The Physics of Sports

by Lisa, Michael

• ISBN13: 9780073513973
• ISBN10: 0073513970
• eBook ISBN(s): 9780077801885
• Edition: 1st
• Format: Paperback
• Copyright: 2015-02-20
• Publisher: McGraw Hill
• More Book Details

Table of Contents

Preface to the student

Preface to the instructor

I Primary Chapters

1 Warm-up: Basic concepts

1.1 Quantifying the world of sports Units, conversions, scientific notation

1.2 When we don’t have exact numbers Estimation, typical scales

1.3 The center of mass Center of mass

Problems

2 Racing, mathematically1D kinematics

2.1 Phelps in BeijingSpeed, velocity, position and graphs

2.2 Bolt in BerlinAcceleration, constant acceleration kinematics

2.3 Rope-climbing and divingVertical motion and gravity

Problems

3 Net Force: Dwight Howard illustratesForces, dynamics

3.1 The Physics of a Dwight Howard Dunk

3.1.1 Waiting for the passWeight, ground reaction force, equilibrium, free-body diagrams, Newton’s first law

3.1.2 Spec sheetWeight and mass

3.1.3 The launchNewton’s 2nd and 3rd Laws; dynamics of a jump; dynamics with non-constant forces; ground reaction force

3.1.4 The flightFreefall dynamics, revisited

3.1.5 The landingCushioning limitations, GRF revisited

3.2 Sideways tractionFriction

3.3 More complex situations2D dynamics and applications

3.3.1 Dwight Howard takes a quick stepVectors

3.3.2 Football tryoutsTwo moving bodies; how to increase friction

3.3.3 Ball throw speedImportant application

3.4 “Imaginary forces” in sports

3.4.1 Imaginary pushes on Dale Earnhardt, Jr.Sensation of force in a non-inertial frame

3.4.2 Two non-traditional Olympic eventsPotential to mistakenly interpret a reaction force

3.4.3 Discus throwCentripetal and “centrifugal” forces

Equations

Problems

4 Punts, Dick Fosbury & other projectilesProjectile Motion

4.1 The math: simpler than you think2D kinematics

4.2 Football punt: range, hangtime and compromiseRange, hangtime

4.3 Shot putThe range when the starting and ending height are not the same

4.4 Human projectilesParabolic motion of CM with changing body shape

4.4.1 The Blake Griffin ballet

4.4.2 Dick Fosbury’s Flop

4.4.3 Bob Beamon’s long jump

Equations

Problems

5 Curveballs, foul shots and bent kicksAerodynamic forces

5.1 Overview4 forces; use of approximations

5.2 Immersion in fluid: BuoyancyBuoyant force

5.3 Moving through fluid: DragDrag force; drag coefficient; terminal velocity

5.4 Sideward forces from asymmetries

5.4.1 The swing of a cricket ballSidewards force from asymmetric surface roughness

5.4.2 Bending a ball’s flightMagnus force

5.5 Aerodynamic forces, one at a timeExamples

5.5.1 Curveballs and subatomic physicsMagnus as a centripetal force; unexpected analogy

5.5.2 Do we need a computer?Constant-force approximation

5.5.3 A simple formula for a curveballSidewards deflection over a short part of the spiral

5.5.4 Roberto Carlos’s “impossible” free kickreal-life spiral example; aero-dominated versus gravity-dominated ball sports

