linear motion: kinematics and kinetics applied kinesiology 420:151
TRANSCRIPT
Linear Motion: Kinematics and Kinetics
Applied Kinesiology420:151
Agenda
Introduction to motion Linear kinematics Linear kinetics Analysis of linear motion
Introduction to Motion
Linear motion (translatory) Rectilinear Curvilinear Circular
Angular motion (rotary) General motion
Shoulder = angular or linear?
Figures 11.1, 2, 3, 4, Hamilton
Agenda
Introduction to motion Linear kinematics Linear kinetics Analysis of linear motion
Linear Kinematics
Linear: A point moving along a line Kinematics: The study of motion
(of a point moving along a line) in respect to displacement, velocity and acceleration
Displacement
Displacement: Change in position Vector quantity Magnitude and
direction Displacement vs. distance SI unit = m
Velocity
Velocity: Rate of displacement V = displacement/time
Vector quantity Velocity vs. speed SI unit = m/s
Average vs. Instantaneous Velocity
Average velocity = displacement/time Entire displacement start to finish
Instantaneous: Velocity at any particular instant within the entire displacement Still average velocity however time
periods much smaller therefore “essentially” instantaneous
s (m) tjohnson (s) tlewis (s) Vjohnson (m/s) Vlewis (m/s)
10 1.86 1.88 5.38 5.32
20 2.87 2.96 6.97 6.76
30 3.8 3.88 7.89 7.73
40 4.66 4.77 8.58 8.39
50 5.55 5.61 9.01 8.91
60 6.38 6.45 9.40 9.30
70 7.21 7.29 9.71 9.60
80 8.11 8.12 9.86 9.85
90 8.98 8.99 10.02 10.01
100 9.83 9.86 10.17 10.14
Instantaneous?
Velocity Figure - Johnson vs. Lewis (1988 Summer Olympics, Seoul Korea)
5.00
6.00
7.00
8.00
9.00
10.00
11.00
10 20 30 40 50 60 70 80 90 100
Meters (m)
Velo
city
(m/s
)
Johnson
Lewis
(m) Splits BJ (s) Splits CL (s) Vinst. BJ Vinst. CL
0 10 1.86 1.88 5.38 5.32
10 20 1.01 1.08 9.90 9.26
20 30 0.93 0.92 10.75 10.87
30 40 0.86 0.89 11.63 11.24
40 50 0.89 0.84 11.24 11.90
50 60 0.83 0.84 12.05 11.90
60 70 0.83 0.84 12.05 11.90
70 80 0.90 0.83 11.11 12.05
80 90 0.87 0.87 11.49 11.49
90 100 0.85 0.87 11.76 11.49
Instantaneous Velocity Figure - Johnson vs. Lewis (1988 Summer Olympics, Seoul Korea)
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
13.00
0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100
Meters (m)
Velo
city
(m/s
)
Johnson
Lew is
Acceleration
Acceleration: Rate of change of velocity A = vf – vi
Vector quantity SI unit = m/s/s or m/s2
Uniform acceleration Very rare Projectiles (more later)
Average vs. Instantaneous Acceleration
Average acceleration = Rate of change in velocity assumes uniform acceleration
Instantaneous: Acceleration between smaller time periods Provides more information Johnson vs. Lewis
Average acceleration for Ben Johnson?
A = (vf – vi) / t
A = (10.17 m/s – 0 m/s) / 9.83 s
A = (10.17 m/s) / 9.83 s
A = 1.03 m/s2
v BJ (m/s) v CL (m/s)
0 0
5.38 5.32
6.97 6.76
7.89 7.73
8.58 8.39
9.01 8.91
9.40 9.30
9.71 9.60
9.86 9.85
10.02 10.01
10.17 10.14
Average acceleration for Carl Lewis?
A = (vf – vi) / t
A = (10.14 m/s – 0 m/s) / 9.86 s
A = (10.14 m/s) / 9.86 s
A = 1.03 m/s2
Enough information?
s (m) t BJ (s) t CL (s) v BJ (m/s) v CL (m/s) a BJ (m/s2) a CL (m/s2)
0 0 0 0 0 0 0
10 1.86 1.88 5.38 5.32 2.89 2.83
20 2.87 2.96 6.97 6.76 0.55 0.49
30 3.8 3.88 7.89 7.73 0.24 0.25
40 4.66 4.77 8.58 8.39 0.15 0.14
50 5.55 5.61 9.01 8.91 0.08 0.09
60 6.38 6.45 9.40 9.30 0.06 0.06
70 7.21 7.29 9.71 9.60 0.04 0.04
80 8.11 8.12 9.86 9.85 0.02 0.03
90 8.98 8.99 10.02 10.01 0.02 0.02
100 9.83 9.86 10.17 10.14 0.02 0.01
Instantaneous?
