Energy Transformation on a Roller Coaster

Part of the physics of a roller coaster is the physics of work and energy. The ride often begins as a chain and motor (or other mechanical device) exerts a force on the train of cars to lift the train to the top of a vary tall hill. Once the cars are lifted to the top of the hill, gravity takes over and the remainder of the ride is an experience in energy transformation.

At the top of the hill, the cars possess a large quantity of potential energy. Potential energy - the energy of vertical position - is dependent upon the mass of the object and the height of the object. The car's large quantity of potential energy is due to the fact that they are elevated to a large height above the ground. As the cars descend the first drop they lose much of this potential energy in accord with their loss of height. The cars subsequently gain kinetic energy. Kinetic energy - the energy of motion - is dependent upon the mass of the object and the speed of the object. The train of coaster cars speeds up as they lose height. Thus, their original potential energy (due to their large height) is transformed into kinetic energy (revealed by their high speeds). As the ride continues, the train of cars are continuously losing and gaining height. Each gain in height corresponds to the loss of speed as kinetic energy (due to speed) is transformed into potential energy (due to height). Each loss in height corresponds to a gain of speed as potential energy (due to height) is transformed into kinetic energy (due to speed). This transformation of mechanical energy from the form of potential to the form of kinetic and vice versa is illustrated in the animation below.

Once a roller coaster has reached its initial summit and begins its descent through loops, turns and smaller hills, the only forces acting upon the coaster cars are the force of gravity, the normal force and dissipative forces such as air resistance. The force of gravity is an internal force and thus any work done by it does not change the total mechanical energy of the train of cars. The normal force of the track pushing up on the cars is an external force. However, it is at all times directed perpendicular to the motion of the cars and thus is incapable of doing any work upon the train of cars. Finally, the air resistance force is capable of doing work upon the cars and thus draining a small amount of energy from the total mechanical energy which the cars possess. However, due to the complexity of this force and its small contribution to the large quantity of energy possessed by the cars, it is often neglected. By neglecting the influence of air resistance, it can be said that the total mechanical energy of the train of cars is conserved during the ride. That is to say, the total amount of mechanical energy (kinetic plus potential) possessed by the cars is the same throughout the ride. Energy is neither gained nor lost, only transformed from kinetic energy to potential energy and vice versa.

Sensations of Weightlessness

The phenomenon of "weightlessness" occurs when there is no force of support on your body. When your body is effectively in "free fall", accelerating downward at the acceleration of gravity, then you are not being supported. The sensation of apparent weight comes from the support that you feel from the floor, from the seat, etc. Different sensations of apparent weight can occur on a roller-coaster or in an aircraft because they can accelerate either upward or downward.

If you travel in a curved path in a vertical plane, then when you go over the top on such a path, there is necessarily a downward acceleration. Taking the example of the roller-coaster which is constrained to follow a track, then the condition for weightlessness is met when the downward acceleration of your seat is equal to the acceleration of gravity. Considering the path of the roller-coaster to be a segment of a circle so that it can be related to the centripetal acceleration, the condition for weightlessness is

The "weightlessness" you may feel in an aircraft occurs any time the aircraft is accelerating downward with acceleration 1g. It is possible to experience weightlessness for a considerable length of time by turning the nose of the craft upward and cutting power so that it travels in a ballistic trajectory. A ballistic trajectory is the common type of trajectory you get by throwing a rock or a baseball, neglecting air friction. At every point on the trajectory, the acceleration is equal to g downward since there is no support. A considerable amount of experimentation has been done with such ballistic trajectories to practice for orbital missions where you experience weightlessness all the time.

                              

Physiological Symptoms of the Coaster.

Some research claims that roller coaster actually put a great amount of psychological strain on you body and can even cause death. The thrill of a roller coaster ride with its climbs, loops and dives can speed up the heart, setting off an irregular heartbeat that could put individuals with heart disease at risk of having a heart attack (American Heart Association's Scientific Sessions 2005). The mental and physical stress from riding on a roller coaster is comparable to a fast game of tennis. For young healthy people there is no risk for heart attack and arrhythmias from riding a roller coaster then that of people with high blood pressure, a previous heart attack, an implanted pacemaker or defibrillator, and others with proven heart disease (Kuschyk, Jurgen M.D.). 

