Chapter 12 Linear Kinetics of Human Movement

1
Chapter 12Linear Kinetics of Human Movement

• Basic Biomechanics, 6th edition
• Susan J. Hall
• Presentation Created by
• TK Koesterer, Ph.D., ATC
• Humboldt State University

2
Objectives

• Identify Newtons laws of motion and gravitation
  and describe practical illustrations of the laws
• Explain what factors affect friction and discuss
  the role of friction in daily activities and
  sports
• Define impulse and momentum and explain the
  relationship between them
• Explain what factors govern the outcome of a
  collision between two bodies
• Discuss the interrelationship among mechanical
  work, power, and energy
• Solve quantitative problems related to kinetic
  concepts

3
Newtons Laws

• Isaac Newton developed the theories of
  gravitation in 1666, when he was 23 years old.
• In 1686 he presented his three laws of motion.

4
Newtons LawsLaw of Inertia

• A body will maintain a state of rest or constant
  velocity unless acted on by an external force
  that changes its state.
• Inertia is the property of a body that causes it
  to remain at rest if it is at rest or continue
  moving with a constant velocity unless a force
  acts on it.

5
Newtons First Law of Motion

• Law of Inertia
• Every body will remain in a state of rest or
  constant motion (velocity) in a straight line
  unless acted on by an external force that changes
  that state
• A body cannot be made to change its speed or
  direction unless acted upon by a force(s)
• Difficult to prove on earth due to the presence
  of friction and air resistance

6
Newtons LawsLaw of Acceleration

• A force (F) applied to a body causes an
  acceleration (a) of that body of a magnitude
  proportional to the force, in the direction of
  the force, and inversely proportional to the
  bodys mass (m).
• Forms the link between force and motion
• Force mass x acceleration or acceleration
  Force mass

7
Applications of Newtons 2nd Law

• Assuming mass remains constant, the greater the
  force the greater the acceleration
• Acceleration is inversely proportional to mass
• if force remains the same and mass is halved,
  then acceleration is doubled
• if force remains the same and mass is doubled,
  then acceleration is halved

m 1.5 kg
8
Newtons LawsLaw of Reaction

• For every action, there is an equal and opposite
  reaction
• When one body exerts a force on a second, the
  second body exerts a reaction force that is equal
  in magnitude and opposite in direction of the
  first body

9
Newtons LawsLaw of Reaction

• During gait, every contact of a foot with the
  ground generates an upward reaction force by the
  ground called (GRF).
• GRF has both horizontal and vertical components.
• What is magnitude of vertical GRF running?

10
Newtons LawsLaw of Gravitation

• All bodies are attracted to one another with a
  force proportional to the product of the masses
  and inversely proportional to the square of the
  distance between them
• Fg G(m1m2 / d2)
• Fg Force of attraction
• Earth mass 5.972 x 1024 kg
• Earth radius 6.378 x 103 km
• Greater mass, greater attraction
• Greater distance, less attraction

11
Implications of Newtons Law of Gravitation

• Mass
• Greater mass greater gravitational force
• Smaller mass lower gravitational force
• Distance
• Greater distance smaller gravitational force
• Smaller distance greater gravitational force

• Most bodies in sport have relatively small mass
• Attractive force between them can be considered
  negligible

12
Newtons LawsLaw of Gravitation
Acceleration Because of Gravity at Sea Level by
Latitude
Latitude Acceleration due to Gravity Sample Locations
0 9.780 Ecuador, Kenya
15 9.784 Philippines, Guatemala
30 9.793 Texas, Israel
45 9.806 Oregon, France
60 9.819 Alaska, Sweden
75 9.829 Greenland
90 9.832 North Pole
Gravitational variations largely accounted for by
the equatorial bulge of the earth rather than
altitude above sea level.
13
Weight

• Weight (W) is the attractive force between the
  earth and any body in contact with it or close to
  its surface
• Product of the mass (m) of the body and the
  acceleration caused by the attractive force
  between it and the earth(g 9.81 ms-2)
• i.e. W m g
• Gravity is based on
• Mass of bodies
• Distance between bodies

rpoles
requator
rradius of earth requator gt rpoles Gequator lt
Gpoles Wequator lt Wpoles
14
Mechanical Behavior of Bodies in ContactFriction

• Friction is a force that acts parallel to the
  surfaces in contact and opposite to the direction
  of motion.
• If there is no motion, friction acts in opposite
  direction to any force that tends to produce
  motion.
• Friction is a necessity for and a hindrance to
  motion.

