PHYSICS OF ROLLERCOASTERSPHYSICS OF ROLLERCOASTERS

Nathaniel McClain IINathaniel McClain IIPHY 3091PHY 3091

Florida State UniversityFlorida State University

PHYSICS OF ROLLERCOASTERSPHYSICS OF ROLLERCOASTERS

• Allen, John (b. May 21, Allen, John (b. May 21, 1907, Philadelphia, 1907, Philadelphia, Pa., U.S.--d. Aug. 17, Pa., U.S.--d. Aug. 17, 1979, Philadelphia), 1979, Philadelphia), American designer of American designer of roller coasters who roller coasters who ignited the coaster ignited the coaster boom of the 1970s boom of the 1970s following the mid-following the mid-century decline in century decline in amusement parks. amusement parks.

PHYSICS OF ROLLERCOASTERSPHYSICS OF ROLLERCOASTERSPOTENTIAL ENERGYPOTENTIAL ENERGY

• Stored energy that Stored energy that depends upon the relative depends upon the relative position of various parts of position of various parts of a system. A train of cars on a system. A train of cars on a gravity-powered roller a gravity-powered roller coaster has more potential coaster has more potential energy raised above the energy raised above the ground at the top of a hill ground at the top of a hill than it has after falling to than it has after falling to the earth along the hill's the earth along the hill's inclined track. In the inclined track. In the elevated position it is elevated position it is capable of doing more capable of doing more work. By extension, the work. By extension, the higher the lift hill, the higher the lift hill, the greater the potential greater the potential energy.energy.

• Potential energy is a property of a Potential energy is a property of a system and not of an individual system and not of an individual body or particle. It depends only on body or particle. It depends only on its initial and final configurations; it its initial and final configurations; it is independent of the path the is independent of the path the object travels. The value of object travels. The value of potential energy is arbitrary and potential energy is arbitrary and relative to the choice of reference relative to the choice of reference point. Gravitational potential point. Gravitational potential energy near the Earth's surface energy near the Earth's surface may be computed by multiplying may be computed by multiplying the weight of an object by its the weight of an object by its distance above the reference point.distance above the reference point.

• Potential energy may be converted Potential energy may be converted into energy of motion, called into energy of motion, called kinetic energy. Traditionally kinetic energy. Traditionally potential energy is included with potential energy is included with kinetic energy as a form of kinetic energy as a form of mechanical energy so that the total mechanical energy so that the total energy in gravitational systems energy in gravitational systems can be calculated as a constant.can be calculated as a constant.

PHYSICS OF ROLLERCOASTERSPHYSICS OF ROLLERCOASTERSPOTENTIAL ENERGYPOTENTIAL ENERGY

• AT THIS POINT IN THE RIDE AT THIS POINT IN THE RIDE . . . at the top of the lift hill, . . . at the top of the lift hill, the the potential energypotential energy of of the gravity-powered the gravity-powered coaster is at its greatest, coaster is at its greatest, because the coaster is at because the coaster is at its highest elevation. its highest elevation. Beyond this point, as Beyond this point, as gravitationgravitation gives the car gives the car velocityvelocity, the potential , the potential energy is transferred into energy is transferred into kinetic energykinetic energy. The coaster . The coaster does, however, regain does, however, regain some potential energy some potential energy each time it climbs another each time it climbs another hill or ramp on the rest of hill or ramp on the rest of the ride. the ride.

PHYSICS OF ROLLERCOASTERSPHYSICS OF ROLLERCOASTERSGRAVITYGRAVITY

• In mechanics, the universal In mechanics, the universal force of attraction that affects force of attraction that affects all matter. It is the weakest of all matter. It is the weakest of the four basic physical forces, the four basic physical forces, but, on the scale of everyday but, on the scale of everyday objects near the Earth, it is objects near the Earth, it is the dominant one. The fall of the dominant one. The fall of bodies released from a height bodies released from a height to the surface of the Earth to the surface of the Earth and the weight of resting and the weight of resting bodies at or near the surface bodies at or near the surface are the most familiar are the most familiar manifestations of gravitation. manifestations of gravitation. Gravity is the traditional Gravity is the traditional source of power for roller source of power for roller coasters, accelerating the coasters, accelerating the cars through all the twists and cars through all the twists and turns of the ride, from the lift turns of the ride, from the lift hill through to the brake run.hill through to the brake run.

