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Linear Kinetics

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Title: Linear Kinetics


1
Chapter 3
  • Linear Kinetics
  • Explaining the Causes of Linear Motion

2
Sir Isaac Newton 1642-1727
Proposed fundamental laws that are the basis of
modern mechanics 3 laws of motion law of
gravitation
3
Newtons Laws of Motion
  • Apple fell on his head.
  • This event led to his Law of Gravitation.

4
Newtons Laws of Motion
  • The Law of Gravitation tells us that objects
    having mass are attracted to each other by the
    force of gravity, with objects of lesser mass
    being drawn in the direction of objects with
    greater mass.
  • This is why the earth pulls on us with a force of
    gravity.

5
Newtons Law of Universal Gravitation
  • Law of gravitation - all bodies are attracted to
    one another with a force proportional to the
    product of their masses and inversely
    proportional to the square of the distance
    between them.

6
g Gravitational acceleration
  • The acceleration of gravity
  • - 9.81 m/s2 (- 10 m/s/s)
  • Why the negative sign???
  • indicates that the acceleration caused by gravity
    is directed downward or toward the center of the
    earth

7
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8
Terminal Velocity
9
Weight
  • Weight
  • the amount of gravitational force exerted on a
    body
  • F m g
  • W m g
  • W weight (wt) (units N or lbs)
  • m mass of the body (units kg or slugs)
  • g gravitational acceleration (units m/s/s)
  • As the mass of a body increases, its weight
    increases proportionally

10
Weight is a force
  • As a force, weight characterized by
  • magnitude
  • proportional to mass
  • direction
  • ALWAYS downward
  • point of application
  • at center of gravity of the body
  • Units Newtons or pounds (mass???)

11
Newtons Laws of Motion
  • However, in the field of mechanics, Sir Isaac
    Newton is also known for his three Laws of
    Motion.
  • These three Laws of Motion explain why objects
    move as they do.
  • They are also used to explain the concept of
    force.

12
Newtons Laws of Motion
  • Newtons 3 Laws of Motion are
  • 1. Law of inertia - an object at rest will stay
    at rest, and an object in motion will stay in
    motion, unless acted upon by a net external
    force.
  • ?F 0 and ?F ??0

13
  • Law of inertia - a body in motion will stay in
    motion and a body at rest will stay at rest
    unless acted upon by a net external force.

14
Law of Inertia
  • An applied example
  • Car in motion
  • You in car
  • Brain in you

15
Law of Inertia
  • An applied example
  • Car in motion
  • You in car
  • Brain in you

16
Law of Inertia
  • An applied example
  • Car in motion
  • You in car
  • Brain in you

17
HANS device
The HANS (Head And Neck Support) Device was
originally designed to limit the extreme front
to back and side-to-side movement of the head and
neck during a violent crash. Using a collar and
yoke system made of carbon fiber and Kevlar, the
device is connected to the helmet with a series
of quick connect tethers. The HANS Device is
worn around the neck and down the front of the
shoulders, underneath the safety belts of the
shoulder harness. This allows for normal movement
of the head and helmet, but limits the extreme
movement of the head and neck that is so common
in the rapid deceleration during a crash
18
Newtons Laws of Motion
  • A key concept important to understanding Newtons
    first law is the concept of inertia.
  • Inertia is an objects resistance to having its
    state of motion changed.
  • The measure of inertia in a body is its mass.
  • The greater an objects mass, the greater its
    inertia.

19
Newtons Laws of Motion
  • 2. Law of acceleration - a force applied to a
    body causes an acceleration of that body by a
    magnitude proportional to the force.
  • F ma

20
Newtons Second Law of Motion
  • Law of acceleration - an unbalanced force applied
    to a body causes an acceleration of that body
    with a magnitude proportional to the force, in
    the direction of the force, and inversely
    proportional to the body's mass.

21
F ma
?
  • Unbalanced force causes a change in motion (an
    acceleration)
  • CAUSE-EFFECT relationship

22
Running and Pelvic Anatomy
During running, if a runner swings his/her arms
across his/her body, there is a compensatory
increase in pelvic rotation. It is more
efficient and better for the pelvis and pelvic
musculature if the runner moves his/her arms
parallel to the motion in which she is running.
23
Narrow Hips
24
Slightly Wider Hips
25
Running and Pelvic Anatomy
  • What is the impact of having a wide pelvis on
    this concept?

