Transcript week2f01 - K-State Courses

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
Resultant vector
Vector #2
Vector #1
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
Example: A ball is thrown into the air
Resultant
Vertical
Horizontal
Vector resolution problems found in
human 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:
Vert comp = F•sin•Θ
Horiz comp = F•cos•Θ
Θ
Θ
Vert comp = F•sinΘ
Horiz comp = F•cosΘ
Θ
Θ
d
Θ
Turning comp = F•d•sinΘ
Radial comp = F•d•cosΘ
(d = d•sinθ)
Vector composition, or addition
Sum of two forces:
Sum of two velocities:
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