PHYSICS OF ROLLERCOASTERSPHYSICS OF ROLLERCOASTERSVELOCITYVELOCITY

• Quantity that designates how fast Quantity that designates how fast and in what direction a point is and in what direction a point is moving. Because it has direction moving. Because it has direction as well as magnitude, velocity is as well as magnitude, velocity is known as a vector quantity and known as a vector quantity and cannot be specified completely by cannot be specified completely by a number, as can be done with a number, as can be done with time or length, which are scalar time or length, which are scalar quantities.quantities.

• A point always moves in a A point always moves in a direction that is tangent to its direction that is tangent to its path; for a circular path, for path; for a circular path, for example, its direction at any example, its direction at any instant is perpendicular to a line instant is perpendicular to a line from the point to the center of the from the point to the center of the circle (a radius). The magnitude of circle (a radius). The magnitude of the velocity (the velocity (i.e.,i.e., the speed) is the the speed) is the time rate at which the point is time rate at which the point is moving along its path.moving along its path.

• Roller coaster rides incur many changes Roller coaster rides incur many changes in speed and direction, or velocity, and in speed and direction, or velocity, and the rate of this change is acceleration. It the rate of this change is acceleration. It is not true, as often thought, that the is not true, as often thought, that the speed of a car at the bottom of a hill is speed of a car at the bottom of a hill is equal to its initial velocity plus its drop equal to its initial velocity plus its drop velocity; actually the greater the drop velocity; actually the greater the drop height, the less initial velocity influences height, the less initial velocity influences final velocity. Along the same lines, final velocity. Along the same lines, speed is not directly proportional to the speed is not directly proportional to the drop height but to the square root of the drop height but to the square root of the drop height. Doubling the speed of a drop height. Doubling the speed of a coaster ride requires quadrupling the coaster ride requires quadrupling the height of the hill.height of the hill.

• AT THIS POINT IN THE RIDE . . . the track AT THIS POINT IN THE RIDE . . . the track curves back upward and the speed drops curves back upward and the speed drops as the roller coaster climbs the second as the roller coaster climbs the second hill. Owing to the change in hill. Owing to the change in velocity,velocity, the the riders experience upward riders experience upward centripetal accelerationcentripetal acceleration in the form of in the form of positive g-forces. This compression positive g-forces. This compression makes them feel heavier than normal. On makes them feel heavier than normal. On the climb the coaster regains some the climb the coaster regains some potential energypotential energy that it had lost to that it had lost to kinetic energykinetic energy on the previous descent. on the previous descent.

PHYSICS OF ROLLERCOASTERSPHYSICS OF ROLLERCOASTERSACCELERATIONACCELERATION

• Time rate at which a velocity is Time rate at which a velocity is changing. Because velocity has both changing. Because velocity has both magnitude and direction, it is called magnitude and direction, it is called a vector quantity; acceleration is also a vector quantity; acceleration is also a vector quantity and must account a vector quantity and must account for changes in both the magnitude for changes in both the magnitude and direction of a velocity.and direction of a velocity.

• If the velocity of a roller coaster If the velocity of a roller coaster moving on a straight path is moving on a straight path is increasing (increasing (i.e.,i.e., if the speed, which is if the speed, which is the magnitude of the velocity, is the magnitude of the velocity, is increasing), the acceleration vector increasing), the acceleration vector will have the same direction as the will have the same direction as the velocity vector. If the velocity is velocity vector. If the velocity is decreasing (that is, the coaster is decreasing (that is, the coaster is decelerating), the acceleration decelerating), the acceleration vector will point in the opposite vector will point in the opposite direction. So, whether the coaster is direction. So, whether the coaster is increasing speed down a hill or increasing speed down a hill or decreasing speed up a hill, it is decreasing speed up a hill, it is regarded as acceleration in the regarded as acceleration in the mathematical sense.mathematical sense.

PHYSICS OF ROLLERCOASTERSPHYSICS OF ROLLERCOASTERSACCELERATIONACCELERATION

• Changes in acceleration greatly contribute to the Changes in acceleration greatly contribute to the thrill of a roller coaster ride. A rider may feel thrill of a roller coaster ride. A rider may feel greater sensations in a low-speed coaster with greater sensations in a low-speed coaster with sharp acceleration changes than on a faster sharp acceleration changes than on a faster coaster with a smoother ride. Pure speed is often coaster with a smoother ride. Pure speed is often not as recognizable as the surge of acceleration not as recognizable as the surge of acceleration during a coaster ride.during a coaster ride.