5.5.5 John Paxson, master of forcesSystematic breakdown of a basketball shot

5.6 More complicated aerodynamics in sportsSemi-quantitative analysis of more complex situations

5.6.1 KnucklingEffects of fluctuating orientation and drag

5.6.2 Tilting into the wind: discusNon-Magnus lift

5.6.3 Human wings: ski jumpsLift with adjustable tilt

5.6.4 Making the world safer for javelin spectatorsChanges in javelin design and rules

5.6.5 Not so fast! Polyurethane swimsuitsDrag effects in water and rule changes

5.7 Not all air is created equalVariations in air density and the effect on sports

5.7.1 Rocky Mountain (Natural) HighAltitude and air density

5.7.2 Hot days are (not) a dragTemperature and air density

5.7.3 It’s not just the heat– it’s the humidityHumidity and air density effects

5.7.4 Storm fronts

Equations

Problems

6 Game changers: collisions in sportsCollisions and momentum

6.1 What is a “collision” and how to think about itMomentum, impulse

6.2 The physics of a football tackleCompletely inelastic collisions, conservation of momentum

6.2.1 The energy of a crunchKinetic energy, energy lost

6.2.2 Helmet designImpulse, relation to force

6.2.3 Forcing a runner out of bounds2D inelastic collisions

6.3 Gentler pursuits - BowlingElastic collisions; also isolated and non-isolated systems

6.3.1 Beginner’s first roll - head-on collision1D elastic collisions

6.3.2 Birthday-party bowlingImportance of an isolated system when using momentum conservation

6.3.3 Off-center hits - converting a lily2D elastic collision

6.3.4 Off-center billiards shotsSpecial case: 2D elastic collisions for m_1 = m_2

6.3.5 Beyond 2D - The upward hop of the pinImpulse and an isolated system

6.4 A happy medium: dribbling and drivingPartially inelastic collisions

6.4.1 The sad, short life of the NBA’s synthetic ballCoefficient of restitution

6.4.2 Pádraig Harrington’s drive and swinging harderinelastic collision with finite-mass objects; COR variation with speed

6.5 Off-center hits: Spinning the ballQualitative intro to torque and spin

6.5.1 Bounce passtorque from friction; translation & rotation motion

6.5.2 Diving shotAerodynamic and collisional aspects of topspin

6.5.3 Backspin on a golf shotAerodynamic and collisional aspects of backspin

Equations

Problems

7 Energy in sports: bursts of powerEnergy, power, work, efficiency, elasticity

7.1 Bouncing basketball - the whole processConversion of energy; elastic and gravitational energy

7.1.1 Heat in basketball: not just for Miamikinetic to thermal energy

7.1.2 Energy during the bounceElastic potential energy

7.1.3 Details of energy during the riseGravitational potential energy

7.2 Efficiencyvarious definitions

7.2.1 The efficiency of a basketball bounce

7.2.2 The efficiency of a golf drive

7.2.3 Heat Death

7.3 The athlete: the energetic starting pointChemical energy and its conversion

7.3.1 The source of energy and its flowFood energy, Calories

7.3.2 The human engine I - energy conversionBiochemistry of food processing; energy storage

7.4 Keeping score - energy accounting in sportsThe energy conservation concept and its application to athletes

7.4.1 The water analogy

7.4.2 How useful is the energy conservation concept, really?In-principle versus practical utility of the concept

7.5 Uncle Rico’s hopes dashedWork, power and the human engine

7.5.1 WorkWork-energy theorem; connection to forces

7.5.2 Power

7.5.3 The human engine II - powerCaloric conversion rates

7.6 Behdad Salimikordsiabi’s clean and jerkQuantitative analysis of power lift; details of motion

7.6.1 Work during a lift

7.6.2 The snatch and clean-and-jerk techniquesDetails of a complicated set of moves

Equations

Problems

8 Energy and timing in elastic equipmentStiffness, timing, elastic energy storage

8.1 The Physics of Archery I - Energy storage and transferHooke’s Law, efficiency of energy transfer

8.1.1 The bow’s energyHooke’s Law

8.1.2 Bow and arrow efficiencyEnergy “loss” depends on system details

8.2 The Physics of Archery II - Fire PowerOscillation frequency and period

8.3 The Physics of Archery III - Archer’s Paradoxstiffness of extended rod, timing details

8.3.1 Oscillations of an arrowCharacterizing the flexibility of a rod

8.3.2 How the archer’s paradox worksBuckling, matching timing, details

8.4 Zdeno Chára’s slapshot - fast storage, faster releaseenergy storage and collisions

8.5 Bungee jumping brides & quadratic equationsExtended example with tension; quadratic equation

8.5.1 Dangling above the waterTension as an equilibrating force

8.5.2 How low will he bounce?non-trivial energy example and the quadratic equation

Equations

Problems

9 The physics of cyclingSustained power generation, rolling friction, more aerodynamics, power balance, rotational dynamics, torque

