, that the speed of a car at
the bottom of a hill is equal to its initial
velocity plus its drop velocity; actually the
greater the drop height, the less initial
velocity influences final velocity. Along the
same lines, speed is not directly proportional
to the drop height but to the square root of
the drop height. Doubling the speed of a
coaster ride requires quadrupling the height
of the hill.
AT THIS POINT IN THE RIDE . . . the track
curves back upward and the speed drops as
the roller coaster climbs the second hill.
Owing to the change in velocity, the riders
experience upward centripetal
acceleration in the form of positive gforces. 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.