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PHYSICS AND SPORTS J P SINGH ASSISTANT PROFESSOR PHYSICS POSTGRADUATE GOVT.COLLEGE SECTOR-11,CHANDIGARH e-mail-jatinder_pal2179@yahoo.co.in Abstract Sports competitions can be understood using physics concepts and mathematical techniques. Grounded in comprehensive statistical survey of the outcome of sports competitions in the major sports leagues, a theoretical model in which the underdog team may upset the favorite team with a fixed probability is developed. This theory captures many observed characteristics of sports competitions in leagues, tournaments, and championships. This theory help us understand sports competitions, provides us with methods for quantifying parity and competitiveness, as well as efficient algorithms for scheduling games.This science is fun and easy to understand. Physics of amusement park People are wild about amusement parks. Each day, we flock by the millions to the nearest park, wait in long lines for a short 60-second ride on our favorite roller coaster. The thought prompts one to consider what is it about a roller coaster ride that provides such widespread excitement among so many of us and such dreadful fear in the rest? Is our excitement about coasters due to their high speeds? Absolutely not! In fact, it would be foolish to spend so much time and money to ride a selection of roller coasters if it were for reasons of speed. It is more than likely that most of us sustain higher speeds on our ride along the interstate highway on the way to the amusement park than we do once we enter the park. The thrill of roller coasters is not due to their speed, but rather due to their accelerations and to the feelings of weightlessness and weightiness which they produce. Roller coasters thrill us because of their ability to accelerate us downward one moment and upwards the next; leftwards one moment and rightwards the next. Roller coasters are about acceleration; that's what makes them thrilling. we will focus on the centripetal acceleration experienced by riders within the circular-shaped sections of a roller coaster track. These sections include the clothoid loops (which we will approximate as a circle), the sharp 180-degree banked turns and the small dips and hills found along otherwise straight sections of the track.The most obvious section on a roller coaster where centripetal acceleration occurs is within the so-called clothoid loop. Roller coaster loops assume a tear-dropped shape which 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 which 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 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 loop. 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.This change in speed as the rider moves through the loop is the second aspect of the acceleration which a rider experiences. For a rider moving through a circular loop with a constant speed, the acceleration can be described as being centripetal or towards the center of the circle. In the case of a rider moving through a noncircular loop at non-constant speed, the acceleration of the rider has two components. There is a component which is directed towards the center of the circle (ac) and attributes itself to the direction change; and there is a component which is directed tangent (at) to the track (either in the opposite or in the same direction as the car's direction of motion ) and attributes itself to the car's change in speed. This tangential component would be directed opposite the direction of the car's motion as its speed decreases (on the ascent towards the top) and in the same direction as the car's motion as its speed increases (on the descent from the top). At the very top and the very bottom of the loop, the acceleration is primarily directed towards the center of the circle. At the top, this would be in the downward direction and at the bottom of the loop it would be in the upward direction. Physics of skating In the case of the speed skater , the force resulting from the contact between ice skates and ice has two components to it. The force is a vector combination of a normal force and a friction force. The normal force is the result of the stable surface providing support for any object pushing downward against it. The friction force is the result of the static friction force resulting from the ice-skate interaction. As the skater leans into the turn, she pushes downward and outward upon the ice. The high pressure and temperature of the blade upon the ice creates a shallow groove in which the blade momentarily rests. The blade pushes outward upon the vertical wall of this groove and downward upon the floor of this groove. As we would expect from Newton's third law of motion, there is a reaction force of the ice pushing upward and inward upon the skate. If this blade-ice action does not occur, the skater could still lean and still try to push outward upon the ice. However, the blade would not get a grip upon the ice and the skater would be at risk of not making the turn. As a result, the ice skater's skates would move out from under her, she would fall to the ice, and she would travel in a straight-line inertial path. Without an inward force, the skater cannot travel through the turn.The same principle of lean which allows the speed skater to make the