THE PHYSICS OF A ROLLER COASTER
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Roller coasters are almost entirely driven by different forces of inertia, gravity,
and centripetal. The physics of a roller coaster also involves work, energy, friction,
inertia, and air resistance. A roller coaster usually begins with a mechanical device,
such as a chain and motor, which exerts a force on the car trains to lift them to the top
of the hill. At this point, gravity takes over and the duration of the ride undergoes energy
transformation.
This first hill of a roller coaster is normally the tallest. Once the cars are pulled to
the top of the hill, they maintain gravitational potential energy. The first hill maintains the
largest amount of potential energy. Gravitational potential energy is the energy an
object possesses because of its position in a gravitational field. It is the amount of work
an object will be able to do with the energy it builds from falling. The equation for
potential energy is PE=mgh. “M” is for the mass, “g” is for the gravity constant of
9.81m/s2, and “h” is for height. This energy is proportional to the mass of the cars and
the height of the hill. As the cars descend down the hill, the potential energy is
exchanged for kinetic energy (Harris, 2007).
Kinetic energy is the energy an object possesses due to its motion. It is the work
needed to accelerate a body of mass from rest to a given velocity. Kinetic energy is
gained when an object accelerates, and the body maintains this energy until its speed
changes. The equation for kinetic energy is KE= ½ mv2, where “m” is the mass of the
object and “v” is the velocity. As the roller coaster descends, it is accelerating, creating
kinetic energy. The kinetic energy is the largest at the bottom of the first hill. The energy
of the roller coaster cars will continue to change from potential to kinetic energy, and
vice versa, as the cars ascend and descend the hills. Due to frictional losses, the total
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energy only decreases throughout the ride; therefore, the maximum hill the cars can
climb gets smaller and smaller (Harris, 2007). The energy built up from the first hill has
to be enough to take the cars to the end of the ride.
This change in energy demonstrates the Law of Conservation of Energy. The
Law of Conservation of Energy states that energy can change from one form to another,
but cannot be created or destroyed. As the roller coaster changes from potential energy
at the top of the hill to kinetic energy at the bottom, it is representing the Law of
Conservation of Energy (Johnson, 2006). The cars are continuously losing and gaining
height throughout the ride. Every height gain corresponds with the loss of speed as
kinetic energy is transformed into potential energy. Every height loss corresponds with a
gain of speed as potential energy is transformed into kinetic energy (Johnson, 2006).
Energy throughout the ride is neither gained nor lost, but is simply transformed from
potential to kinetic energy and vice versa.
The work and energy relationship is demonstrated in a roller coaster ride. The
work done by an external force is capable of changing the total amount of mechanical
energy. The equation KEinitial + PEinitial + W external = KEfinal + PEfinal explains the
relationship. The amount of work done by external forces is equal to the amount of
change in the total mechanical energy of the object. The left side of the equation
includes the total mechanical energy for the initial state plus the work done by external
forces. The right side of the equation includes the total mechanical energy for the final
state of the object.
The weight of the roller coaster is pulled down by gravity, meaning that the cars
are falling. Gravity applies a constant downward force on the roller coaster cars. The
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force of gravity is an internal source, so any work done by it does not change the total
mechanical energy of the cars. Gravity, along with energy, friction, and inertia, allow the
cars to stay on the track. These factors also explain why people don’t fall out of roller
coaster cars when they go upside down. According to Newton’s First Law of Motion, an
object in motion tends to stay in motion, unless another force acts against it. This
remains true for the potential and kinetic energy changes in roller coasters. The other
force acting upon the car in motion is the incline or decline of a hill.
The two major types of roller coasters are steel and wood. The features in these
wheel designs prevent the cars from flipping off the track. Wooden tracks tend to have
less complex loops as steel tracks, because it is more inflexible than steel. Tubular steel
tracks were introduced in the 1950s. The nylon or polyurethane wheels run along the
top, bottom, and side of the tube. This secures the cars to the track while it travels
through loops and twists. As the cars flip during loops, inertia keeps one in his seat.
Inertia is the resistance of any object to any change in its state of motion. It is the
tendency of an object to continue motion in a straight line at a constant linear velocity
(Roller Coasters, 2013). This includes Newton’s First Law of Motion. Although gravity
pulls us towards the earth, the acceleration force at the top of a loop is pulling upwards
stronger than gravity is pulling downwards, thus counteracting gravity and allowing one
to remain in the cart. A loop but also be elliptical rather than a circle, because the
centripetal force would be too strong for both safety and comfort. Centripetal force is a
force that acts on a body moving in a circular path and is directed toward the center
around which the body is moving. When the roller coaster goes around a turn, the
centripetal force pushes you against the outside of the car to help keep you in the car.
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Friction is a force that resists the relative motion or tendency to such motion of
two bodies or substances in contact. Some of the energy in a coaster is changed into
friction; therefore, each successive hill in a roller coaster is made smaller because
factors such as friction slow down the roller coaster. Friction slows the roller coaster
down by holding the car down. Less friction will increase a roller coaster’s velocity.
When the cars of the roller coaster ascend hills, they have to fight off both friction and
gravity to get to the top. Once the cars have reached the top of the hill, friction is
overcome. At this point, the potential energy becomes kinetic and the speed of the cars
increases until the bottom of the hill (Ratliff, 2011). Wind resistance and the rolling of
wheels also use energy.
The energy during a roller coaster ride is spread into different areas. A lot of the
energy goes to the friction between the roller coaster and the track, which allows the
roller coaster car to slow down. Additional energy is lost due to wind resistance and
gravity. If gravity overcame the forward motion of the roller coaster cars as they climbed
the hills, then the ride would never make it to the top of a hill. Energy is also lost in
angular momentum from twists and turns.
Ultimately in roller coasters, the energy will always be dispersed. It is nearly
impossible to make a 100% efficient roller coaster, or else it would never end. Higher
efficiency in the wheels and better streamlining have made a big difference in how long
the system can retain energy, but it will never be perfect. Factors such as friction, air
resistance, and the Law of Conservation of Energy make it impossible for perfect
efficiency.
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Chandler, M. (2012, January 1). How Roller Coasters Work. Kidzworld. Retrieved, from
http://www.kidzworld.com/article/4633-how-roller-coasters-work
Harris, T. (2007, August 9). How Roller Coasters Work. HowStuffWorks. Retrieved, from
http://science.howstuffworks.com/engineering/structural/roller-coaster.htm
Johnson, T. (2006, July 11). First Hill on A Roller Coaster is the Biggest. University of
Illinois. Retrieved, from http://van.physics.illinois.edu/qa/listing.php?id=31
Ratliff, D. (2011, June 6). What Causes Roller Coasters to Slow Down?. eHow.
Retrieved from http://www.ehow.com/info_8549322_causes-roller-coastersslow-down.html
Unknown. (2013, August 13). Roller coasters. Why don’t I fall out when a roller coaster
goes upside down? (Everyday Mysteries: Fun Science Facts from the Library of
Congress). Retrieved, from
http://www.loc.gov/rr/scitech/mysteries/rollercoaster.html
Meaghan Bilyeu