Clothoid Loop

The most obvious section on a roller coaster where centripetal acceleration occurs is within the so-called clothoid loops. Roller coaster loops assume a tear-dropped shape that is geometrically referred to as a clothoid. A clothoid is a section of a spiral in which the radius is constantly changing. Unlike a circular loop in which the radius is a constant value, the radius at the bottom of a clothoid loop is much larger than the radius at the top of the clothoid loop. A mere inspection of a clothoid reveals that the amount of curvature at the bottom of the loop is less than the amount of curvature at the top of the loop. To simplify our analysis of the physics of clothoid loops, we will approximate a clothoid loop as being a series of overlapping or adjoining circular sections. The radius of these circular sections is decreasing as one approaches the top of the loop. Furthermore, we will limit our analysis to two points on the clothoid loop - the top of the loop and the bottom of the loop. For this reason, our analysis will focus on the two circles that can be matched to the curvature of these two sections of the clothoid. The diagram at the right shows a clothoid loop with two circles of different radius inscribed into the top and the bottom of the loop. Note that the radius at the bottom of the loop is significantly larger than the radius at the top of the loop.


    As a roller coaster rider travels through a clothoid loop, she experiences an acceleration due to both a change in speed and a change in direction. A rightward moving rider gradually becomes an upward moving rider, then a leftward moving rider, then a downward moving rider, before finally becoming a rightward-moving rider once again. There is a continuous change in the direction of the rider as she moves through the clothoid loop. And as learned in Lesson 1, a change in direction is one characteristic of an accelerating object. In addition to changing directions, the rider also changes speed. As the rider begins to ascend (climb upward) the loop, she begins to slow down. As energy principles would suggest, an increase in height (and in turn an increase in potential energy) results in a decrease in kinetic energy and speed. And conversely, a decrease in height (and in turn a decrease in potential energy) results in an increase in kinetic energy and speed. So the rider experiences the greatest speeds at the bottom of the loop - both upon entering and leaving the loop - and the lowest speeds at the top of the loop.

PHAULTY PHYSICS

The History of Roller Coasters & Some Early Disaters

Roller coaster car derails

(December 31, 2010) - A roller coaster car derailed at a carnival in Timaru, New Zealand, leaving two people with minor injuries. The accident happened on a kiddie roller coaster. The injured were riding in the car when it left the track of the ride. They managed to escape from the car, which was left dangling from the track about four feet from the ground.

Girl, 3, killed inside kiddie ride

(February 6, 2011) - At a carnival in Moral de Calatrava, Spain, a 3-year-old girl was fatally injured inside an amusement attraction for children. The girl got caught between a moving cylinder and the wheel that turns it.
The location of the cylinder is inside the ride and not visible to the ride attendant. The girl remained trapped until her father noticed that she did not exit the attraction with the other children. Firefighters rushed inside and managed to free the victim, but she died in an ambulance on the way to a hospital.
According to El Dia newspaper, witnesses said that it appeared that a floor board either gave way or was missing, causing the victim to fall upon the moving wheel, where her head got caught.
The ride passed an inspection and was properly insured.

Man killed in fall from roller coaster

(January 30, 2011) - At Tokyo Dome City amusement park in Tokyo, Japan, a 34-year-old man suffered fatal injuries when he was ejected from a roller coaster and fell 20-25 feet. The accident happened on 'Maihime' -- a steel roller coaster whose cars spin as they roll along the track.
Tokyo Police are investigating reports that the victim may have too large to ride; that the victim's lap bar did not lock properly because of his size; that the ride operator did not manually check to ensure that the safety bar was locked; and that employees did not receive proper training.
According to investigators, the ride operator, a part-time employee, said that she did not manually check the victim's lap bar because it "appeared to be locked as it was positioned right on his stomach." The ride's lap bars are designed to rest and lock across riders' legs. Normally, a lap bar is not effective as a restraining device if it rests upon a rider's stomach, even if it is locked. Police suspect that the victim exceeded the size limit of a rider, and that he should not have been allowed to ride.
According to the Daily Yomiuri, the ride operator told police: "I told passengers to lock the safety bars, but I didn't confirm [whether they were in the correct position] with my hand. I thought customers would lock [the bars] by themselves because they're grownups."
The report also indicates that the operator was quoted as saying, "At the time of the accident I was looking at a staff assignment sheet, so I didn't monitor the roller coaster operation at all."
The ride has been ordered closed while police continue their investigation.

G Forces in Relation to Roller Coasters

Newton's Three Laws of Motion

This video helps to explain Newton's Three Laws of Motion. Newton's Three Laws are used in the constrction of roller coasters.