Chapter 12: The Conditions of Linear Motion

1. Chapter 12:The Conditions of Linear Motion Nature of Force, Newton�s Laws, Forces The modify Motion, Free Body Diagrams, Work, Power, and Energy, The Analysis of Linear Motion,

2. Objectives 1. Name, define, and use the terms of linear motion 2. Define magnitude, direction, and point of application of force and use terms properly 3. Explain changes magnitude, direction, and point of application of force on the motion state of a body 4. Define and give examples of linear forces, concurrent forces, and parallel forces 5. Determine magnitude, direction, and point of application of muscles forces 6. State Newton�s laws as they apply to linear motion

3. Objectives 7. Explain cause and effect relationship between forces of linear motion and objects experiencing the motion 8. Name & define basic external forces that modify motion 9. Draw and analyze a 2D free-body diagrams 10. Explain work-energy relationship applied to a body experiencing linear motion 11. Define and use properly the terms work, power, kinetic energy, and potential energy 12. Perform a mechanical analysis of a motor skill

4. THE NATURE OF FORCE Force is that which pushes or pulls through direct mechanical contact or through the force of gravity to alter the motion of an object Internal forces are muscle forces that act on various structure of the body External forces are those outside the body Weight, gravity, air or water resistance, friction, or forces of other objects acting on the body

5. Aspects of Force Force is a vector quantity Magnitude, and Direction Also a Point of Application All three characteristics must be identified For a weight lifter to lift a 250 N barbell Lifter must apply a force greater than 250 N, in an upward direction, through the center of gravity of the barbell

6. Magnitude Amount of force being applied Force exerted by the barbell had a magnitude of 250 N This force was the result of gravity acting on the mass of the barbell In this since, force is referred to as weight Weight is mass times acceleration due to gravity

7. Magnitude of Muscular Force Direct proportion to the number & size of fibers contracting in a muscle Muscles normally act in groups Their force or strength is measured collectively Maximum muscular strength is measured by a dynamometer Measures force applied by a group of muscle through an anatomical lever

8. Point of Application Point at which force is applied to an object Where gravity is concerned this point is always through the center of gravity For muscular force, that point is assumed to be the muscle�s attachment to a bony lever Technically, it is the point of intersection of line of force and mechanical axis of the bone

9. Direction Direction of a force is along its action line Direction of gravity is vertically downward Gravity is a downward-directed vector starting at the center of gravity of the object Direction of muscular force vector is the direction of line of pull of the muscle

10. Direction of Muscular Force Vector Muscle angle of pull: angle between line of pull and the portion of mechanical axis between the point of application and the joint

11. Resolution of Forces Magnitude is line A Point of application is at point B Direction is represented by the arrowhead and the angle ?

12. Angle of Pull Force may be resolved into a vertical and a horizontal component Size of each depends on angle of pull A muscle�s angle of pull changes with every degree of joint motion So do the horizontal & vertical components The larger the angle (00 - 900), the greater the vertical and less the horizontal components

13. Angle of Pull Vertical component is perpendicular to the lever, called rotary component Horizontal component is parallel to the lever and is the nonrotary component Most resting muscles have an angle of pull < 900

14. Rotary vs. Nonrotary Components Angle of pull < 900 Nonrotary force is directed toward fulcrum Stabilizing effect Helps maintain integrity of the joint

15. Rotary vs. Nonrotary Components Angle of pull > 900 Nonrotary force is directed away fulcrum Dislocating component Does not occur often Muscle is at limit of shortening range and not exerting much force

16. Rotary vs. Nonrotary Components Angle of pull = 900 Force is all rotary Angle of pull = 450 Rotary & nonrotary components are equal Muscular force functions: Movement Stabilization

17. Anatomical Pulley Changes the angle of pull of the muscle providing the force This increase in angle of pull increases the rotary component Patella for the quadriceps

18. Resolution of External Forces Accomplished in the same manner as muscular forces applied at oblique angle Only horizontal force will move table Vertical force serves to increase friction

19. Composite Effects of Two or More Forces Two or more forces can be applied to objects A punted ball�s path is the result of force of the kick, force or gravity, and force of wind A muscle rarely act by itself Usually muscle work in combination Composite forces on the body may be classified according to their direction and application as linear, concurrent, or parallel

20. Linear Forces Forces applied in the same direction, the resultant is the sum of the forces a + b = c Forces applied in the opposite direction, the resultant is the sum of the forces a + (-b) = c

21. Concurrent Forces Acting at the same point of application at different angles Resultant of Two or more concurrent forces depends on both the magnitude of each force and the angle of application