Acceleration Figure - Johnson vs. Lewis (1988 Summer Olympics, Seoul Korea)
0
0.5
1
1.5
2
2.5
3
0 10 20 30 40 50 60 70 80 90 100
Distance (m)
Acce
lera
tion
(m/s
/s)
Johnson
Lewis
(m) Splits BJ (s) Splits CL (s) Vinst. BJ Vinst. CL a BJ (m/s2) a CL (m/s2)
0 10 1.86 1.88 5.38 5.32 2.89 2.83
10 20 1.01 1.08 9.90 9.26 4.48 3.65
20 30 0.93 0.92 10.75 10.87 0.92 1.75
30 40 0.86 0.89 11.63 11.24 1.02 0.41
40 50 0.89 0.84 11.24 11.90 -0.44 0.80
50 60 0.83 0.84 12.05 11.90 0.98 0.00
60 70 0.83 0.84 12.05 11.90 0.00 0.00
70 80 0.90 0.83 11.11 12.05 -1.04 0.17
80 90 0.87 0.87 11.49 11.49 0.44 -0.64
90 100 0.85 0.87 11.76 11.49 0.32 0.00
Instantaneous Acceleration Figure - Johnson vs. Lewis (1988 Summer Olympics, Seoul Korea)
-2.00
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100
Meters (m)
Velo
city
(m/s
/s)
Johnson
Lew is
Positive and Negative Acceleration
Motion to the right or up is considered in the positive direction Velocities in these directions also
positive Motion to the left or down is
considered in the negative direction Velocities in these directions also
negative
Positive and Negative Acceleration Increasing speed in the positive
direction is + acceleration Decreasing speed in the positive
direction is – acceleration Increasing speed in the negative
direction is – acceleration Decreasing speed in the negative
direction is + acceleration
Use positive/negative acceleration as opposed to acceleration and deceleration
Uniform Acceleration Most common form of uniform
acceleration is projectile motion 9.8 m/s2
Laws of uniform acceleration Acceleration is constant Allows you to solve for:
Velocity: Initial or final Distance traveled by implement Time in the air
Uniform Acceleration Solve for final velocity when initial
velocity, time and acceleration are known
vf = vi + at Manipulate the formula
vi = vf – at t = vf – vi /a
What if initial or final velocity = 0?
What is the final velocity at 4 seconds if you know the velocity at 2 seconds?vf = vi + atVf = -19.6 m/s + (-9.8 m/s2)
(2s)Vf = -39.2 m/s
How long was it in the air if you know the initial and final velocities?t = -49 m/s – 0 m/s /-9.8 m/s2
t = -49 m/s / -9.8 m/s2
t = 5 s
What is the initial velocity if you know the velocity at 5 seconds?vi = vf – atVi = -49 m/s – (-9.8 m/s2)(5s)Vi = 0 m/s
Uniform Acceleration
Solve for velocity when initial velocity, distance and acceleration are known
vf2 = vi
2 + 2as Manipulate the formula
vi2 = vf
2 - 2as s = vf
2 - vi2 /2a
What if initial or final velocity = 0?
Page 288 of text book:
Assuming that a ball is thrown upward so that it reaches a height of 5 meters before starting to fall, what is its initial velocity? What is its final velocity?
