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**Outline**• Kinetics (external) • Forces in human motion • Impulse-momentum • Mechanical work, power, & energy • Locomotion Energetics**Outline**• Kinetics • Forces in human motion • Gravity • Ground reaction • Inertial (F = ma) • Centripetal • Friction • Fluid Resistance • Multi force Free body diagrams • Dynamic and Static Analysis with Newton’s Laws**Reading**• Newton’s Laws • Ch 2: pages 41-44; 46-61 • Friction • Ch 2: pages 61-62 • Static/Dynamic Analyses & FBDs • Ch 3: pages 107-124 • Fluid Resistance • Ch 2: pages 63-68 • Linear Impulse/Momentum • Ch 2: pages 68-72 • Mechanical Energy/Work/Power • Ch 2: pages 81-90 • Applications (Locomotion, Jumping) • Ch 4: pages 145-159**Factors affecting fluid resistance**• Density • mass per unit volume • resistance to motion through a fluid increases with density • Viscosity • a measure of the fluid’s resistance to flow**Figure 2.20**Components of Fluid Resistance Drag Force: Opposes motion Lift Force: perpendicular to motion**Components of drag force**• Surface drag: friction of fluid rubbing on surface • Pressure drag: front-back pressure differential • Wave drag: waves at interface of two fluids.**Streamlines**Drag force is effected by: 1) different velocities of the streamlines 2) the extent to which the relative motion of the streamlines is disturbed**Laminar flow**Uniform layers of different speed Slowest layer closest to the surface of the object**Laminar flow:**Surface drag dominates Velocity of air Air direction relative to ball**Surface drag**• also called skin friction • Depends on • velocity of fluid relative to surface • roughness of surface • surface area of object • properties of fluid**Reducing surface drag**• Speed skater: wearing a smooth spandex suit • 10% less surface drag than wool clothes • Cyclist: wearing Lycra long sleeved shirt, tights, and shoe covers • Swimmer: Shaving body hair**Surface drag**• Surface drag: Friction within boundary layer • human movement in air: surface drag (3-5%) • small compared to pressure drag (95-97%)**Pressure drag: dominant form of drag in human movement**• Turbulent flow: Non-uniform flow of fluid around an object • Pressure differential causes a “pressure drag force”. Higher Pressure Lower Pressure**Streamlining reduces turbulence and pressure drag**• Flow remains laminar for longer -- less turbulence • less pressure drag Enoka, Figure 2.3A**Pressure drag vs. surface drag**• Pressure drag: dominates for large objects moving in low density & viscosity fluids • e.g., human running, cycling in air • Surface drag: dominates when small objects moving in high viscosity fluids, e.g. sperm swimming**Pressure drag force**• Fd = (0.5 CD)Av2 • = fluid density • air: 1.2 kg/m3 • water: 1000 kg/m3 • CD = coefficient of drag • A = projected area (m2, frontal area as object moves through the fluid) • v = velocity of the fluid relative to the object (m/s)**Coefficient of drag (CD): combines shape & aspect ratio**index • Unitless • Magnitude depends on • shape of object • orientation of object relative to fluid flow • Independent of size • Streamlining reduces CD**Coefficient of drag examples**• Mackerel: 0.0053 • Rainbow trout: 0.15 • Pigeon or vulture: 0.4 • Sphere: 0.47 • Human swimmer: 0.66 • Cyclist and bike: 0.9 • Runner: 0.9 • Flat plate: 1.0**vobject**Velocity (v) of fluid relative to the object v = vobject - vair • Example: vcyclist = 7 m/s • Still air: vair = 0 • Headwind: vair = 7 m/s • Tailwind: vair = 7 m/s**vair**vobject Velocity (v) of fluid relative to the object v = vobject - vair • Example: vcyclist = 7 m/s • Still air: vair = 0 v = 7 m/s • Headwind: vair = -7 m/s v = 14 m/s • Tailwind: vair = 7 m/s v = 0 m/s**Components of drag force**• Surface drag: friction of fluid rubbing on surface • Pressure drag: front-back pressure differential • Wave drag: waves at interface of two fluids.**Figure 2.20**Components of Fluid Resistance Drag Force: Opposes motion Lift Force: perpendicular to motion**Lift Force**Asymmetric objects Spinning object Bernoulli’s Principle: Pressure is inversely proportional to the velocity of the fluid**High Velocity**Low Pressure Low Velocity High Pressure**Drag acts in horizontal (x) direction, opposite to the**direction of locomotion Drag**Drag in locomotion (Fd = 0.5 CDAv2)**• Walking or running in air (CD = 0.9, = 1.2 kg/m3) • 0.5 CD = 0.55 kg/m3 • Fd = 0.55Av2 • Frontal area (A) = 0.4 m2 • Fd (Newtons) = 0.22 * v2**Role of Fd in locomotion**• Person in still air • Walk (1.25 m/s): Fd ~ 0.001 Fg,x • Run (4 m/s): Fd ~ 0.01 Fg,x • Run (8 m/s): Fd ~ 0.025 Fg,x • Person in headwind of 17 m/s (~ 35 mph) • Run (8 m/s): Fd ~ 0.25 Fg,x**Drag in cycling (Fd = 0.5 CDAv2)**• For cyclist in air (CD = 0.9, = 1.2 kg/m3) • 0.5 CD = 0.55 kg/m3 • Fd = 0.55Av2 • Frontal area (A) of cyclist & bike • Touring position (upright): 0.5 m2 • Racing position: 0.3 m2 • Recumbent position: 0.2 m2**Touring**Cycling Racer Recumbent**Swimming**• Water density >> air density • greater pressure drag • Fd = 0.5 CDAv2 • = 1000 kg/m3 • CD = 0.66 • A = 0.073 m2 • Fd (swimming) = 24* v2 • Comparison: Fd (walk, run) = 0.22 * v2**Drag: walking vs. swimming**• Drag force comparison at a given speed • Fd (swimming) ~ 100 x > Fd (walk, run in air) • Reasons • Water density >> air density • frontal area less • Cd less for swimming position**Total force: walking vs. swimming**• Swimming • Drag: largest force • 2 m/s ---> Fd ~ 0.14 * body weight • Walking • Ground reaction force: largest force • 2 m/s ---> Fg ~ 1.5 * body weight**Fn**mg q Problem: Friction force on slope Find maximum friction force in terms of mg, q, & µs.**Fn**mg q Friction force on slope Fs,max = Fn• µs Fn= mg cosq Fs,max = µs • mg cosq Fparallel (force pulling downhill parallel to slope) = mg sin q**Friction vs. Gravity force parallel**• m=70kg • µs = 0.5 • theta = 30 degrees • Solve for static friction force and the component of gravitational force pulling parallel to the slope.**Recitation**• a skier starts at the top of a 30 degreeincline,init. vel. = 0 • considering gravity, air resist. & friction, draw a FBD.**Recitation**• a skier starts at the top of a 30 degreeincline,init. vel. = 0 • considering gravity, air resist. & friction, draw a FBD • If m = 0.050 and mass is 70.0kg, what is max. frictional force? add that number to FBD**Recitation**• If frontal area is 0.600 m^2, air density is 1.200 kg/m^3, Cd is 0.9, what is air resist force when velocity = 10 m/sec • add this # value to your FBD**Neglect or Do Not Neglect?**• if we include air resistance, kinematic problems get more difficult. • In the bike lab we will take aero force into account and use an iterative computer approach.**Recitation**• What is the fastest velocity that can be reached by the skier. i.e. what is terminal velocity?