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