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Vector Summation and Composition
• Kinetic vector quantities – force weight, pressure, specific weight &
torque
• Kinematic vector quantities– Displacement, velocity & acceleration
• Scalar quantities– Mass, volume, length & speed
Vector Composition (Addition)
• Resultant vector
• “Tip-to-tail” vector composition
Vector #1
Vector #2
Resultant vector
Vector Addition Problems found in human motion analysis
• Combining forces– Net effect of two forces applied to any object– What is maximum safe speed for a curve?
• Centrifugal force, frictional force, & gravity
– What makes a curveball curve?• Wind force and weight
• Combining velocities– In crossing a river, what direction is best?
• Velocity of water and swimmer
– In aviation, correcting for wind• air speed and ground speed
Vector Resolution
Vertical
Horizontal
Example: A ball is thrown into the air
Resultant
Vector resolution problems found inhuman motion analysis (pp 76-81)
• Projectile motion situations– Find horizontal velocity– Find vertical velocity
• Friction problems – Find horizontal force component (Friction)– Find vertical component (Normal)
• First step in adding, or combining vectors– When more than one force is acting on an object– When adding velocity vectors
Trigonometric Solution of Vector Problems
• A more accurate procedure for quantitatively dealing with vector problems
Vector resolution:
Turning comp = F•d•sinΘRadial comp = F•d•cosΘ(d = d•sinθ)
Vert comp = F•sinΘHoriz comp = F•cosΘ
Θ
Vert comp = F•sin•ΘHoriz comp = F•cos•Θ
Θ Θ
Θ
Θ
d
Sum of two forces: Sum of two velocities:
Vector composition, or addition
Final step – what is the effect of the sum of these vectors?If the vectors are forces, then the net effect is to accelerate the object: a = F/m
6. Effect of net force: a = F/m = 86.9 N/ 2 kg = 43.45 ms-2
Homework assignment on Vector Summation
• Handout homework problem to turn in Monday, February 9
• Self-test problems:– Additional problems, p 81 # 4 and 5
COM Concepts and calculation procedures
• Obbjectives– To review concept of COM– To review reasons for studying COM– To review calculation method for calculating COM of
human body
Why study Center of Mass of Human Body?
• It simplifies the movement of the complex system so that we can understand its overall motion
• It allows us to easily consider the effect of net external forces (F = ma; a = F/m)
• Example of important issues related to COM– Is COM different for children and adults in a way that
affects movement?– Can an athlete really “hang in the air”– Is COM different for males and females in a way that
affects movement?
COM/COG Calculation Method (pp 436-445: Kreighbaum pp 116-123, 586-587)
• Concept of balancing segmental torques
• Segmental Calculation of COM – General calculation method– Information needed
• Proportionate mass of each segment (p 520)
• location of COM of each segment (p 521)
– Homework problem (handout in class)
Segmental concept of center of mass
Segmental Calculations&
Homework Problem
Segmental concept of center of mass
–Information needed
•Proportionate mass of each segment (p 520)
•location of COM of each segment (p 521)
Summary• Chapter 3 introduced basic concepts related to kinetics:
– Several types of mechanical loads act on the human body.– The distribution of force within a body structure is termed
mechanical stress.– Vectors quantities have magnitude & direction– Vector problems may be solved by a graphic or a
trigonometric approach. – Calculation methods for vector summation and resolution of
vectors were presented– Center of mass (COM) concepts were reviewed– Calculation methods for total body COM were presented
Next Class – Wednesday, Feb 11
• Read text, pp 329-347• Take web-based quiz for Chapter 10 • Objectives
– Review characteristics of projectile motion – Review factors influencing projectile motion – Present and explain calculation methods for analyzing projectile
motion
• Homework – due Monday, Feb 16– Problems 7,9,10 on page 347