Chapter 12: The Conditions of Linear Motion

Chapter 12:The Conditions of Linear Motion KINESIOLOGY Scientific Basis of Human Motion, 10th edition Luttgens & Hamilton Presentation Created by TK Koesterer, Ph.D., ATC Humboldt State University

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

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

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

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

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 w = mg

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

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

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

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 Fig 12.1

Resolution of Forces • Magnitude is line A • Point of application is at point B • Direction is represented by the arrowhead and the angle  Fig 12.2

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

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 Fig 12.1a

Rotary vs. Nonrotary Components Angle of pull < 900 • Nonrotary force is directed toward fulcrum • Stabilizing effect • Helps maintain integrity of the joint Fig 12.1a

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 Fig 12.1c

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 Fig 12.1c

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 Fig 12.5

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 Fig 12.7

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

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 b c a + = b c a + =

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 Fig 12.8

Parallel Forces • Forces not in the same action line, but parallel to each other • Three parallel forces • two upward • one downward Fig 12.9

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 Fig 12.10

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

Law of Inertia • A body continues in its state of rest or of uniform motion unless an unbalanced force acts on it Fig 12.12

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

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) Fig 12.13

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

Law of Reaction For every action there is an equal and opposite reaction Fig 12.14 & 12.15

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 Fig 12.16

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 becausemass is  • Sequential transfer of momentum continues with mass decreasing and velocity increasing • Until momentum is transferred to thrown ball

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 Fig 12.17

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 12.18

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

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 Fig 12.19 W = weight T = reactive force of table P = force needed to move F = force resisting motion

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

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 12.20

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

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 12.22b

e = bounce height drop height 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

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 e = v1 – v2 / u1 – u2

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 Fig 12.23

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

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

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

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

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 Fig 12.25 b

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 12.25 a

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 Fig 12.25 c

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 Fig 12.26a

Chapter 12: The Conditions of Linear Motion