1. Linear Motion: Kinematics and Kinetics Applied Kinesiology 420:151

2. Agenda Introduction to motion Linear kinematics Linear kinetics Analysis of linear motion

3. Introduction to Motion Linear motion (translatory) Rectilinear Curvilinear Circular Angular motion (rotary) General motion

4. Shoulder = angular or linear? Figures 11.1, 2, 3, 4, Hamilton

5. Agenda Introduction to motion Linear kinematics Linear kinetics Analysis of linear motion

6. Linear Kinematics Linear: A point moving along a line Kinematics: The study of motion (of a point moving along a line) in respect to displacement, velocity and acceleration

7. Displacement Displacement: Change in position Vector quantity  Magnitude and direction Displacement vs. distance SI unit = m

8. Velocity Velocity: Rate of displacement V = displacement/time Vector quantity Velocity vs. speed SI unit = m/s

9. Average vs. Instantaneous Velocity Average velocity = displacement/time Entire displacement  start to finish Instantaneous: Velocity at any particular instant within the entire displacement Still average velocity however time periods much smaller therefore “essentially” instantaneous

11. s (m)tjohnson (s)tlewis (s)Vjohnson (m/s)Vlewis (m/s) 101.861.885.385.32 202.872.966.976.76 303.83.887.897.73 404.664.778.588.39 505.555.619.018.91 606.386.459.409.30 707.217.299.719.60 808.118.129.869.85 908.988.9910.0210.01 1009.839.8610.1710.14 Instantaneous?

13. (m)Splits BJ (s)Splits CL (s)Vinst. BJVinst. CL 0 101.861.885.385.32 10 201.011.089.909.26 20 300.930.9210.7510.87 30 400.860.8911.6311.24 40 500.890.8411.2411.90 50 600.830.8412.0511.90 60 700.830.8412.0511.90 70 800.900.8311.1112.05 80 900.87 11.49 90 1000.850.8711.7611.49

15. Acceleration Acceleration: Rate of change of velocity A = v f – v i Vector quantity SI unit = m/s/s or m/s 2 Uniform acceleration Very rare Projectiles (more later)

16. Average vs. Instantaneous Acceleration Average acceleration = Rate of change in velocity  assumes uniform acceleration Instantaneous: Acceleration between smaller time periods Provides more information Johnson vs. Lewis

17. Average acceleration for Ben Johnson? A = (v f – v i ) / t A = (10.17 m/s – 0 m/s) / 9.83 s A = (10.17 m/s) / 9.83 s A = 1.03 m/s 2 v BJ (m/s)v CL (m/s) 00 5.385.32 6.976.76 7.897.73 8.588.39 9.018.91 9.409.30 9.719.60 9.869.85 10.0210.01 10.1710.14 Average acceleration for Carl Lewis? A = (v f – v i ) / t A = (10.14 m/s – 0 m/s) / 9.86 s A = (10.14 m/s) / 9.86 s A = 1.03 m/s 2 Enough information?

18. s (m)t BJ (s)t CL (s)v BJ (m/s)v CL (m/s)a BJ (m/s2)a CL (m/s2) 0000000 101.861.885.385.322.892.83 202.872.966.976.760.550.49 303.83.887.897.730.240.25 404.664.778.588.390.150.14 505.555.619.018.910.080.09 606.386.459.409.300.06 707.217.299.719.600.04 808.118.129.869.850.020.03 908.988.9910.0210.010.02 1009.839.8610.1710.140.020.01 Instantaneous?

20. (m) Splits BJ (s)Splits CL (s) Vinst. BJVinst. CL a BJ (m/s2)a CL (m/s2) 0 101.861.885.385.322.892.83 10 201.011.089.909.264.483.65 20 300.930.9210.7510.870.921.75 30 400.860.8911.6311.241.020.41 40 500.890.8411.2411.90-0.440.80 50 600.830.8412.0511.900.980.00 60 700.830.8412.0511.900.00 70 800.900.8311.1112.05-1.040.17 80 900.87 11.49 0.44-0.64 90 1000.850.8711.7611.490.320.00

22. Positive and Negative Acceleration Motion to the right or up is considered in the positive direction Velocities in these directions also positive Motion to the left or down is considered in the negative direction Velocities in these directions also negative

