CHAPTER 12:PART 2 THE CONDITIONS OF LINEAR MOTION KINESIOLOGY Scientific Basis of Human Motion, 12 th edition Hamilton, Weimar & Luttgens Presentation Created by TK Koesterer, Ph.D., ATC Humboldt State University Revised by Hamilton & Weimar Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

12B-2 Forces That Modify Motion Weight 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 Fig Weight

12B-3 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. Fig Reaction Action

12B-4 Contact Forces: Friction Friction is the force that opposes efforts to slide or roll one body over another. In some cases we try to increase friction for a more effective performance. In other cases we try to decrease friction for a more effective performance. The amount of friction depends on the nature of the surfaces and the forces pressing them together.

12B-5 Friction Friction is proportional to the force pressing two surfaces together. Force of friction acts parallel to the surfaces and opposite to the direction of motion. W = weight T = reactive (normal) force of table P = force needed to move F = force resisting motion Fig 12.18

12B-6 Coefficient of friction,  The ratio of force needed to overcome the friction, P, to the force holding the surface together, W:  = P / W or  = F max /F N Large coefficient surfaces cling together. Small coefficient surfaces slide easily. Coefficient of 0.0 = frictionless surface.

12B-7 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. Fig 12.19

12B-8 Elasticity and Rebound Objects rebound in a predictable manner. The nature of rebound is governed by elasticity, mass, and velocity of rebounding surface, friction between surfaces, and angle of contact. Elasticity is the ability to resist distorting influences and to return to the original size and shape.

12B-9 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. Fig 12.21b

12B-10 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. e = bounce height drop height

12B-11 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 v f2 and v f1 are velocities after impact, and v i1 and v i2 are velocities before impact. e = (v f1 – v f2 ) / (v i1 – v i2 )

12B-12 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 changes variations will occur. Fig 12.22

12B-13 Effects of Spin on Bounce A ball with topspin will rebound from 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 surfaces will react in the same manner as with horizontal surfaces, but in relation to the vertical surface.

12B-14 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.

12B-15 Buoyancy Archimedes’ Principle: a body immersed in a liquid is buoyed up by a force equal to the weight of the liquid displaced. This explains why some things float and some things sink. Density is a ratio of the weight of an object to its volume.

12B-16 Specific gravity Ratio of the density of an object to the density of water. An object the same weight for 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.

12B-17 Lift and Drag Drag is the resistance to forward motion through a fluid. Result of : fluid pressure on the leading edge of the object. amount of backward pull produced by turbulence on the trailing edge. Fig b

12B-18 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. Fig a

12B-19 Lift and Drag Lift is the result of changes in fluid pressure as the result of difference in air flow velocities. Bernoulli’s Principle: the pressure in a moving fluid decreases as the speed increases. Fig c V  P  V  P  Lift Drag

12B-20 Ball Spin (Magnus Effect) 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. Fig 12.25

12B-21 Free Body Diagrams In analyzing any technique, one should consider all external forces, by accounting for the effect of each one on 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.

12B-22 Direction & Point of Application of External Forces Force Direction of Force Point of Application Weight (W)DownwardCenter of Gravity Normal (R)PerpendicularPoint of contact Friction (F)Along surfacePoint of Contact Buoyancy (B) UpwardCenter of buoyancy Drag (D)Opposite flowCenter of Gravity Lift (L)Perpendicular to dragCenter of Gravity

12B-23 Free Body Diagram Magnitude arrow length Direction arrow head Point of application arrow tail Weight (W) Reactive force (R) Friction (F) Fig 12.26

12B-24 Free Body Diagram Also used to show forces on a body segment. Thigh is isolated: Weight of thigh (W) Muscle force Hip (M H ) Reactive Forces Hip (H x & H y ) Knee (K x & K y )) Fig 12.28

12B-25 Work, Power, and Energy Work Work is the product of force expended and the distance over which force is applied. W = Fs Work (W), Force (F), Distance (s) Units are any combination of force & distance: foot/pounds, joule = 10 7 x 1 gram / 1 centimeter

12B-26 Work A 20 N suitcase is place on a shelf 2 m above the ground: Work done against gravity= 40 Nm Same suitcase lifted along a 4 m incline is still 40 Nm of work against gravity. Horizontal distance not included. 4 m 2 m 30 o

12B-27 Positive & Negative Work Positive work – force acts in the same direction as that of the objects motion. Negative work – force acts in the direction opposite to that of the objects motion.

12B-28 Mechanical Muscular Work Example: a rectangular muscle 10 cm x 3 cm, that exerts 240 N of force. Average muscle fiber shortens 1/2 its length. W = Fs W = 240 N x 5 cm W = 1200 Ncm or 120 Nm

12B-29 Force per Muscle Cross Section If force of the muscle is not known, it is computed from the muscle’s cross section. Example: Assume same muscle is 1cm thick: Cross section = width x thickness 3 cm X 1 cm = 3 sq cm Average force = 360 N per sq cm F = 360 x 3 = 1080 N W = Fs W = 1080 N x 5 cm = 5400 N cm or 540 Nm

12B-30 Muscular Work If the internal structure of the muscle is rectangular, a simple geometric cross-sectional measure can be used. For penniform & bipenniform muscle, physiological cross section must be determined. “s” represents 1/2 the length of the average fiber. Force per square inch depends on whose research the student accepts.

12B-31 Muscle Work by Physiological Cross Section (PCS) W = Average force x PCS (sq cm) x.5 length of fibers (cm) Divide by 100 to convert N-cm to Nm W (Nm) = 360 x PCS (sq cm) x.5 fiber length (cm) 100

12B-32 Power The rate at which work is done. P = Fs / t or P = W / t or P = Fv P = Powert = time W = workv = velocity = s / t

12B-33 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.

12B-34 Potential Energy Potential energy: energy based on position. Potential energy is the product of the weight of an object and the distance over which it can act: PE = mgh m = mass, g = gravity, h = height

12B-35 Kinetic Energy Energy based on motion: KE = 1/2 mv 2 m = mass, v = velocity Work done is equal to the kinetic energy acquired, or Fs = 1/2 mv 2

12B-36 Analysis of Linear Motion First identify the nature of the forces involved in the motion of interest: Weight Propulsive forces Ground Reaction Force Friction Buoyancy, Drag, & Lift

12B-37 Analysis of Linear Motion The principles that govern the mechanical aspects of a movement can be summarized by examining some of the basic concepts involved in the kinetics of linear motion: Inertia Impulse Work & Power Potential & Kinetic Energy