Initial velocity:
vi2 = vf2 – 2as
vi2 = (0 m/s)2 - 2(-9.8 m/s2)(5m)
vi2 = 0 m2/s2 + 98 m2/s2
vi2 = 98 m2/s2 (sq. root both sides)
vi = 9.9 m/s
Final velocity:
vf2 = vi2 + 2as
vf2 = (0 m/s)2 + 2(-9.8 m/s2)(5m)
vf2 = 0 m2/s2 - 98 m2/s2
vf2 = -(98 m2/s2) (sq. root both sides)
vf = -9.9 m/sCheck work by solving for
distance
s = vf2 - vi2 / 2a
s = (-9.9)2 – (0)2 / 2(-9.8m/s2)
s = 98 m2/s2 / 19.6 m/s2
s = 5 m
Uniform Acceleration
Solve for distance when initial velocity, acceleration and time are known
s = vit + ½ at2
Manipulate the formula
How far will an object drop if you let if fall for 3 seconds?s = vit + ½ at2
s = 0 + ½ (-9.8 m/s2)(3 s)2
s = 0 + -4.9 m/s2 (9 s2)s = -44.1 m
How high will an object go in the air in 2 seconds if thrown with an initial velocity of 29.4 m/s?s = vit+ ½ at2
s = 29.4 m/s (2 s) + ½(-9.8 m/s2)(2 s)2
s = 58.8 m – 19.6 ms = 39.2 m
Vi = 0
Vf = -9.8 m/s
V = -4.9 m/s S = -4.9 m1 s
2 s
Vf = -19.6 m/s
V = -14.7 m/s
s = -14.7 m
3 s
Vf = -29.4 m/s
V = -24.5 m/s
s = -24.5 m
Total distance traveled:
(-4.9)+(-14.7)+(-24.5) = -44.1 m
1 s
Vi = 29.4 m/s
Vf = 19.6 m/s
V = 24.5 m/s S = 24.5 m
2 s
Vf = 9.8 m/s
V = 14.7 m/s S = 14.7 m
Total distance traveled:
14.7+24.5 =
39.2 m
Vacuum no air resistance
Unlimited constant acceleration
Real world air resistance
Terminal velocity
Continued acceleration until air resistance = gravity
Terminal velocity of skydiver = 120 mph
Agenda
Introduction to motion Linear kinematics Linear kinetics
Newton’s laws Types of force Work, power, energy
Analysis of linear motion
Linear Kinetics
What causes motion? Force Newton’s Three Laws of Motion:
Cannot be proved Universally accepted
1st Law: Law of Inertia
Law: A body continues in its state of rest/motion unless an unbalanced force acts upon it
Inertia: The resistance to motion proportionate to mass
Unbalanced forces during start? Unbalanced forces during stop?
2nd Law: Law of Acceleration
Law: The acceleration of an object is proportional to the force causing it and inversely proportional to its mass
F = ma a = F/m Impulse: The product of force and
time F = ma = m(vf – vi)/t Ft = m(vf – vi)
Impulse Max acceleration of an object = max
force and max time Hammer throw Baseball swing (quickness vs. velocity)
Manipulation of impulse Two basketball players of 100 kg Player A = 2500 N over 0.25 s Player B = 3000 N over 0.21 s Advantage?
Impulse and Momentum
Momentum = mv Ft = m(vf – vi) = mvf – mvi
Any change in momentum is equal to the impulse that produced it
Applications? Shot put: Effect of force, arm length? Catching a fastball
40 m/s or 90 mph
Weight = 5 oz.
Mass = 0.14 kg
Momentum = mv
Momentum = 40 m/s (0.14 kg)
Momentum = 5.6 kg*m/s
If you want to stop this pitch with your bare hands
(change mv from 5.6 kg*m/s to 0), this change in momentum will equal the impulse that creates the change in momentum!
If you try to stop the pitch in 0.05 seconds, it will require 112
N of force (5.6/0.05 = 112). This is approximately 25 lbs of
force!
Ft = mvf - mvi 112(0.05) = 5.6 - 0
Why does a 5 story fall typically result in
death?
Why wasn’t he able to hold on?
(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.
3rd Law: Law of Reaction Law: For every action there is an equal and
opposite reaction Objects at rest are in equilibrium the
weight of the object is balanced by the force of the surface pushing back against it
Ground reaction forces Cement vs. sand
Examples: Objects colliding? Conservation of momentum
Momentum lost by one body = momentum gained by other body
Unequal masses = unequal accelerations
Agenda
Introduction to motion Linear kinematics Linear kinetics
Newton’s laws Types of force Work, power, energy
Analysis of linear motion
Types of Forces
Gravity Ground reaction forces Friction Rebound Air resistance (drag)
Gravity “The force that causes objects to fall to
earth, the moon to orbit the earth and the planets to orbit the sun”
Weight: The attractive force of the earth 9.8 m/s/s Weight = mg 1 N = 0.2248 lbs
Gravity is a force vector Magnitude = weight Direction = straight down
Ground Reaction Force GRF: The reaction force
from a surface upon which one is moving
GRFs are force vectors Magnitude: Equal to amount
of force expressed into ground
Direction: Opposite direction from which force was expressed into ground
Energy can be transformed (ie sand)
Figure 12.18, Hamilton
Friction
Friction: the force that opposes efforts to slide or roll one body across/over another
Can work for us or against us More friction can be good Less friction can be good