15
Magnitude of friction forces determine relative
ease or difficulty of motion for two objects in
contact.
12-5
16
Mechanical Behavior of Bodies in ContactFriction

• Starting friction is greater than moving
  friction.
• It takes more force to start moving an object
  than it does to keep it moving.
• Maximum static friction (Fm)
• As magnitude of applied force becomes greater and
  greater, magnitude of opposing friction force
  increases to a critical point.
• Kinetic (sliding) friction (Fk)
• Magnitude of kinetic friction remains constant.

17
Mechanical Behavior of Bodies in ContactFriction

• For static bodies, friction is equal to the
  applied force. For bodies in motion, friction is
  constant and less than maximum static friction.

18
Mechanical Behavior of Bodies in ContactFriction

• Ff ?R
• Ff frictional force ? coefficient of
  friction R normal (-) reaction force
• Coefficient of friction number that serves as
  index
• Coefficient of static friction (?s)
• Coefficient of kinetic (sliding) friction (?k)
• Normal reaction force (-) force acting . . .
• Rolling friction influence by weight, radius,
  deformability of rolling object, plus ?

19
Mechanical Behavior of Bodies in ContactFriction

• Ff ?R
• Amount of friction changed by altering µ.
• Gloves in racquetball, golf, batting
• Wax on surfboard or cross country skis
• Rosin on dance floor
• Provides large ? s
• Provides significantly smaller ?k
• Amount of friction changed by altering R.
• Press surfaces together ( or weight)

20
Mechanical Behavior of Bodies in ContactFriction
Material Starting Friction Sliding Friction
Hardwood on hardwood Steel on steel Steel on steel (oiled) Rubber on dry concrete Rubber on wet concrete 0.40 0.58 0.13 2.0 1.5 0.25 0.20 0.13 1.0 0.97
Synovial fluid present in many joints reduces
friction between articulating bones.
21
Mechanical Behavior of Bodies in ContactFriction

• Artificial turf and cleats coefficient of
  friction cause more injuries?
• Shoe traction dry
• µ .90 to 1.50
• Shoe traction wet
• µ 1.10 to 1.50
• FIFA recommendation
• µ 0.35 to 0.75

22
Mechanical Behavior of Bodies in Contact

• Momentum is quantity of motion a body possesses.
• Linear Momentum M or p
• M m v
• Units kg m/s (or slug ft/s)
• Downhill skier example 55 kg 30 m/s 1650 kg
  m/s

Newtons laws can be expressed in terms of
momentum.
23
Mechanical Behavior of Bodies in Contact

• Newtons first law (inertia) states that in the
  absence of external forces the momentum of an
  object remains constant.
• M constant
• Principle of Conservation of Momentum
• Newtons second law (acceleration) states that
  the rate of change of momentum equals the net
  external force acting on it.

24
Mechanical Behavior of Bodies in Contact

• Newtons third law (action-reaction) may be
  stated in momentum terms as whenever two bodies
  exert forces on one another, the resulting
  changes of momentum are equal and opposite.
• Principle of conservation of momentum
• In the absence of external forces, the total
  momentum of a given system remains constant. M1
  M2

25
Mechanical Behavior of Bodies in Contact

• Principle of conservation of momentum
• In the absence of external forces, the total
  momentum of a given system remains constant. M1
  M2 or (mv)1 (mv)2
• Initial momentum (M1) of objects before collision
• Final momentum (M2) of objects after collision

26
Mechanical Behavior of Bodies in Contact

• Golf Ball and Club example
• Golf Ball mass .045 kg, Golf Club mass .200
  kg
• GBv1 0, GCv1 270 m/s GBv2360 m/s, GCv2 ?
• How much does Golf Club slow down?
• Momentum before Momentum after impact
• .045 0 .2 270 m/s .045 360 m/s .2
  GCv2
• 0 54 kg m/s 16.2 kg m/s .2 kg GCv2
• 37.8 kg m/s ? .2 kg 189 m/s GCv2
• Golf Club Velocity Decreases (189 270) - 81
  m/s

27
Mechanical Behavior of Bodies in ContactImpulse

• Changes in momentum depend on force and length of
  time during which force acts.
• Impulse product of force and time interval the
  force acts
• Impulse (J) F ? t
• Derived from Newtons Second law
• F ma (a v2 - v1 / t)
• F m (v2 - v1 / t) (mv2 mv1)/ t
• Ft (mv2) - (mv1)
• Ft M2 M1 ?M
• This is the impulse-momentum relationship.