• A common fallacy is that acceleration increases A common fallacy is that acceleration increases along with the weight of the riders and the car, along with the weight of the riders and the car, when actually the acceleration of a coaster in free-when actually the acceleration of a coaster in free-fall is independent of its mass. Acceleration does fall is independent of its mass. Acceleration does increase, however, with a steeper angle of descent.increase, however, with a steeper angle of descent.

PHYSICS OF ROLLERCOASTERSPHYSICS OF ROLLERCOASTERSACCELERATIONACCELERATION

• AT THIS POINT IN THE RIDE . AT THIS POINT IN THE RIDE . . . at the bottom of the . . at the bottom of the second hill, the coaster, in second hill, the coaster, in theory, reaches an instant of theory, reaches an instant of zero zero acceleration,acceleration, at the at the point where its speed is point where its speed is greatest, relative to greatest, relative to anywhere else on that hill. anywhere else on that hill. Zero acceleration also Zero acceleration also occurs for an instant at the occurs for an instant at the top of a hill, where in turn top of a hill, where in turn the speed is at its lowest the speed is at its lowest level. At the bottom of the level. At the bottom of the dip, the riders experience dip, the riders experience compression, or compression, or acceleration stressacceleration stress, owing to , owing to forces greater than their forces greater than their usual weight.usual weight.

PHYSICS OF ROLLERCOASTERSPHYSICS OF ROLLERCOASTERSFRICTIONFRICTION

• Force that resists the sliding or rolling of one Force that resists the sliding or rolling of one solid object over another. Frictional forces, solid object over another. Frictional forces, such as the traction needed to walk without such as the traction needed to walk without slipping, may be beneficial; but they also slipping, may be beneficial; but they also present a great measure of opposition to present a great measure of opposition to motion. Friction, along with air resistance, or motion. Friction, along with air resistance, or wind drag, are dissipative forces that are wind drag, are dissipative forces that are neglected in idealized discussions of neglected in idealized discussions of fundamental mechanics, in which gravitation fundamental mechanics, in which gravitation is the only force considered.is the only force considered.

PHYSICS OF PHYSICS OF ROLLERCOASTERSROLLERCOASTERS

PHYSICS OF ROLLERCOASTERSPHYSICS OF ROLLERCOASTERSACCELERATION STRESSACCELERATION STRESS

• Physiological changes Physiological changes that occur in the that occur in the human body in motion human body in motion as a result of rapid as a result of rapid increase of speed. increase of speed. Rapid acceleration Rapid acceleration and surges in and surges in acceleration are felt acceleration are felt more critically than more critically than are gradual shifts.are gradual shifts.

PHYSICS OF ROLLERCOASTERSPHYSICS OF ROLLERCOASTERSCENTRIFUGAL FORCECENTRIFUGAL FORCE

• Quantity, peculiar to a Quantity, peculiar to a particle moving on a particle moving on a circular path, that has circular path, that has the same magnitude the same magnitude and dimensions as the and dimensions as the force that keeps the force that keeps the particle on its circular particle on its circular path (the centripetal path (the centripetal force) but points in the force) but points in the opposite direction.opposite direction.

PHYSICS OF PHYSICS OF ROLLERCOASTERSROLLERCOASTERSKINETIC ENERGYKINETIC ENERGY

• Form of energy that an object or a particle Form of energy that an object or a particle has by reason of its motion. If work, which has by reason of its motion. If work, which transfers energy, is done on a roller transfers energy, is done on a roller coaster by applying a net force, such as coaster by applying a net force, such as gravity, the coaster speeds up and thereby gravity, the coaster speeds up and thereby gains kinetic energy. Kinetic energy is a gains kinetic energy. Kinetic energy is a property of a moving object and depends property of a moving object and depends not only on its motion but also on its mass. not only on its motion but also on its mass. The kind of motion may be translation (or The kind of motion may be translation (or motion along a path from one place to motion along a path from one place to another), rotation about an axis, vibration, another), rotation about an axis, vibration, or any combination of these.or any combination of these.