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Terminology and Measurements in Biomechanics Kinesiology

Objectives. 1. Define: Mechanics

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Terminology and Measurements in Biomechanics Kinesiology

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    1. Terminology and Measurements in Biomechanics (Kinesiology) Vector Scalar Manipulations Dr. Judith Ray

    2. Objectives 1. Define: Mechanics & Biomechanics 2. Define: Kinematics, Kinetics, Statics, & Dynamics, and state how each related to biomechanics 3. Convert units of measure; metric & U.S. system 4. Describe scalar & vector quantities, and identify 5. Demonstrate graphic method of the combination & resolution of two-dimensional (2D) vectors 6. Demonstrate use of trigonometric method for combination & resolution of 2D vectors 7. Identify scalar & vector quantities represented in motor skill & describe using vector diagrams

    3. Mechanics Area of scientific study that answer the questions, in reference to forces and motion What is happening? Why is it happening? To what extent is it happening? Deals with Force, Matter, Space & Time All motion subjects to laws and principles of force and motion

    4. Biomechanics The study of mechanics limited to living thing, especially the human body An interdisciplinary science based on the fundamentals of physical and life sciences Concerned with basic laws that effect forces on the state or rest or motion of humans

    5. Language of Biomechanics Descriptive and numerical analysis of movement. Kinesiological analysis of movement What does that mean to you in describing a skill or movement? Analysis is the key component to Kinesiology

    6. Statics and Dynamics Biomechanics includes: statics & dynamics Statics: all force acting on a body are balanced The Body is in equilibrium Dynamics: deals with unbalanced forces Causes object to change speed or direction Excess force in one direction A turning force Principles of work, energy, & acceleration are included in the study of dynamics

    7. Kinematics and Kinetics Kinematics: geometry of motion Describe time, displacement, velocity, & acceleration Motion may be straight line or rotating Kinetics: forces that produce or change motion Linear causes of linear motion Angular causes of angular motion

    8. QUANTITIES IN BIOMECHANICS The Language of Science Careful measurement & use of mathematics are essential for Classification of facts Systematizing of knowledge Enables us to express relationship quantitatively rather than merely descriptively Mathematics is needed for quantitative treatment of mechanics

    9. Vectors and the Basic Principles of Mathematics Addition, Subtraction, Multiplication, and Division Addition of Vectors Communities: a + b = b + a Associative: a +(b +c) =(a +b) + c 5+ (3+ 4) = (5 + 3) + 4 Distributive: a (b +c) = a b +a c 6 (5 + 4) = 6 x 5 + 6 x 4

    10. Qualitative and Qualitative Qualitative descriptive datum can be narrative empirical or observed situations Quantities numerical datum composed of units of measurements scalar or vector quantities

    11. Units of Measurement Expressed in terms of space, time, and mass U.S. system: current system in the U.S. Inches, feet, pounds, gallons, second Metric system: currently used in research Meter, liter, kilogram, newton, second Table 10.1 present some common conversions used in biomechanics

    12. Units of Measurement Length: Metric; all units differ by a multiple of 10 US; based on the foot, inches, yards, & miles Area or Volume: Metric: Area; square centimeters of meters Volume; cubic centimeter, liter, or meters US: Area; square inches or feet Volume; cubic inches or feet, quarts or gallons

    13. Units of Measurement Mass: quantity of matter a body contain Weight: depends on mass & gravity Force: a measure of weight Metric: newton (N) is the unit of force US: pound (lb) is the basic unit of force Time: basic unit in both systems in the second

    14. Scalar & Vector Quantities Scalar: single quantities Described by magnitude Size or amount Ex. Velocity of 8 km/hr Vector: double quantities Described by magnitude and direction Ex. Velocity of 8 km/hr heading northwest

    15. VECTOR ANALYSIS Vector Representation Vector is represented by an arrow Length is proportional to magnitude

    16. Vector Quantities Equal if magnitude & direction are equal Which of these vectors are equal?

    17. Combination of Vectors Vectors may be combined be addition, subtraction, or multiplication New vector called the resultant (R)

    18. Combination of Vectors

    19. Resolution of Vectors Any vector may be broken down into two component vectors acting at right angle to each other Figure represent the velocity the shot was put

    20. Resolution of Vectors What is the vertical velocity (A)? What is the horizontal velocity (B)? A & B are components of resultant (R)

    21. Resolution of Vectors Is the summation of all vectors in the equation the resultant is the summation of all vectors. The answer

    22. Location of Vectors in Space Position of a point (P) can be located using Rectangular coordinates Polar coordinates Horizontal line is the x axis Vertical line is the y axis Coordinates for point P are represented by two numbers (13,5) 1st number of x units 2nd number of y units

    23. Location of Vectors in Space Rectangular coordinates for point P are represented by two numbers (13,5) 1st number of x units 2nd number of y units Polar coordinates for point P that describe line R make with x axis (r,?) Distance (r) of point P from origin Angle (?)