turn around a portion of the circle applies to the wealth of other sporting events where participants lean into the turn in order to momentarily move in a circle. A downhill skier makes her turn by leaning into the snow. The snow pushes back in both an inward and an upward direction - balancing the force of gravity and supplying the centripetal force. A football player makes his turn by leaning into the ground. The ground pushes back in both an inward and upward direction - balancing the force of gravity and supplying both the centripetal force. A cyclist makes his turn in a similar manner as he leans at an angle to the horizontal. The road surface pushes with an upward component of force to balance the downward force of gravity. The road surface also pushes with a horizontal component of force towards the center of the circle through which the cyclist is turning. A bobsled team makes their turn in a similar manner as they rise up onto the inclined section of track. Upon the incline, they naturally lean and the normal force acts at an angle to the vertical; this normal force supplies both the upward force to balance the force of gravity and the centripetal force to allow for the circular motion. Spinning the Basketball Spinning the ball when you shoot is not done to affect air resistance, or to make air resistance cause the ball's path to curve, as is the case in baseball. Basketballs move too slowly for that to happen. Once the basketball leaves the shooter's hand, it travels in an unchanging parabolic path. So what's the purpose of backspin? Backspin on the ball is used to help it to bounce into the net when it hits the rim. It will usually hit something, unless the throw was very high. The backspin, after contact with the back rim or board, will result in a change in velocity opposite to the spin direction, changing an equal-angle rebound into a velocity more toward the net. This makes it more likely that the ball will go in. Receiving a Pass: The impact of a hard pass can be lessened, making it less likely the ball will knock the wind out of you, if it is caught into the body. The ball coming at you has momentum, m•v. By increasing the time over which you decelerate the ball, you lessen the force. In other words, since m•v = F•t, then F = (m•v) / t ... increasing t causes F to get smaller. This is the same principle that makes an air bag in your car work. The time over which you decelerate is lengthened, resulting in a lower force. Of course, catching a ball into your chest has other benefits. It makes it less likely you'll drop the ball, and harder for someone to grab. Starting, Stopping, and Changing Direction: A players' shoes must have good traction, which is the same as saying that the coefficient of frictionf between the shoe and the floor must be high. Friction is the force that opposes the motion of two surfaces that are in contact. Every surface is rough, on the microscopic scale, and when two surfaces come in contact, the high points on each surface temporarily make contact. The opposing or attracting forces of the surface molecules cause a 'frictional' force. A basketball player will also make use of static friction; a foot firmly planted, rather than slipping across the floor, will provide more friction when he has to stop or turn suddenly. This is because static friction is greater than sliding friction . It is also why shoes must have a good grip on the floor in any direction you push off from, and why some shoes are unsuitable for basketball ... they may have lots of forward traction, but slip too easily when pushing sideways. It's just like driving ... spinning tires have less frictional force than non-spinning ones. References ________________________________________ Allan V. Abbott and David G. Wilson, editors, Human Powered Vehicles, Human Kinetics, Champaign, IL, 1995. P. W. Bearman and J. K. Harvey, "Golf Ball Aerodynamics," Aeronautical Quarterly, 27:112-122, 1976. James E. Counsilman, Competitive Swimming, Counsilman Co., Inc., Bloomington, IN, 1977. Ira Flatow, Rainbows, Curveballs, William Morrow and Company, New York, 1988. Leonard Koppett, The New Thinking Fan's Guide to Baseball, Simon and Schuster, New York, 1991. Cliff Frohlich, "Aerodynamic Effects on Discus Flight," American Journal of Physics, 49:1125-1132, 1981. R. V. Ganslen, "Aerodynamic and Mechanical Forces in Discus Flight," The Athletic Journal, 44, 1964. Felix Hess, "Aerodynamics of Boomerangs," Scientific American, 219:123-136, 1968. Dr. Stancil Johnson E.D. Frisbee, Workman Publishing Company, New York, 1975. Joseph Katz, Race Car Aerodynamics: Designing for Speed, Robert Bentley Inc., Cambridge, MA, 1995. Ernest W. Maglischo, Swimming Faster: A Comprehensive Guide to the Science of Swimming, Mayfield Publishing Co., 1982. Bernard S. Mason, Boomerangs: How to Make and Throw Them, Dover Publications, Inc., New York, 1974. Roy McLeavy, Hovercraft and Hydrofoils, Arco Publishing Company, Inc., New York, 1976. Rabindra D. Mehta, "Aerodynamics of Sports Balls," Annual Review of Fluid Mechanics, 17:151-189, 1985. Howard Payne and Rosemary Payne, The Science of Track and Field Athletics, Pelham Books Ltd., London, 1981. Dan Roddick, Frisbee Disc Basics, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1980.
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