26
Newtons Laws of Motion
  • Newtons second law of motion concerns
    acceleration and momentum, and it tells how the
    quantities of force, mass, and acceleration are
    related and how to measure force when it exists.

27
Newtons Laws of Motion
  • Some of the key factors associated with this law
    are
  • a. the acceleration that occurs when you apply a
    force to an object will be in the line of
    direction of your applied force.
  • b. the acceleration will also be inversely
    proportional to the mass of the object.

28
Newtons Laws of Motion
  • If you want to move a massive object, you need to
    apply a massive force.

29
Newtons Laws of Motion
  • Units the force unit is the lb. when
    acceleration is in feet/sec/sec and mass is in
    slugs.
  • When acceleration is in meters/sec/sec and mass
    is in kg, force is expressed in Newtons (N).
  • One lb 4.45 N
  • Mass wt/g, therefore F (wt/g)a

30
Newtons Laws of Motion
  • What is the force necessary to accelerate a 160
    lb object 2 ft/sec2 ?
  • F (wt/g)a
  • (160 lbs/32 ft/sec2) 2 ft/sec2
  • 10 lbs

31
Newtons Laws of Motion
  • 3. Law of action-reaction
  • for every action, there is an equal and opposite
    reaction.
  • F -F

32
Newtons Third Law of Motion
  • Law of action-reaction - for every action, there
    is an equal and opposite reaction
  • There are two bodies (at least) involved when
    force is exerted

33
Action-Reaction
  • The force on each body is the same size, but in
    opposite directions
  • True even when the bodies are of significantly
    different mass

34
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35
Newtons Laws of Motion
  • With respect to Newtons 3rd law, an important
    concept to remember here is that this
    relationship holds true even if the bodies in
    contact are of significantly different masses.
  • This can have a tremendous impact on risk of
    injury.

36
Newtons Laws of Motion
  • For instance
  • If you are trying to stop a 200 lb object from
    moving, you had better be prepared to absorb at
    least 200 lbs of force.

37
Newtons Laws of Motion
  • Examples
  • Law of inertia - football lineman.
  • Law of acceleration - kicking a ball.
  • Law of action-reaction - starting blocks.
  • Friction, air resistance, gravity.

38
It is important to know how Newtons 3 laws apply.
39
Review Newtons ???? Laws of Motion
40
Newton I Law of Inertia
  • A body will maintain its current state of motion
    unless acted on by an unbalanced external force
  • External forces include air-resistance and
    friction
  • Examples
  • passenger in car
  • projectile motion (horizontal)

41
Newton II Law of Acceleration
  • ?F ma
  • A force applied to a body causes an acceleration
    of the body of a magnitude proportional to the
    force, in the direction of the force, and
    inversely proportional to the body mass
  • Example, kicking a soccer ball
  • At an instant in time

42
Newton III Law of Reaction
  • For every action there is an equal and opposite
    reaction (forces act in mirrored pairs)
  • Ground reaction forces

43
How measurement has changed.
44
Current state of motion
  • How fast and in what direction
  • velocity a vector quantity
  • How resistant to changing state of motion
  • inertia quantified by mass

Momentum mass x velocity Momentum mv
45
Momentum
  • Newton I Law of inertia
  • Principal of Conservation of Momentum
  • In the absence of external forces, the total
    momentum of a given system remains constant

46
Momentum Example
(15 July 1999, Alabama) A 25-year-old soldier
died of injuries sustained from a 3-story fall,
precipitated by his attempt to spit farther than
his buddy. His plan was to hurl himself towards
a metal guardrail while expectorating, in order
to add momentum to his saliva. In a tragic
miscalculation, his momentum carried him right
over the railing, which he caught hold of for a
few moments before his grip slipped, sending him
plummeting 24 feet to the cement below. The
military specialist had a blood alcohol content
of 0.14, impairing his judgment and paving the
way for his opportunity to win a Darwin Award.
47
Elastic Collisions
  • When two objects collide in a head-on collision,
    their combined momentum is conserved
  • We can use this principle to predict the
    post-collision movements of the objects if we
    know their masses and their pre-collision
    velocities.