23. Positive and Negative Acceleration Increasing speed in the positive direction is + acceleration Decreasing speed in the positive direction is – acceleration Increasing speed in the negative direction is – acceleration Decreasing speed in the negative direction is + acceleration

24. Use positive/negative acceleration as opposed to acceleration and deceleration

25. Uniform Acceleration Most common form of uniform acceleration is projectile motion 9.8 m/s 2 Laws of uniform acceleration Acceleration is constant Allows you to solve for: Velocity: Initial or final Distance traveled by implement Time in the air

26. Uniform Acceleration Solve for final velocity when initial velocity, time and acceleration are known v f = v i + at Manipulate the formula v i = v f – at t = v f – v i /a What if initial or final velocity = 0?

27. What is the final velocity at 4 seconds if you know the velocity at 2 seconds? vf = vi + at Vf = -19.6 m/s + (-9.8 m/s 2) (2s) Vf = -39.2 m/s How long was it in the air if you know the initial and final velocities? t = -49 m/s – 0 m/s /-9.8 m/s 2 t = -49 m/s / -9.8 m/s 2 t = 5 s What is the initial velocity if you know the velocity at 5 seconds? vi = vf – at Vi = -49 m/s – (-9.8 m/s2)(5s) Vi = 0 m/s

28. Uniform Acceleration Solve for velocity when initial velocity, distance and acceleration are known v f 2 = v i 2 + 2as Manipulate the formula v i 2 = v f 2 - 2as s = v f 2 - v i 2 /2a What if initial or final velocity = 0?

29. Page 288 of text book: Assuming that a ball is thrown upward so that it reaches a height of 5 meters before starting to fall, what is its initial velocity? What is its final velocity? Initial velocity: vi 2 = vf 2 – 2as vi 2 = (0 m/s) 2 - 2(-9.8 m/s 2 )(5m) vi 2 = 0 m 2 /s 2 + 98 m 2 /s 2 vi 2 = 98 m 2 /s 2 ( sq. root both sides ) vi = 9.9 m/s Final velocity: vf 2 = vi 2 + 2as vf 2 = (0 m/s) 2 + 2(-9.8 m/s 2 )(5m) vf 2 = 0 m 2 /s 2 - 98 m 2 /s 2 vf 2 = -(98 m 2 /s 2 ) ( sq. root both sides ) vf = -9.9 m/s Check work by solving for distance s = vf 2 - vi 2 / 2a s = (-9.9) 2 – (0) 2 / 2(-9.8m/s 2 ) s = 98 m 2 /s 2 / 19.6 m/s 2 s = 5 m

30. Uniform Acceleration Solve for distance when initial velocity, acceleration and time are known s = v i t + ½ at 2 Manipulate the formula

31. How far will an object drop if you let if fall for 3 seconds? s = vit + ½ at 2 s = 0 + ½ (-9.8 m/s 2 )(3 s) 2 s = 0 + -4.9 m/s 2 (9 s 2 ) s = -44.1 m How high will an object go in the air in 2 seconds if thrown with an initial velocity of 29.4 m/s? s = vit+ ½ at 2 s = 29.4 m/s (2 s) + ½(-9.8 m/s 2 )(2 s) 2 s = 58.8 m – 19.6 m s = 39.2 m

32. Vi = 0 Vf = -9.8 m/s V = -4.9 m/sS = -4.9 m 1 s 2 s Vf = -19.6 m/s V = -14.7 m/ss = -14.7 m 3 s Vf = -29.4 m/s V = -24.5 m/s s = -24.5 m Total distance traveled: (-4.9)+(-14.7)+(-24.5) = -44.1 m

33. 1 s Vi = 29.4 m/s Vf = 19.6 m/s V = 24.5 m/s S = 24.5 m 2 s Vf = 9.8 m/s V = 14.7 m/sS = 14.7 m Total distance traveled: 14.7+24.5 = 39.2 m

34. Vacuum  no air resistance Unlimited constant acceleration Real world  air resistance Terminal velocity Continued acceleration until air resistance = gravity Terminal velocity of skydiver = 120 mph

35. Agenda Introduction to motion Linear kinematics Linear kinetics Newton’s laws Types of force Work, power, energy Analysis of linear motion

36. Linear Kinetics What causes motion?  Force Newton’s Three Laws of Motion: Cannot be proved Universally accepted

37. 1 st Law: Law of Inertia Law: A body continues in its state of rest/motion unless an unbalanced force acts upon it Inertia: The resistance to motion proportionate to mass Unbalanced forces during start? Unbalanced forces during stop?