22. Parallel Forces Forces not in the same action line, but parallel to each other Three parallel forces two upward one downward

23. Parallel Forces 10 N weight at 900 Gravity at points B & C A is the force of biceps Effect of parallel forces on an object depends on magnitude, direction & application point of each force

24. NEWTONS� LAWS OF MOTIONLaw of Inertia A body continues in its state of rest or of uniform motion unless an unbalanced force acts on it An object at rest remains at rest An object in motion remains in same motion Unless acted on by a force Friction & air resistance effect objects in motion

25. Law of Inertia A body continues in its state of rest or of uniform motion unless an unbalanced force acts on it

26. Law of Acceleration F = ma The acceleration of an object is directly proportional to the force causing it and inversely proportional to the mass of the object What is the force needed to produce a given linear acceleration? Since m = w/g, F = (w/g) x a Force to accelerate a 300 N object 2 m/sec2 F = (300 N / 9.8m/s2) x 2 m/s2 = 61 N

27. Impulse Ft = m(v � u) The product of force and the time it is applied F = ma Substitute (v � u) / t for a F= M(v � u) / t Multiply both sides by time Ft = m(u � v)

28. Momentum Ft = mv - mu The product of mass and velocity 20 N force falling for 5 sec has equal momentum as 100 N force falling for 1 sec Any change in momentum, is equal to the impulse that produces it Force applied in direction of motion will increase momentum Force applied opposite to direction of motion will decrease momentum

29. Law of Reaction For every action there is an equal and opposite reaction

30. Conservation of Momentum In any system where forces act on each other the momentum is constant An equal and opposite momentum change must occur to object producing reactive force Therefore: m1v1 � m1v1 = m2v2 � m2v2

31. Summation of Forces Force generated by muscle may be summated form one segment to another Typical throwing pattern Force from legs is transferred to the trunk Further muscular force ? momentum, and is transferred to upper arm Mainly as an ? velocity because mass is ? Sequential transfer of momentum continues with mass decreasing and velocity increasing Until momentum is transferred to thrown ball

32. FORCES THAT MODIFY MOTIONWeight The force of gravity is measured as the weight of the body applied through the center of gravity of the body and directed toward the earth�s axis W = mg

33. Contact Forces:Normal Reaction For every action there is an equal and opposite reaction The jumper pushes off the ground and the ground pushes back

34. Contact Forces:Friction Friction is the force that opposes efforts to slide or rill one body over another Some cases we try to increase friction for a more effective performance Other cases we try to decrease friction for a more effective performance The amount of friction depends on the nature of the surface and the forces pressing them together

35. Friction Friction is proportional to the force pressing two surface together Force of friction acts parallel to the surfaces and opposite to the direction of motion

36. Coefficient of friction, ? The ratio of force needed to overcome the friction, P, to the force holding the surface together, W ? = P / W Large coefficient surfaces cling together Small coefficient surfaces slide easily Coefficient of 0.0 = frictionless surface

37. Coefficient of Friction May be found by Placing one object on a second and tilt the second until first begins to slide The tangent of the angle with horizontal is the coefficient of friction

38. Elasticity and Rebound Objects rebound is a predictable manner The nature of rebound is governed by elasticity, mass, and velocity of rebounding surface, friction between surface, and angle of contact Elasticity is the ability to resist distorting influences and to return to its original size and shape

39. Elasticity and Rebound Stress is the force that acts to distort Strain is the distortion that occurs Stress may take the form of tension, compression, bending, or torsion

40. Coefficient of Elasticity Is defined as the stress divided by the strain Most commonly determined in the compression of balls by comparing drop height with the bounce height The closer to 1.0 the more perfect the elasticity

41. Coefficient of Elasticity Also may be found using the Law of Conservation of Momentum Using the change in velocity of the two objects, assuming masses remain constant Where v2 and v1 are velocities after impact, and u1 and u2 are velocities before impact

42. Angle of Rebound For a perfectly elastic object, The angle of incidence (striking) is equal to the angle of reflection (rebound) As coefficient of elasticity varies variations will occur

43. Effects of Spin on Bounce A ball with topspin will rebound form horizontal surface lower and with more horizontal velocity A ball with backspin will rebound higher and with less horizontal velocity A ball with no spin will develop topspin A ball with topspin will gain more topspin A ball with backspin may be stopped or reversed Spinning balls hitting vertical surface will react in the same manner, as with horizontal surfaces, but in relation to the vertical surface

44. Fluid Forces Water and air are both fluids and as such are subject to many of the same laws and principles The fluid forces of buoyancy, drag, and lift apply in both mediums and have considerable effect on the movements of the human body