9.1 Input to the bike - sustained human power

9.1.1 Caloric power requirements for long-term effortMetabolic Equivalent Task (MET) ratings

9.1.2 Oxygen uptake, VO2max and powerdefinition of VO_2max; rider efficiency

9.1.3 Power-to-weight ratioPWR

9.2 Power outputPower, force and velocity

9.2.1 HillsGravitational force along a slope

9.2.2 Rolling resistance Dissipation during rolling

9.2.3 Wind dragDrag in still and moving air

9.2.4 The Bicycle Power EquationIterative solution to complicated equations

9.2.5 Cycling versus other modes of transportComparison of power requirements

9.2.6 DraftingAerodynamics of more than one object

9.3 Talansky drives the bikeTorque and rotational motion

9.3.1 RollingConnection between linear and rotational motion

9.3.2 Drivetrain I - GearsGeometry of chain rings, importance of cadence

9.3.3 That annoying 2π – angular velocityAngular velocity, the radian

9.3.4 Drivetrain II - Chain actionTorque with fixed right angle lever arm

9.3.5 Drivetrain III - Chain reactionClarifying Newton’s Third Law

9.3.6 Drivetrain IV - Pushing the pedalsLine of action. Torque for forces at an angle

9.3.7 Rolling friction, revisitedTorque nature of “rolling friction”, lever arm when line of action is not tangent to edge

9.3.8 Back to basics - the wheel againMoment of inertia, angular acceleration, rotational kinetic energy

Equations

Problems

10 Twisting athletes in flightAngular motion with changing moment of inertia, rotation about fixed axes and in free space, conservation of angular momentum

10.1 Human rotationAnatomical axes and moments of inertia

10.2 Backward Giant CircleTorque, energy, rotation around fixed axis

10.2.1 Torques and spin rateTorque changes with lever arm

10.2.2 Maximal force at the bottom of the swingConservation of energy with rotational motion; centripetal Force

10.2.3 Swinging to speed up

10.2.4 Dismount Angular momentum and conservation

10.3 Figure skating -spinning on ice Angular momentum and work done by “internal” force

10.4 Rotational Action and Reaction Angular momentum of different body parts

10.4.1 Acrobatics of a long-jumper, revisited Rotational “action/reaction” about the transverse axis

10.4.2 Throwing, kicking, twisting Rotation and counter-rotation along the longitudinal axis

10.4.3 Balance Beam Rotation and counter-rotation about the anteroposterior axis

Equations

Problems

II Supplemental Chapters

11 Lines of action on the line of scrimmage: the torque wars

12 A Barry Bonds home run Ball-bat collisions

12.1 Ball-Bat Collision: Speeds, impulse, force

12.2 BBS –Batted Ball Speed

12.3 Focus on the bat Collision with an extended object

12.3.1 Bonds’ swing

12.3.2 The bat as an extended object Sweet spot, vibrations, effective mass

13 The Pole Vault

13.1 Origins

13.2 The modern event

13.2.1 Performance progression

13.2.2 Contributions to height

13.3 Pole Vault 101 –Energy flow

13.3.1 Energy-based estimate of vaulting height

13.3.2 What matters, in the simple calculation

13.4 Pole Vault 102 –Beyond energy flow

13.4.1 Maximizing initial energy - carry weight

13.4.2 Minimizing inelastic energy “loss”

13.4.3 Fully exploiting the energy: flexibility and timing

13.4.4 Work done by the athlete

14 Is it better to run through first base, or to dive?

14.1 The story according to Sport Science

14.2 Too close to call

14.3 Diving speed

14.3.1 “50% deceleration”

14.3.2 Newton’s First Law and air drag

14.4 What’s really happening: Torque and impulse

14.5 Other issues

14.6 Concluding remarks

Answers to odd-numbered problems

Unit conversions

Tables of relevant physical properties

Bibliography, Further Reading

Index