38. 2 nd Law: Law of Acceleration Law: The acceleration of an object is proportional to the force causing it and inversely proportional to its mass F = ma  a = F/m Impulse: The product of force and time F = ma = m(v f – v i )/t Ft = m(v f – v i )

39. Impulse Max acceleration of an object = max force and max time Hammer throw Baseball swing (quickness vs. velocity) Manipulation of impulse Two basketball players of 100 kg Player A = 2500 N over 0.25 s Player B = 3000 N over 0.21 s Advantage?

40. Impulse and Momentum Momentum = mv Ft = m(v f – v i ) = mv f – mv i Any change in momentum is equal to the impulse that produced it Applications? Shot put: Effect of force, arm length? Catching a fastball

41. 40 m/s or 90 mph Weight = 5 oz. Mass = 0.14 kg Momentum = mv Momentum = 40 m/s (0.14 kg) Momentum = 5.6 kg*m/s If you want to stop this pitch with your bare hands (change mv from 5.6 kg*m/s to 0), this change in momentum will equal the impulse that creates the change in momentum! If you try to stop the pitch in 0.05 seconds, it will require 112 N of force (5.6/0.05 = 112). This is approximately 25 lbs of force! Ft = mvf - mvi112(0.05) = 5.6 - 0 Why does a 5 story fall typically result in death?

43. Why wasn’t he able to hold on? (15 July 1999, Alabama) A 25-year-old soldier died of injuries sustained from a 3-story fall, precipitated by his attempt to spit farther than his buddy. His plan was to hurl himself towards a metal guardrail while expectorating, in order to add momentum to his saliva. In a tragic miscalculation, his momentum carried him right over the railing, which he caught hold of for a few moments before his grip slipped, sending him plummeting 24 feet to the cement below. The military specialist had a blood alcohol content of 0.14%, impairing his judgment and paving the way for his opportunity to win a Darwin Award.

44. 3 rd Law: Law of Reaction Law: For every action there is an equal and opposite reaction Objects at rest are in equilibrium  the weight of the object is balanced by the force of the surface pushing back against it Ground reaction forces Cement vs. sand Examples: Objects colliding? Conservation of momentum Momentum lost by one body = momentum gained by other body Unequal masses = unequal accelerations

45. Agenda Introduction to motion Linear kinematics Linear kinetics Newton’s laws Types of force Work, power, energy Analysis of linear motion

46. Types of Forces Gravity Ground reaction forces Friction Rebound Air resistance (drag)

47. Gravity “The force that causes objects to fall to earth, the moon to orbit the earth and the planets to orbit the sun” Weight: The attractive force of the earth  9.8 m/s/s Weight = mg 1 N = 0.2248 lbs Gravity is a force vector Magnitude = weight Direction = straight down

48. Ground Reaction Force GRF: The reaction force from a surface upon which one is moving GRFs are force vectors Magnitude: Equal to amount of force expressed into ground Direction: Opposite direction from which force was expressed into ground Energy can be transformed (ie sand) Figure 12.18, Hamilton

49. Friction Friction: the force that opposes efforts to slide or roll one body across/over another Can work for us or against us More friction can be good Less friction can be good

50. Friction Friction depends on: Nature of surfaces (coefficient of friction) Forces involved Push FfFf Coefficient of frictionWeight of book Figure 12.14, Hamilton Starting vs. sliding friction

51. Rebound Rebound: The force that causes objects to rebound from each other after contact Amount of rebound depends on several factors Elasticity Angle of rebound Spin Momentum

52. Rebound - Elasticity Objects that receive a stress will strain (become distorted/deformed) Elasticity: Ability to return to original shape once stress is removed Coefficient of restitution = stress/strain Greater elasticity = greater rebound

53. Rebound – Angle of Rebound Assume COR = 1.0  angle of incidence = angle of reflection As COR decreases, so does angle of reflection relative to angle of incidence Figure 12.23, Hamilton

54. Rebound - Spin Topspin: Increase Hv, decrease Vv Backspin: Increase Vv, decrease Hv Sidespin: Rebound in direction of spin

