vector algebra vector kinetic vector quantities –force weight, pressure, specific weight &...
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Vector Algebra
• Vector
• Kinetic vector quantities – force weight, pressure, specific weight & torque
• Kinematic vector quantities– Displacement, velocity & acceleration
• Scalar quantities– Mass, volume, length & speed
Vector Composition
• Resultant vector
• “Tip-to-tail” vector composition
Vector #1
Vector #2
Resultant vector
Graphic Solution of Vector Problems
• Graphic vector manipulation may yield approximate result
30 N = 3 cm
35 N = 4.5 cm
1 cm = 10 N
Trigonometric Solution of Vector Problems
• A more accurate procedure for quantitatively dealing with vector problems
Vector Resolution Problems(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
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
Vector Addition Problems
• 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
Self-test Problems for Chapter 3on Kinetic concepts
• Introductory problems, p 80– #1,2, 5
• Additional problems, p 81– #1, 4, 5, 7
Projectile Motion characteristics and analysis procedures (PP 329-347)
• Objectives– Review characteristics of projectile motion (pp 329-347)– Review factors influencing projectile motion – Present and explain calculation methods for analyzing
projectile motion
Projectile motion characteristics
• It is a freely falling body, subject to only two forces – gravity and wind resistance
• May be dropped, or projected• (1) vertically, (2) horizontally, • or (3) obliquely• Flight pattern is determined by initial velocity
– Speed (V0)– Direction ()
Projectile motion, cont’d• Projectile height plays a role in optimal
projection angle for horizontal distance
Projectile motion, cont’d• If projection angle is constant, range increases
directly with magnitude of velocity
Projectile motion, cont’d
• Resolving projectile motion into vertical and horizontal components – the first step in calculating motion parameters of interest
Vv = V sin Vh = V cos
Projectile motion, cont’d
• Primary motion quantities of interest are usually:– Time of flight
– Zenith, or maximum height
– Range, or horiz dist
– If time is calculated first,
this reduces to: Dhoriz = VhorizT = V cos T
Self-test problems on Projectile motion
• Introductory problems• #6, 7, 8, 9 p 345-346
Additional Problem
#10, p 347
Hint: Solve for time of flight:
then solve for Dhoriz : Dhoriz = VhorizT = V cos T
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• To review reasons for studying 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
Segmental concept of center of mass
–Information needed
•Proportionate mass of each segment (p 520)
•location of COM of each segment (p 521)
Summary• This chapter 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. • Kinematic concepts related to projectile motion were
introduced• Calculation methods for total body COM were presented
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