After this activity, students should be able to:

• The underlying principle of all roller coasters is the Law of Conservation of Energy, which states that energy can neither be lost nor can it be created. Energy is only transferred from one form to another. In roller coasters, the two forms of energy that are most important are gravitational potential energy and kinetic energy. Gravitational potential energy is the energy that an object has because of its height and is equal to the object's mass multiplied by its height multiplied by the gravitational constant (P.E. = mgh). Gravitational potential energy is greatest at the highest point of a roller coaster and least at the lowest point. Kinetic energy is energy an object has because of its motion and is equal to one-half multiplied by the mass of an object multiplied by its velocity squared (K.E. = 1/2 mv²). Kinetic energy is greatest at the lowest point of a roller coaster and least at the highest point. Potential and kinetic energy can be exchanged for one another, so at certain points the cars of a roller coaster may have just potential energy (like at the top of the first hill), just kinetic energy (like at the lowest point), or some combination of kinetic and potential energy (like at all other points).
• The first hill of a roller coaster is always the highest point of the roller coaster because friction and drag immediately begin robbing the car of energy. At the top of the first hill, a car's energy is almost entirely gravitational potential energy (because its velocity is zero or almost zero). This is the maximum energy that the car will ever have during the ride. That energy can become kinetic energy (which it does at the bottom of this hill when the car is moving fast) or a combination of potential and kinetic energy (like at the tops of smaller hills), but the total energy of the car cannot be more than it was at the top of the first hill. If a taller hill were placed in the middle of the roller coaster, it would represent more gravitational potential energy than the first hill, so a car would not be able to ascend to the top of this taller hill.
• Cars in roller coasters always move the fastest at the bottom of hills. This is related to the first concept in that at the bottom of hills all of the potential energy has been converted to kinetic energy, which means more speed. Likewise, cars always move the slowest at their highest point, which is the top of the first hill.
• A web-based simulation demonstrating the relationship between vertical position and the speed of a car in a roller coaster various shapes is provided at the MyPhysicsLab Roller Coaster Physics Simulation.
• Friction exists in all roller coasters, and it takes away from the useful energy provided by roller coaster. Friction is caused in roller coasters by the rubbing of the car wheels on the track and by the rubbing of air (and sometimes water!) against the cars. Friction turns the useful energy of the roller coaster (gravitational potential energy and kinetic energy) into heat energy, which serves no purpose associated with propelling cars along the track. Friction is the reason roller coasters cannot go on forever, so minimizing friction is one of the biggest challenges for roller coaster engineers. Friction is also the reason that roller coasters can never regain their maximum height after the initial hill unless there is a second chain lift somewhere on the track.
• Cars can only make it through loops if they have enough speed at the top of the loop. This minimum speed is referred to as the critical velocity, and is equal the square root of the radius of the loop multiplied by the gravitational constant (v_c = (rg)^1/2). This calculation is too complex for the vast majority of seventh graders, but they will intuitively understand that if a car is not moving fast enough at the top of a loop it will fall. Most roller coasters have wheels on both sides of the track to prevent them from falling for safety reasons.
• Most roller coaster loops are not perfectly circular in shape, but have a teardrop shape called a clothoid. Roller coaster designers discovered that if a loop is circular, the rider experiences the greatest force at the bottom of the loop when the cars are moving fastest. After many riders sustained neck injuries, the looping roller coaster was abandoned in 1901 and revived only in 1976 when Revolution at Six Flags Magic Mountain became the first modern looping roller coaster using a clothoid shape. In a clothoid, the radius of curvature of the loop is widest at the bottom, reducing the force on the riders when the cars move fastest, and smallest at the top when the cars are moving relatively slowly. This allowed for a smoother, safer ride and the teardrop shape is now in use in roller coasters around the world.
• Riders may experience weightlessness at the tops of hills (negative g-forces) and feel heavy at the bottoms of hills (positive g-forces). This feeling is caused by the change in direction of the roller coaster. At the top of a roller coaster, the car goes from moving upward to flat to moving downward. This change in direction is known as acceleration and the acceleration makes the riders feel as if there is a force acting on them, pulling them out of their seats. Similarly, at the bottom of hills, the riders go from moving downward to flat to moving upward, and thus feel as if there is a force pushing them down into their seats. These forces can be referred to in terms of gravity and are called gravitational forces, or g-forces. One "g" is the force applied by gravity while standing on Earth at sea level. The human body is used to existing in a 1 g environment. If the acceleration of a roller coaster at the bottom of a hill is equal to the acceleration of gravity (9.81 m/s²), another g-force is produced and, when added to the standard one g, we get two g's. If the acceleration at the bottom of the hill is twice the acceleration of gravity, the overall force is three g's. If this acceleration acts instead at the top of a hill, it is subtracted from the standard one g. In this way, it can be less than 1 g, and it can even be negative. If the acceleration at the top of a hill were equal to the acceleration of gravity, the overall force would be zero g's. If the acceleration at the top of the hill were twice the acceleration of gravity, the resulting overall force would be negative one g. At zero g's the rider feels completely weightless and at negative g's, they feel as though there is a force lifting them out of their seats. This concept may be too advanced for students, but they should understand the basic principles and where g-forces greater than or less than 1 g can occur, even if they cannot fully relate them to the acceleration of the roller coaster.

Bennett, David. Roller Coaster. Aurum Ltd., 1999.

Roller Coaster Database. Copyright 1996-2007. Duane Marden. Accessed 5/3/2007. http://www.rcdb.com/.

Funderstanding Roller Coaster. Copyright 1998. Funderstanding. Accessed 5/3/2007. http://www.funderstanding.com/k12/coaster/.

Loop (Roller Coaster). Modified April 9, 2007. Wikipedia. Accessed 5/3/2007. http://en.wikipedia.org/wiki/Loop_%28roller_coaster)

Pescovitz, David. Roller Coaster Physics. Copyright 1998-1999. Encyclopedia Britannica, Inc. Accessed 5/3/2007. http://search.eb.com/coasters/ride.html.

Neumann, Erik. Roller Coaster Physics Simulation. Copyright 2004. MyPhysicsLab. Accessed 5/3/2007. http://www.myphysicslab.com/RollerSimple.html.