55. Rebound - Momentum Momentum = mv As mass and/or velocity increase, so does rebound

56. Air Resistance (Drag) Air resistance: The force that occurs as a result of fluid pressure at the leading edge of an object and the backward pull created by turbulence on the trailing edge Figure 12.25, Hamilton

57. Agenda Introduction to motion Linear kinematics Linear kinetics Newton’s laws Types of force Work, power, energy Analysis of linear motion

58. Work, Power, Energy Work: The product of force expended and distance through which force succeeds in overcoming resistance W = Fd SI unit = J or N*m Distance measured vertically only

59. F 2 m Force needed to overcome inertia of block = 20 N Total vertical distance = 2 m Work = 20 N * 2 m Work = 40 J or 40 N*m Figure 12.30, Hamilton

60. Work performed climbing stairs Work = Fd Force Subject weight From mass, ie 65 kg Displacement Height of each step Typical 8 inches (20cm) Work per step 636 N x 0.2 m = 127 Nm Multiply by the number of steps

61. Work on a stair stepper Work = Fd Force Push on the step ???? Displacement Step Height 8 inches Work per step ???N x.203 m = ???Nm

62. Work on a cycle ergometer Work = Fd Force belt friction on the flywheel mass ie 3 kg Displacement revolution of the pedals Monark: 6 m per rev Work per revolution 3kg x 6 m = 18 kgm

63. Work, Power, Energy Work can be positive or negative Work done in direction of force application is positive work Concentric actions Work done in opposite direction of force application is negative work Eccentric actions

64. Work, Power, Energy Power: The rate at which work is performed Power = Work/time or Fv SI unit = W or J/s or N*m/s

65. Calculate & compare power During the ascent phase of a rep of the bench press, two lifters each exert an average vertical force of 1000 N against a barbell while the barbell moves 0.8 m upward Lifter A: 0.50 seconds Lifter B: 0.75 seconds

66. Calculate & compare power Lifter A F = 1000 N d = 0.8 m t = 0.50 s Power = Fd/t Power = 1000 N*0.8 m /0.50 s Power = 800 J/ 0.50 s Power = 1600 W Lifter B?

67. Power on a cycle ergometer Power = Fd/t Power = Fd*rev/min How much power output is there? Force = 3 kg d = 6 m / revolution 60 revolutions / min Power = 3kg*6m*60 rev/min Power = 1080 kg*m/min Note: 1 Watt = ~ 6 kg*m/min How many Watts? 180 Watts

68. Other Ways to Calculate Power Treadmill sprinting Work = weight*vertical displacement (angle of treadmill) Time = length of sprint Vertical jumping (Lewis equation) Work = weight*vj height Power is estimated with an equation Stair stepper Work = resistance of step*displacement of step Time = time to move step Stair running (Margaria-Kalaman test) Work = weight*vertical displacement*# steps Time = time it takes to get up the stairs

69. Work, Power, Energy Energy: The capacity to do work Amount of energy = work accomplished Many types of energy Heat, sound, light, electric, chemical, atomic Mechanical energy  Two main types Potential energy Kinetic energy

70. Mechanical Energy Potential energy: Energy a body possesses due to its position PE = mgh Kinetic energy: Energy a body possesses due to its motion KE = ½ mv 2

71. PE = Maximum KE = 0 PE = Decreasing KE = Increasing PE = 0 KE = Maximum Energy can neither be created nor destroyed

73. Agenda Introduction to motion Linear kinematics Linear kinetics Newton’s laws Types of force Work, power, energy Analysis of linear motion

74. General Analysis of Linear Motion Linear kinematics: Linear displacement Linear velocity Linear acceleration Linear kinetics: Effect of a force in an instant in time F = ma Effect of a force applied over a period of time Impulse and momentum Effect of a force applied over a distance Work, power, energy

75. General Phases of Skill Performance Ritual Phase Full of idiosyncrasies, useful for mental focus Does the ritual phase affect performance negatively, positively? Preparation Phase Wind up (force, velocity, accuracy, combination?) Is energy storage required? Force Phase Is the force applied in the right direction? Is there enough force, too much? Follow Through Phase Is there enough time to slow down body parts? Does the follow through promote correct application of force?