Chapter 10: Linear Kinematics of Human Movement


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1 Chapter 10: Linear Kinematics of Human Movement Basic Biomechanics, 4 th edition Susan J. Hall Presentation Created by TK Koesterer, Ph.D., ATC Humboldt State University
2 Objectives Discuss the interrelationship among kinematic variables Correctly associate linear kinematic quantities with their units of measure Identify & describe effects of factors governing projectile trajectory Explain why the horizontal and vertical components of projectile motion are analyzed separately Distinguish between average & instantaneous quantities & identify circumstance which each is a quantity of interest
3 Linear Kinematic Quantities Kinematics: describes appearance of motion Kinetics: study of forces associated with motion Linear kinematics: involves the study of the shape, form, pattern and sequencing of linear movement through time Qualitative: major joint actions & sequencing Quantitative: Range of motion, forces, distance etc.
4 Distance & Displacement Measured in units of length Metric: meter, kilometer, centimeter, etc. English: inch, foot, yard & mile Distance: Scalar quantity Linear displacement: Vector quantity: length & direction (compass directions, left, right, up, & down, or positive & negative
5 Speed & Velocity Speed = length (or distance) change in time Velocity (v) = change in position = Δ position change in time Δ time v = displacement = d change in time Δ t
6 Speed & Velocity Velocity = position 2  position 1 time 2  time 1 Velocity is a vector quantity direction and magnitude of motion Laws of vector algebra
7 102
8 Acceleration Acceleration (a) = change in velocity = change in time Δv Δt a = v 2  v 1 Δt When acceleration is zero, velocity is constant
9 Positive/Negative Acceleration
10 Average & Instantaneous Quantities Instantaneous : Instantaneous values Average: Average velocity = final displacement total time
11 Velocity Curve for Sprinting
12 Velocity Curves for Two Sprinters
13 Kinematics of Projectile Motion Bodies projected into the air are projectiles Horizontal & Vertical Components Vertical is influenced by gravity No force (neglecting air resistance) affects the horizontal Horizontal relates to distance Vertical relates to maximum height achieved
14 Kinematics of Projectile Motion Influence of Gravity Major influence of vertical component Not the horizontal component Force of Gravity: Constant, unchanging Negative acceleration (9.81 m/s 2 ) Apex: The highest point in the trajectory
15 106
16 Kinematics of Projectile Motion Influence of Air Resistance In a vacuum, horizontal speed of a projectile remain constant Air resistance affects the horizontal speed of a projectile This chapter, velocity will be regarded as constant
17 Factors Influencing Projectile Trajectory Trajectory: Angle of projection Projection speed Relative height of projection
18 109
19 Factors Influencing Projectile Trajectory Angle of Projection General shapes Perfectly vertical Parabolic Perfectly horizontal Implications in sports Air resistance may cause irregularities
20 1010
21 Factors Influencing Projectile Trajectory Projection speed: Range: Relative Projection Height:
22 1014
23 Optimum Projection Conditions Maximize the speed of projection Maximize release height Optimum angle of projection Release height = 0, then angle = 45 0 Release height, then angle Release height, then angle
24 Range at Various Angles
25 Analyzing Projectile Motion Initial velocity: Horizontal component is constant Horizontal acceleration = 0 Vertical component is constantly changing Vertical acceleration = m/s 2
26 1017
27 Equations of Constant Acceleration Galileo s Laws of constant acceleration v 2 = v 1 + at D = v 1 t + ½at 2 V 2 2 = v ad d = displacement; v = velocity; a = acceleration; t = time Subscript 1 & 2 represent first or initial and second or final point in time
28 Equations of Constant Acceleration Horizontal component : a = 0 v 2 = v 1 D = v 1 t V 2 2 = v2 1
29 Equations of Constant Acceleration Vertical component: a = m/s 2 v 2 = at D = ½ at 2 V 2 2 = 2ad Vertical component at apex: v = 0 0 = v ad 0 = v 1 + at
30 Goals for Projectiles Maximize range (shot put, long jump) Maximize total distance (golf) Optimize range and flight time (punt) Maximize height (vertical jump) Optimize height and range (high jump) Minimize flight time (baseball throw) Accuracy (basketball shot)
31 Goals for Projectiles Maximize range (shot put, long jump) Shot put optimum angle is approximately 42 Long jump theoretical optimum is approximately 43 ; however, due to human limits, the actual angle for elite jumpers is approximately 2022
32 Goals for Projectiles Maximize total distance (golf) Because the total distance (flight plus roll) is most important, trajectory angles are lower than 45 Distance is controlled by the pitch of the club Driver ~ 10
33 Goals for Projectiles Optimize range and flight time (punt) Maximum range occurs with 45 trajectory Higher trajectory increases hang time with minimal sacrifice in distance Lower trajectory usually results in longer punt returns Less time for kicking team to get downfield to cover the punt returner
34 Goals for Projectiles Maximize height (vertical jump) Maximize height of COM at takeoff Maximize vertical velocity by exerting maximum vertical force against ground.
35 Goals for Projectiles Optimize height and range (high jump) Basic goal is to clear maximum height Horizontal velocity is necessary to carry jumper over bar into pit Typical takeoff velocity for elite high jumpers is approximately 45
36 Goals for Projectiles Minimize flight time (baseball throw) Baseball players use low trajectories (close to horizontal) Outfielders often throw the ball on one bounce with minimal loss of velocity
37 Goals for Projectiles Accuracy (basketball shot)
38 Projecting for Accuracy
39 Minimum Speed Trajectory
40 Angle of Entry
41 Margin for Error
42 Free Throw Optimum Angle
43 Summary Linear kinematics is the study of the form or sequencing of linear motion with respect to time. Linear kinematic quantities include the scalar quantities of distance and speed, and the vector quantities of displacement, velocity, and acceleration. Vector quantities or scalar equivalent may be either an instantaneous or an average quantity
44 Summary A projectile is a body in free fall that is affected only by gravity and air resistance. Projectile motion is analyzed in terms of its horizontal and vertical components. Vertical is affected by gravity Factors that determine the height & distance of a projectile are: projection angle, projection speed, and relative projection height The equation for constant acceleration can be used to quantitatively analyze projectile motion.
45 The End
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