28
Mechanical Behavior of Bodies in Contact Impulse

• Bunch start results in clearing blocks sooner but
  with less velocity.
• Highest proportion of best runs are from 16-in
  stance.
• Elongated stance of 26- in results in greater
  velocity leaving blocks but lost within 10 yds

Block Spacing 11 in. 16 in. 21 in. 26 in.
Time on Blocks, i.e. time from gun to foot leaving 0.345 s 0.374 s 0.397 s 0.426 s
Block Velocity, i.e. horizontal velocity as leave blocks 6.63 ft/s 7.41 ft/s 7.50 ft/s 7.62 ft/s
Time to 10 yd (9.1 m) 2.070 s 2.054 s 2.041 s 2.049 s
Time to 50 yd (45.7 m) 6.561 s 6.479 s 6.497 s 6.540 s
Adapted from Henry, F. M. (1952) Research
Quarterly, 23306.
29
Impulse
Since Impulse F x t, i.e. the amount of force
applied during a period of time, impulse is the
area under the force curve. Which jump generated
greater change in momentum (vertical velocity)?
12-10
30
Impulse

• Horizontal (sagittal) Plane
• If initial negative impulse lt push off positive
  impulse, horizontal velocity increased.
• If initial negative push off impulse equal, no
  change in horizontal velocity.
• If initial negative impulse gt push off positive
  impulse, horizontal velocity decreased.

31
Mechanical Behavior of Bodies in ContactImpact

• Impact collision of two bodies over small time
• Elasticity an objects ability to return to its
  original size and shape when outside forces are
  removed.
• Perfectly elastic impact relative velocities
  same
• Perfectly plastic impact at least one body loses
  velocity, bodies dont separate
• Most impacts are neither perfectly elastic nor
  perfectly plastic.

32
Mechanical Behavior of Bodies in Contact
The differences in two balls velocities before
impact is proportional to the difference in their
velocities after impact. The factor of
proportionality is the coefficient of restitution.
33
Mechanical Behavior of Bodies in ContactImpact

• Impact (cont.)
• Coefficient of restitution
• When two bodies undergo a direct collision, the
  difference in their velocities immediately after
  impact is proportional to the difference in their
  velocities immediately before impact
• -e relative velocity after impact v1 - v2
• relative velocity before impact u1 - u2

34
Elasticity

• In case of impact between moving body and
  stationary one, e ?hb/hd
• Coefficient of restitution describes interaction
  between two bodies, not a single object or
  surface.

35
Elasticity

• Factors Affecting C of R
• Velocities
• Temperature
• Material
• Spin

C of R Concrete Wood
Basketball 0.57 0.80
Golf ball 0.89 0.66
Racquetball 0.86 0.84
Baseball 0.57 0.45
36
Elasticity - Spin

• Magnitude of horizontal forces exerted on ball
  are influenced by amount of spin.
• Horizontal velocity of points on ball sum of 2
  component velocities translational component
  rotational component.

37
Elasticity - Spin

• The angle of incidence (approach) equals the
  angle of reflection in perfectly elastic impact
  with no spin imparted.

38
Elasticity - Spin

• When topspin applied, translational component of
  part of ball that contacts the floor is offset by
  rotational component evoked frictional force is
  less as is the decrease in balls forward
  velocity.

39
Elasticity - Spin

• When backspin applied, the translational
  rotational components complement each other, the
  evoked frictional reaction is increased, and
  post-impact velocity is less.
• Backspin causes ball to bounce more slowly at
  higher angle.

40
Summary

• Linear kinetics is the study of the forces
  associated with linear motion
• Friction is a force generated at the interface of
  two surfaces in contact
• Magnitudes of maximum static friction and kinetic
  friction are determined by the coefficient of
  friction and normal reaction force pressing the
  two surfaces together.
• Linear momentum is the product of an objects
  mass and its velocity

41
Summary

• Total momentum in a given system remains constant
  barring the action of external forces
• Changes in momentum result from impulses,
  external forces acting over a time interval
• The elasticity of an impact governs the amount of
  velocity in the system following impact
• The relative elasticity of is represented by the
  coefficient of restitution