Download Roller Coaster Physics

P_Physics - Energy
NAME: ______________________
~Roller Coaster Physics~
The Science Behind the Thrills
University of Alaska, Fairbanks
History:
The beginning of American roller coasters was near the end of the
19 century when railway companies set up amusement parks at the end
of their lines to increase business on the weekends. In 1884 the first real
roller coaster in America was introduced: a gravity driven switchback
train. Passengers would climb a set of stairs to board the car, which was then pushed from the station to travel
down a hill and over a few bumps. At the bottom, the passengers got out and climbed another set of stairs while
workers hoisted the car to the top of the second station. The passengers got back into the car and rode to the
first station on a second track.
th
An attempt at a vertical loop was tried in 1898, and was called the Flip-Flap Railway. However, the
loop on this ride was a circle, as opposed to the clothoid loops that are used in roller coaster design today. This
caused a problem: the forces generated by the circular loop were so strong that riders’ necks were snapped.
The beginning of the 20th Century saw great leaps in roller coaster safety. The first roller coaster to employ
trains with an up-stop wheel system that held to the track rather than just sitting atop it was built in 1912. This
was a huge leap as it gave the opportunity for greater speed and steeper hills.
Disneyland, America’s first theme park, opened in 1955, and brought with it a new era for amusement
parks. Disney introduced the first tubular steel roller coaster, the Matterhorn, in 1959. Before this, roller
coasters had always been built from wood, but the steel track was a huge improvement, offering not only greater
stability, but also opening the door for loops and corkscrews.
Gravity and Potential Energy
Gravity is the driving force of a roller coaster. From the moment the roller coaster train passes the peak
of the lift hill, it is the acceleration due to gravity that brings it back to the beginning. When the train is released
from the top of the lift hill, gravity pulls it down. The train begins slowly, then picks up speed as it approaches
the bottom of the hill. As it begins to climb the next hill, the speed decreases. This is because of the
acceleration due to gravity, which occurs at 9.8 m/s2 (often rounded to 10m/s2) straight down toward the center
of the Earth.
The initial hill, or the lift hill, is the tallest in the entire ride. As the train is pulled to the top, it is gaining
potential, or stored energy. The higher the lift, the greater the amount of potential energy gained by the train.
This is shown by the equation for potential energy:
PEg = magh
Where PEg is potential energy, m is mass in kilograms, ag is acceleration due to gravity, and h is the
distance above the ground in meters. Because mass and gravity are constant for the train, if the height of the
train above the ground is increased, the potential energy must also increase. This means that the potential
energy for the roller coaster system is greatest at the highest point on the track: the top of the lift hill.
Velocity and Kinetic Energy
As the roller coaster train begins its descent from the lift hill, its velocity increases. This causes the train
to gain kinetic energy, which is the energy of motion. The faster the train moves, the more kinetic energy the
train gains. This is shown by the equation for kinetic energy:
KE = 1/2mv2
Where KE is kinetic energy, m is mass in kilograms, and v is velocity in meters per second. Because the
mass is constant, if the velocity is increased, the kinetic energy must also increase. This means that the kinetic
energy for the roller coaster system is greatest at the bottom of the highest hill on the track: the bottom of the lift
hill. When the train begins to climb the next hill on the track, the train starts to slow down, thereby decreasing
its kinetic energy.
Conservation of Energy
Energy cannot be created or destroyed, but it can be converted from one form to another. For the
idealized roller coaster, all energy is conserved through conservative forces, such as gravity. As the train
accelerates down the lift hill, potential energy is converted into kinetic energy. When the train ascends another
hill, the kinetic energy is converted into potential energy again. This is conservation of mechanical energy, and
it continues throughout the entire ride. The total mechanical energy for the train is shown by the equation:
Etotal = KE + PE
Where E is the total mechanical energy, KE is kinetic energy, and PE is potential energy. From this, the
equation for conservation of total mechanical energy can be derived:
Ei = Ef
or
KEi + PEi = KEf + PEf
Where Ei is total initial mechanical energy and Ef is total final mechanical energy. This shows that the
total initial mechanical energy equals the total final mechanical energy for the system. It is because of this
phenomenon that a roller coaster is called a “coaster.” After the initial input of energy to carry the train up the
lift hill, the roller coaster simply coasts through the rest of the ride.
Friction
For a non-idealized roller coaster system, not all of the energy is conserved. Friction is the main cause
of energy leaks in the system and the reason why mechanical energy is not fully conserved for a real roller
coaster. This is because friction is a nonconservative force. Nonconservative forces are forces that cause a
change in total mechanical energy. Friction opposes motion by working in the opposite direction. The friction
between the train and its tracks as well as between the train and the air take energy out of the system, slowing
the train and creating both heat and sound. This effect is most noticeable at the end of the ride as all remaining
kinetic energy is taken out of the system though brakes. Because of the energy leaks due to friction, each
successive hill or loop on a roller coaster must be shorter than all the hills or loops previous to it, otherwise the
train will not have enough energy to make it all the way over.
After reading the article, answer the following questions:
1. Why is the first hill, the lift hill, on a roller coaster always
the tallest?
2. When will the cart be traveling the fastest, at the top of the
lift hill, or at the bottom of the lift hill?
3. When the cart starts climbing the second hill on the track,
its speed slows down. As the speed slows down, what
happens to the height of the cart?
4. When the cart starts traveling down the second hill, what does its PE start turning into?
5. At any point along the ride, the total PE and KE must equal what percent?
6. If KE starts decreasing, what will happen to PE?
7. Under real life conditions, when the ride nears its end, both the speed and height are both low. Explain
why this occurs.
8. In the roller coaster diagram below, list the point (A,B,C, or D), that best answers the following
questions:
i.
Which point has the greatest PE?
ii.
Which point has the second greatest PE?
iii.
KE and PE are equal at which point?
iv.
Which point has the greatest KE?
v.
At which point will the roller coaster be traveling the fastest?