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PHYSICS OF ROLLERCOASTERS Nathaniel McClain II PHY 3091 Florida State University PHYSICS OF ROLLERCOASTERS • Allen, John (b. May 21, 1907, Philadelphia, Pa., U.S.--d. Aug. 17, 1979, Philadelphia), American designer of roller coasters who ignited the coaster boom of the 1970s following the mid-century decline in amusement parks. PHYSICS OF ROLLERCOASTERS POTENTIAL ENERGY • Stored energy that depends • Potential energy is a property of a upon the relative position of system and not of an individual body or particle. It depends only on its various parts of a system. A initial and final configurations; it is train of cars on a gravity- independent of the path the object powered roller coaster has travels. The value of potential energy more potential energy raised is arbitrary and relative to the choice of reference point. Gravitational above the ground at the top of potential energy near the Earth's a hill than it has after falling to surface may be computed by the earth along the hill's multiplying the weight of an object by inclined track. In the elevated its distance above the reference point. position it is capable of doing • Potential energy may be converted into energy of motion, called kinetic more work. By extension, the energy. Traditionally potential energy higher the lift hill, the greater is included with kinetic energy as a the potential energy. form of mechanical energy so that the total energy in gravitational systems can be calculated as a constant. PHYSICS OF ROLLERCOASTERS POTENTIAL ENERGY • AT THIS POINT IN THE RIDE . . . at the top of the lift hill, the potential energy of the gravity-powered coaster is at its greatest, because the coaster is at its highest elevation. Beyond this point, as gravitation gives the car velocity, the potential energy is transferred into kinetic energy. The coaster does, however, regain some potential energy each time it climbs another hill or ramp on the rest of the ride. PHYSICS OF ROLLERCOASTERS GRAVITY • In mechanics, the universal force of attraction that affects all matter. It is the weakest of the four basic physical forces, but, on the scale of everyday objects near the Earth, it is the dominant one. The fall of bodies released from a height to the surface of the Earth and the weight of resting bodies at or near the surface are the most familiar manifestations of gravitation. Gravity is the traditional source of power for roller coasters, accelerating the cars through all the twists and turns of the ride, from the lift hill through to the brake run. PHYSICS OF ROLLERCOASTERS VELOCITY • Quantity that designates how fast and • Roller coaster rides incur many changes in in what direction a point is moving. speed and direction, or velocity, and the Because it has direction as well as rate of this change is acceleration. It is not true, as often thought, that the speed of a magnitude, velocity is known as a car at the bottom of a hill is equal to its vector quantity and cannot be initial velocity plus its drop velocity; actually specified completely by a number, as the greater the drop height, the less initial can be done with time or length, which velocity influences final velocity. Along the are scalar quantities. same lines, speed is not directly proportional to the drop height but to the square root of • A point always moves in a direction the drop height. Doubling the speed of a that is tangent to its path; for a coaster ride requires quadrupling the height circular path, for example, its direction of the hill. at any instant is perpendicular to a line • AT THIS POINT IN THE RIDE . . . the track from the point to the center of the curves back upward and the speed drops as circle (a radius). The magnitude of the the roller coaster climbs the second hill. velocity (i.e., the speed) is the time Owing to the change in velocity, the riders rate at which the point is moving along experience upward centripetal its path. acceleration in the form of positive g- forces. This compression makes them feel heavier than normal. On the climb the coaster regains some potential energy that it had lost to kinetic energy on the previous descent. PHYSICS OF ROLLERCOASTERS ACCELERATION • Time rate at which a velocity is changing. Because velocity has both magnitude and direction, it is called a vector quantity; acceleration is also a vector quantity and must account for changes in both the magnitude and direction of a velocity. • If the velocity of a roller coaster moving on a straight path is increasing (i.e., if the speed, which is the magnitude of the velocity, is increasing), the acceleration vector will have the same direction as the velocity vector. If the velocity is decreasing (that is, the coaster is decelerating), the acceleration vector will point in the opposite direction. So, whether the coaster is increasing speed down a hill or decreasing speed up a hill, it is regarded as acceleration in the mathematical sense. PHYSICS OF ROLLERCOASTERS ACCELERATION • Changes in acceleration greatly contribute to the thrill of a roller coaster ride. A rider may feel greater sensations in a low-speed coaster with sharp acceleration changes than on a faster coaster with a smoother ride. Pure speed is often not as recognizable as the surge of acceleration during a coaster ride. • A common fallacy is that acceleration increases along with the weight of the riders and the car, when actually the acceleration of a coaster in free-fall is independent of its mass. Acceleration does increase, however, with a steeper angle of descent. PHYSICS OF ROLLERCOASTERS ACCELERATION • AT THIS POINT IN THE RIDE . . . at the bottom of the second hill, the coaster, in theory, reaches an instant of zero acceleration, at the point where its speed is greatest, relative to anywhere else on that hill. Zero acceleration also occurs for an instant at the top of a hill, where in turn the speed is at its lowest level. At the bottom of the dip, the riders experience compression, or acceleration stress, owing to forces greater than their usual weight. PHYSICS OF ROLLERCOASTERS FRICTION • Force that resists the sliding or rolling of one solid object over another. Frictional forces, such as the traction needed to walk without slipping, may be beneficial; but they also present a great measure of opposition to motion. Friction, along with air resistance, or wind drag, are dissipative forces that are neglected in idealized discussions of fundamental mechanics, in which gravitation is the only force considered. PHYSICS OF ROLLERCOASTERS PHYSICS OF ROLLERCOASTERS ACCELERATION STRESS • Physiological changes that occur in the human body in motion as a result of rapid increase of speed. Rapid acceleration and surges in acceleration are felt more critically than are gradual shifts. PHYSICS OF ROLLERCOASTERS CENTRIFUGAL FORCE • Quantity, peculiar to a particle moving on a circular path, that has the same magnitude and dimensions as the force that keeps the particle on its circular path (the centripetal force) but points in the opposite direction. PHYSICS OF ROLLERCOASTERS KINETIC ENERGY • Form of energy that an object or a particle has by reason of its motion. If work, which transfers energy, is done on a roller coaster by applying a net force, such as gravity, the coaster speeds up and thereby gains kinetic energy. Kinetic energy is a property of a moving object and depends not only on its motion but also on its mass. The kind of motion may be translation (or motion along a path from one place to another), rotation about an axis, vibration, or any combination of these.