(Note: You will need to understand cross multiplication, constants, variables, squares and square roots in order to understand this reading. They are explained in the Mathematical Glossary. In introducing this lesson, your teacher will discuss these and other important math terms that are new to members of your class.)
"Please tell everyone good-bye for me" or "I don't know why I'm doing this." These are remarks you may hear if you are waiting in line to take a roller coaster ride. Why, for the last hundred years, has the roller coaster been the undisputed "king of the park?"
The answers lie within us: the challenge of the unknown, the excitement and thrill of the swift and steep falls, the quick turns, the momentary feelings of extreme heaviness alternating with weightlessness. But why don't we experience the sensations of falling while riding upside down in the roller coaster? The answers can be found in some basic fundamentals of physics, known to all engineers:
Centrifugal force (F) = mv2/R
Potential energy (PE) = mgh
Kinetic energy (KE) = 1/2 mv2
where
m = the mass of the train and riders
v = the speed of the train, in feet per second (ft/s)
R = the radius of the turn
h = height, feet
g = acceleration due to gravity, or 32.2 ft/s2
In designing a roller coaster in this example, you will assume that a centrifugal force of 2mg is to be achieved. This is twice the force that gravity would normally exert on the train and its riders. Then, when the riders are riding upside down, they will feel a force equal to the normal force of gravity holding them in the car. With F now equal to 2mg, we have
F = mv2/R = 2mg
Your teacher will explain to the class how all these equations can be used to design a roller coaster.
DEFINITIONS:
Centrifugal force:
The force that causes a body revolving around a center (for example, a ball on a string that you are swinging in circles) to tend to move outward (away from the center). If you were swinging a ball on a string and released the string at some instant, the ball would stop moving in its circular path and would continue moving in a straight line.
Centripetal force:
The radial force required to keep a particle or object moving in a circular path, which can be shown to be directed toward the center of the circle.
Gravity:
The force of attraction that pulls all objects toward the earth's surface. Gravity causes falling objects to accelerate at a rate of 32.2 feet per second, or 32.3 ft/s2. This value is a constant and is the same for all objects regardless of their mass or weight.
Kinetic Energy:
The energy a body possesses because of its motion or velocity.
Potential Energy:
The capacity to do work, or the energy available, due to the position of a body or its configuration. An object that's in a position from which it can roll downhill or drop has potential energy.
Radius:
One half the diameter of a circle; also, a line drawn from the center of a circle to a point on the circumference, or boundary, of the circle.
Rise:
An upward slope; a movement upward. | 
