Tuesday, 17 May 2011
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Sunday, 8 May 2011
G-forces
Roller coaster rides are notorious for creating accelerations and g-forces which are capable of transforming stomach contents into airborne projectiles. As a rider starts the descent down the first drop, she begins a one-minute adventure filled with various sensations of weightlessness, heaviness, and jerkiness. The parts of the ride which are most responsible for these sensations of weightlessness and heaviness are the clothoid loops. The explanation for the various sensations experienced on a roller coaster loop are associated with Newton's laws of motion and the physics of circular motion.
A clothoid loop has a constantly curving shape with sections which resemble the curve of a circle (in actuality, it is considered to be a section of a cornu spiral having a constantly changing radius). A coaster rider is continuously altering her direction of motion while moving through the loop. At all times, the direction of motion could be described as being tangent to the loop. This change in direction is caused by the presence of unbalanced forces and results in an acceleration. Not only is there an acceleration, the magnitude and direction of the acceleration is continuously changing. Within nearly a one second time interval, the riders may experience accelerations of 20 m/s/s downwards to 30 m/s/s upwards; such drastic changes in acceleration normally occur as the rider moves from the top of the loop to the bottom of the loop. These drastic changes in accelerations are the cause of much of the thrill (and the occasionally dizziness) experienced by coaster riders.
To understand the feelings of weightlessness and heaviness experienced while riding through a loop, it is important to think about the forces acting upon the riders. To simplify the discussion, we will assume that there are negligible amounts of air resistance acting upon the riders. Thus, the only forces exerted upon the riders are the force of gravity and the normal force (the force of the seat pushing up on the rider). The force of gravity is at all times directed downwards and the normal force is at all times directed perpendicular to the seat of the car. Since the orientation of the car on the track is continuously changing, the normal force is continuously changing its direction. The magnitude and direction of these two forces during the motion through the loop are depicted in the animation below.
For an object to move along a circular path at a constant speed, there must be a net inward force acting upon the rider. This is commonly referred to as the centripetal force requirement. The motion through a coaster loop isn't precisely an example of moving in a circle at constant speed since the loop is neither circular not the speed constant. Nonetheless, because of the similarity of the motion along the loop's path to uniform circular motion, principles of uniform circular motion can be applied to the rider. The net force acting upon the rider has an inwards direction (towards the center of the circle). Since the net force is the vector sum of all the forces, the head-to-tail addition of the normal force and the gravity force should sum to a resultant force which points inward. The diagram below depicts the free-body diagrams for a rider at four locations along the loop. The diagram also shows that the vector sum of the two forces (i.e., the net force) points mostly towards the center of the loop for each of the locations.
Feelings of weightlessness and heaviness are associated with the normal force; they have little to do with the force of gravity. A person who feels weightless has not lost weight. The force of gravity acting upon the person is the same magnitude as it always is. Observe that in the animation above the force of gravity is everywhere the same. The normal force however has a small magnitude at the top of the loop (where the rider often feels weightless) and a large magnitude at the bottom of the loop (where the rider often feels heavy). The normal force is large at the bottom of the loop because in order for the net force to be directed inward, the normal force must be greater than the outward gravity force. At the top of the loop, the gravity force is directed inward and thus, there is no need for a large normal force in order to sustain the circular motion. The fact that a rider experiences a large force exerted by the seat upon her body when at the bottom of the loop is the explanation of why she feels heavy. In actuality, she is not heavier; she is only experiencing the large magnitude of force which is normally exerted by seats upon heavy people while at rest.
conservation of energy
A roller coaster ride is a thrilling experience which involves a wealth of physics. 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.
A roller coaster ride also illustrates the work and energy relationship. The work done by external forces is capable of changing the total amount of mechanical energy from an initial value to some final value. The amount of work done by the external forces upon the object is equal to the amount of change in the total mechanical energy of the object. The relationship is often stated in the form of the following mathematical equation.
The left side of the equation includes the total mechanical energy (KEinitial + PEinitial) for the initial state of the object plus the work done on the object by external forces (Wexternal) while the right side of the equation includes the total mechanical energy (KEfinal + PEfinal) for the final state of the object.
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.
The conservation of mechanical energy by the coaster car in the above animation can be studied using a calculator. At each point in the ride, the kinetic and potential energies can be calculated using the following equations.
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velocity and kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.[1] It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest.
The speed, and thus the kinetic energy of a single object is frame-dependent (relative): it can take any non-negative value, by choosing a suitable inertial frame of reference. For example, a bullet passing an observer has kinetic energy in the reference frame of this observer, but the same bullet is stationary, and so has zero kinetic energy, from the point of view of an observer moving with the same velocity as the bullet.[2] By contrast, the total kinetic energy of a system of objects cannot be reduced to zero by a suitable choice of the inertial reference frame, unless all the objects have the same velocity. In any other case the total kinetic energy has a non-zero minimum, as no inertial reference frame can be chosen in which all the objects are stationary. This minimum kinetic energy contributes to the system's invariant mass, which is independent of the reference frame.
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 9.80m/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:
Ug = mgh
Where Ug is potential energy, m is mass in kilograms, g 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.
Roller coaster history
THE BEGINNING
Every history has a starting point and most roller coaster historians agree that the roller coaster's origins were the Russian Ice Slides.
The origin of the Roller Coaster dates back to the Russian Ice Slides built in the mid-1600's.
There is some dispute as to who actually added wheels to the equation and created a rolling coaster. Robert Cartmell, who wrote the book The Incredible Scream Machine: A History of the Roller Coaster, gives the Russians credit for building the first wheeled machine. He states that it was in the Gardens of Orienbaum in St. Petersburg. Cartmell says that this ride was built in 1784 and featured carriages that undulated over hills within grooved tracks. Other historians say it was the French who added wheels to the slides. For now this historian will have to side with those who give the credit to the French. After examining Cartmell's book I can find no source cited for his claim giving the Russians credit, only an engraving which might be coaster, dated c. 1784.
Russes a Belleville was the first roller coaster to lock the cars to the track.
The Aerial Walk in France was one of the world's first roller coasters.
The Aerial Walk featured a heart-shaped layout with two tracks that flowed in opposite directions from a central tower. They then went around the course, came together at the bottom and ascend parallel lift hills.
The first looping coaster was located in Frascati Gardens in Paris, France. The hill was 43 feet high, had a 13 foot-wide loop and was tested with everything under the sun before humans were allowed on. The layout was simple: the rider rode down the gentle slope on a small cart and through a small metal circle.
The world's first looping roller coaster with a 13-foot diameter loop was imported to France from England.
The ride ran for about twenty seasons and the pleasure railway grew out of fashion. A Centrifugal Railway was built in the Circus Napoleon, but fell victim to an accident on the trial run and was quickly shut down. It would be several years until a man named La Marcus Thompson would create the first roller coaster in the United States and change the amusement industry forever.
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