48
Elastic Collisions
  • Penny and nickel example (Fig 3.3, p 83)
  • Penny hits stationary nickel, penny stops, nickel
    moves.

49
Elastic Collisions
  • How fast is the nickel traveling post-collision?
  • Given
  • Mass of penny 2.5 g
  • Mass of nickel 5.0 g
  • Pre-collision velocity of penny 2 m/s
  • Pre-collision velocity of nickel 0 m/s

50
Elastic Collisions
  • mpvp1 mnvn1 mpvp2 mnvn2
  • (2.5g)(2 m/s) (5.0g)(0 m/s) (2.5g)(0 m/s)
    (5.0g)(?)
  • 5g.m/s (5.0g)(vn2)
  • 5g.m/s
  • 5.0g

vn2
51
Elastic Collisions
  • Other examples
  • Shooter marble and other marbles
  • Cue ball and other pool balls
  • Bowling ball and bowling pins

52
Inelastic Collisions
  • Not all collisions are perfectly elastic.
  • The opposite of a perfectly elastic collision is
    a perfectly inelastic collision which is also
    called a perfectly plastic collision.

53
Plastic Collisions
  • In a plastic collision, momentum is still
    conserved, but rather than bouncing off each
    other, the objects stay together after the
    collision and move together with the same
    velocity.
  • Example - play dough sticking to a moving truck.

54
Plastic Collisions
  • Example
  • An 110 kg fullback collides in midair with a 120
    kg linebacker at the goal line during a goal line
    stand.
  • The FB was moving at 6 m/s at the LB was moving
    at 5 m/s at the point of collision.

55
Plastic Collisions
  • If the collision is perfectly elastic, would the
    FB move forward and score or would the LB drive
    him backward preventing the TD?

56
Plastic Collisions
  • Use the equation
  • m1v1 m2v2 (m1 m2) v
  • (110 kg)(6 m/s) (120 kg)(-5 m/s) (110 kg
    120 kg) v
  • 660 kg . m/s - 600 kg . m/s (230 kg) v
  • 60 kg . m/s (230 kg) v
  • v (60 kg . m/s) / 230 kg 0.261 m/s
  • HE SCORES!

57
Coefficient of Restitution
  • Defined as the absolute value of the ratio of the
    velocity of separation to the velocity of
    approach.
  • The velocity of separation is the difference
    between the velocities of 2 colliding objects
    just after collision.

58
Coefficient of Restitution
  • The velocity of approach is the difference
    between the velocities of 2 colliding objects
    just before the collision.

59
Coefficient of Restitution
  • The coefficient of restitution has no units
  • For perfectly elastic collisions, the c of r 1
  • For perfectly plastic collisions, the c or r 0

60
Coefficient of Restitution
  • In addition to the velocity of the objects, it is
    also affected by the nature of the objects in the
    collision
  • The composition of the objects is very important
  • What elastic properties do the objects have?
  • What plastic properties do the objects have?

61
Coefficient of Restitution
  • When dropping a ball from a fixed height, c of r
    can be calculated by
  • e ? bounce height/drop height
  • Velocity is constant (acceleration due to
    gravity) when balls are dropped from same height

62
Coefficient of Restitution
  • Why is this important in sports where different
    sporting balls are used?

63
Newton II Law of Acceleration
  • ?F ma

Develop the impulse-momentum relationship from
this equation
64
Impulse
  • Impulse - the product of a force and its time of
    application.
  • Impulse Ft.

65
Impulse to Increase Momentum and Decrease
Momentum
  • Mechanical objective of human performance
  • move at a particular speed in a particular
    direction
  • gt momentum
  • Alter performance (momentum)
  • force magnitude, direction, point of
    application, line of action
  • time duration of force application

66
Vertical jump
  • Jump
  • increase momentum to some high value
  • rest to upward motion
  • Certain impulse is required
  • m (vf - vi)
  • Alter time of force application
  • short time, large force
  • long time, small force

67
Soft and stiff landings
  • Landing
  • decrease momentum to Zero
  • downward motion to rest
  • Certain impulse is required
  • m (vf - vi) same with landing from a
    height
  • Alter time of force application
  • short time, large force
  • long time, small force

68
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69
Child is uninjured because 1) soft ground and
leaves increase time over which child
stops Effect on Force???
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