    24. Cartesian Coordinate System X is the horizontal axis Y is the vertical axis The intersect at (0,0) where x = zero and y = zero

    25. Location of Vectors in Space

    26. Location of Vectors in Space Degree are measured in a counterclockwise direction

    27. Graphic Resolution Quantities may be handled graphically Consider a jumper who take of with a velocity of 9.6 m/sec at an angle of 180 Since take-off velocity has both magnitude & direction, the vector may be resolved Select a linear unit of measurement to represent velocity, 1 cm = 1 m/sec Draw a line of appropriate length at an angle of 180 to the x axis

    28. Graphic Resolution Given Velocity = 5.5 m/sec; Angle =18 0 Solution 1 cm = 1 m/sec; Horizontal velocity x = 5.2 m/sec Vertical velocity y = 1.7 m/sec

    29. Combination of Vectors Resultant vector may be obtained graphically Construct a parallelogram Sides are linear representation of two vectors Mark a point P Draw two vector lines to scale, with the same angle that exists between the vectors

    30. Parallelogram Method Lines parallel form parallelograms

    31. Combination of Vectors Construct a parallelogram for the two line drawn Diagonal is drawn from point P Represents magnitude & direction of resultant vector R

    32. Polygrams Two are more vectors Addition of vectors cumulative Addition of vectors associative

    33. Combination of Vectors with Three or More Vectors Find the R1 of 2 vectors Repeat with R1 as one of the vectors

    34. Another Graphic Method of Combining Vectors Vectors added head to tail Muscle J, K pull on bone E-F Muscle J pulls 1000 N at 100 Muscle K pulls 800 N at 400

    35. Another Graphic Method of Combining Vectors 1 cm = 400 N Place vectors in reference to x,y Tail of force vector of Muscle K is added to Head of force vector of Muscles J Draw line R

    36. Another Graphic Method of Combining Vectors Measure line R & convert to N 4.4 cm = 1760 N Use a protractor to measure angle Angle = 23.50 Not limited to two vectors

    37. Component Method Vector Components also called components of the resultant Trigonometric functions to solve problems Use of the Sine, Cosine, tangent ratio relationships

    38. Trigonometric Resolution and Combination of Vectors Method has value for portraying the situation Serious drawbacks, when calculating results Accuracy is difficult to control Dependent on drawing and measuring Procedure is slow and unwieldy A more accurate & efficient approach uses trigonometry for combining & resolving vectors

    39. Trigonometric Resolution of Vectors Any vector may be resolved if trigonometry relationships of a right triangle are employed Same jumper example as used earlier Find: Horizontal velocity (Vx) Vertical velocity (Vy)

    40. Trigonometric Resolution of Vectors

    41. Trigonometric Resolution of Vectors Given: R = 9.6 m/sec ? = 180 To find Value Vy: sin ? = opp = Vy hyp R Vy = sin 180 x 9.6 = .3090 x 9.6 = 3.0 m/sec

    42. Trigonometric Resolution of Vectors Given: R = 9.6 m/sec ? = 180 To find Value Vx: cos ? = adj = Vx hyp R Vx = cos 180 x 9.6 = .9511 x 9.6 = 9.1 m/sec

    43. Trigonometric Combination of Vectors If two vectors are applied at right angle to each other, the solution should appear reasonable obvious If a baseball is thrown with a vertical velocity of 15 m/sec and a horizontal velocity of 26 m.sec What is the velocity of throw & angle of release?

    44. Trigonometric Combination of Vectors Given: Vy = 15 m/sec Vx = 26 m/sec Find: R and ? Solution: R2 = Vy2 + Vx2 R2 = 152 + 262 = 901 R = 901 R = 30 m/sec

    45. Trigonometric Combination of Vectors Solution: ? = arctan Vy/Vx ? = arctan 15/26 ? = 300 Velocity = 30 m/sec Angle = 300

    46. Trigonometric Combination of Vectors If more than two vectors are involved If they are not at right angles to each other Resultant may be obtained by determined the x and y components for each vector and then summing component to obtain x and y components for the resultant Lets consider the example with Muscle J; 1000 N at 100, and Muscle K; 800 N at 400

    47. Muscle J r = (1000N, 100) y = r sin ? y = 1000 x .1736 y = 173.6 N (vertical) x = r cos ? x = 1000 x .9848 x = 984.8 N (Horizontal)

    48. Muscle K r = (800N, 400) y = r sin ? y = 800 x .6428 y = 514.2 N (vertical) x = r cos ? x = 800 x ..7660 x = 612.8 N (Horizontal)

    49. Trigonometric Combination of Vectors Given: ?y = 687.8 N ?x = 1597.6 Find: ? and r

    50. Trigonometric Combination of Vectors Solution: = arctan ?y / ?x = arcntan 687.8 1597.6 = .4305 = 23.30 R = 687.8 / sin 23.30 R = 687.8 / .3955 R = 1739 N

    51. Value of Vector Analysis The ability to handle variable of motion and force as vector or scalar quantities should improve ones understanding of motion and the force causing it The effect that a muscles angle of pull has on the force available for moving a limb is better understood when it is subjected to vector analysis The same principles may be applied to projectiles

    52. Summary and Discussion Scalar and Vector Quantities Scalar have magnitude only Vector Quantities have magnitude and direction

    53. Vector Quantities Cartesian Coordinate System (points, lines and 2 dimensional orientation) Graphic method Polygon Parallelogram Pythagorean Theorem Component Method - adding the sine, cosine, tangent ratio to vectors

    54. Vectors and the Basic Principles of Mathematics Addition, Subtraction, Multiplication, and Division Addition of Vectors Communities: a + b = b + a Associative: a +(b +c) =(a +b) + c 5+ (3+ 4) = (5 + 3) + 4 Distributive: a (b +c) = a b +a c 6 (5 + 4) = 6 x 5 + 6 x 4

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