45. Buoyancy Archimedes� Principle states: a body immersed in a liquid is buoyed up by a force equal to the weight of the liquid displaced This explains why something float and something sink Density is a ratio of the weight of an object and its volume

46. Specific gravity Ratio of the density of an object and density of water An object the same weight and volume as water has a specific gravity of 1.0 An object with specific gravity > 1.0 will sink An object with specific gravity < 1.0 will float

47. Lift and Drag Drag is the resistance to forward motion Result of fluid pressure on the leading edge of the object amount of backward pull produced by turbulence on the trailing edge

48. Lift and Drag Laminar flow is a smooth, unbroken flow of fluid around an object A smooth surface will have better laminar flow than a rough surface, resulting in less drag

49. Lift and Drag Lift is the result of changes in fluid pressure as the result of difference in air flow velocities Bernoulli�s Principle states: the pressure in a moving fluid decreases as the speed increases

50. Ball Spin Bernoulli�s Principle applies here also A ball will move in the direction of least air pressure A ball spinning drags a boundary layer of air with it, causing air to move faster, reducing pressure on one side

51. FREE BODY DIAGRAMS In analyzing any technique, one should consider all external forces, by accounting for effect of each one of the body The isolated body is considered a separate mechanical system Easier to identify forces & represent as vectors Can help determine the application and direction of forces acting on the body

52. Direction & Point of Application of External Forces

53. Free Body Diagram Magnitude arrow length Direction arrow head Point of application arrow tail Weight (W) Reactive force (R) Friction (F)

54. Free Body Diagram Weight (W) Buoyancy (B) Lift (L) Drag (D) State of motion or rest of the body depends on the vector sum of all these forces

55. Free Body Diagram Also used to show forces on a body segment Thigh isolated Weight of thigh (W) Muscle force Hip (MH) Reactive Forces Hip (Hx & Hy) Knee (Kx & Ky))

56. WORK, POWER, AND ENERGYWork Work is the product of force expended and the distance force is applied W = Fs Work (W), Force (F), Distance (s) Units any combination of force & distance foot/pounds, joule = 107 x 1 gram / 1 centimeter

57. Work 20N suitcase place on a shelf 2m high Work = 40Nm Same suitcase lifted along a 4m incline is still 40Nm of work Horizontal distance not included

58. Positive & Negative Work Positive work � work done in the same direction that the body moves overcoming gravity is more work Negative work � in the opposite direction resisting gravity is less work One performs more work walking up a mountain than walking back down

59. Mechanical Muscular Work Example: a rectangular muscle 10 cm x 3 cm, that exerts 240N of force Average muscle fiber shortens � its length W = Fs W = 240N x 5cm W = 1200N-cm or 120 Nm

60. Force per Muscle Cross Section IF force of the muscle is not known, it is computed form the muscle�s cross section Example: Assume same muscle is 1cm thick Cross section = width x thickness 3cm X 1 cm = 3 sq cm Average force = 360 N per sq cm F = 360 x 3 = 1080N W = Fs W = 1080N x 5cm = 5400 N cm or 540 Nm

61. Muscular Work Internal structure of the muscle is rectangular A simple geometric cross-sectional measure could be used For penniform & bipenniform muscle, physiological cross section must be determined s - represents � the length of average fiber Force per square inch depends on whose research the student accepts

62. Muscle Work by Physiological Cross Section (PCS) W = Average force x PCS (sq cm) x � length of fibers (cm) Divide by 100 to convert N-cm to Nm W (Nm) = 360 x PCS (sq cm) x � fiber length (cm) 100

63. Power The rate at which work is done P = Fs / t or P = W / t or P = Fv P = Power t = time W = work v = velocity = s / t

64. Energy The capacity to do work Law of Conservation of Energy: The total amount of energy possessed by a body or an isolated system remains constant

65. Potential Energy Potential energy is the product of the force an object has and the distance over which it can act PE = mgh m = mass, g = gravity, h = height

66. Kinetic Energy The energy due to its motion KE = � mv2 m = mass, v = velocity Work done is equal to the kinetic energy acquired, or Fs = � mv2

67. ANALYSIS OF LINEAR MOTION First identify the nature of the force involved in the motion of interest Weight, Propulsive forces, Normal reaction, Friction, Buoyancy, Drag, & Lift

68. ANALYSIS OF LINEAR MOTION The principles that govern the mechanical aspect of a movement performance can be summarized by examining some of the basic concepts involved in the kinetic of linear motion Inertia, Impulse, Work, & Kinetic Energy