Friction Friction depends on:
Nature of surfaces (coefficient of friction) Forces involved
PushFf
Coefficient of friction
Weight of book
Figure 12.14, Hamilton
Starting vs. sliding friction
Rebound Rebound: The force that causes objects
to rebound from each other after contact
Amount of rebound depends on several factors Elasticity Angle of rebound Spin Momentum
Rebound - Elasticity Objects that receive a stress will strain
(become distorted/deformed) Elasticity: Ability to return to original
shape once stress is removed Coefficient of restitution = stress/strain Greater elasticity = greater rebound
Rebound – Angle of Rebound Assume COR = 1.0 angle of incidence
= angle of reflection As COR decreases, so does angle of
reflection relative to angle of incidence
Figure 12.23, Hamilton
Rebound - Spin
Topspin: Increase Hv, decrease Vv Backspin: Increase Vv, decrease
Hv Sidespin: Rebound in direction of
spin
Rebound - Momentum
Momentum = mv As mass and/or velocity increase,
so does rebound
Air Resistance (Drag) Air resistance: The force that occurs as a result
of fluid pressure at the leading edge of an object and the backward pull created by turbulence on the trailing edge
Figure 12.25, Hamilton
Agenda
Introduction to motion Linear kinematics Linear kinetics
Newton’s laws Types of force Work, power, energy
Analysis of linear motion
Work, Power, Energy
Work: The product of force expended and distance through which force succeeds in overcoming resistance
W = Fd SI unit = J or N*m Distance measured vertically only
F
2 m
Force needed to overcome inertia of block = 20 N
Total vertical distance = 2 m
Work = 20 N * 2 m
Work = 40 J or 40 N*m
Figure 12.30, Hamilton
Work performed climbing stairs Work = Fd Force
Subject weight From mass, ie 65 kg
Displacement Height of each step
Typical 8 inches (20cm) Work per step
636 N x 0.2 m = 127 Nm Multiply by the number of steps
Work on a stair stepper
Work = Fd Force
Push on the step ????
Displacement Step Height
8 inches
Work per step ???N x .203 m = ???Nm
Work on a cycle ergometer
Work = Fd Force
belt friction on the flywheel mass ie 3 kg
Displacement revolution of the pedals
Monark: 6 m per rev
Work per revolution 3kg x 6 m = 18 kgm
Work, Power, Energy
Work can be positive or negative Work done in direction of force
application is positive work Concentric actions
Work done in opposite direction of force application is negative work Eccentric actions
Work, Power, Energy
Power: The rate at which work is performed
Power = Work/time or Fv SI unit = W or J/s or N*m/s
Calculate & compare power During the ascent phase of a rep of
the bench press, two lifters each exert an average vertical force of 1000 N against a barbell while the barbell moves 0.8 m upward
Lifter A: 0.50 seconds Lifter B: 0.75 seconds
Calculate & compare power
Lifter AF = 1000 Nd = 0.8 m
t = 0.50 s
Power = Fd/tPower = 1000 N*0.8 m /0.50 sPower = 800 J/ 0.50 sPower = 1600 W
Lifter B?
Power on a cycle ergometer
Power = Fd/tPower = Fd*rev/min
How much power output is there?Force = 3 kgd = 6 m / revolution60 revolutions / min
Power = 3kg*6m*60 rev/min
Power = 1080 kg*m/min
Note: 1 Watt = ~ 6 kg*m/min
How many Watts? 180 Watts
Other Ways to Calculate Power Treadmill sprinting
Work = weight*vertical displacement (angle of treadmill)
Time = length of sprint Vertical jumping (Lewis equation)
Work = weight*vj height Power is estimated with an equation
Stair stepper Work = resistance of step*displacement of step Time = time to move step
Stair running (Margaria-Kalaman test) Work = weight*vertical displacement*# steps Time = time it takes to get up the stairs
Work, Power, Energy Energy: The capacity to do work Amount of energy = work
accomplished Many types of energy
Heat, sound, light, electric, chemical, atomic
Mechanical energy Two main types Potential energy Kinetic energy
Mechanical Energy
Potential energy: Energy a body possesses due to its position PE = mgh
Kinetic energy: Energy a body possesses due to its motion KE = ½ mv2
PE = Maximum
KE = 0
PE = Decreasing
KE = Increasing
PE = 0
KE = Maximum
Energy can neither be created nor destroyed
Agenda
Introduction to motion Linear kinematics Linear kinetics
Newton’s laws Types of force Work, power, energy
Analysis of linear motion
General Analysis of Linear Motion Linear kinematics:
Linear displacement Linear velocity Linear acceleration
Linear kinetics: Effect of a force in an instant in time
F = ma Effect of a force applied over a period of time
Impulse and momentum Effect of a force applied over a distance
Work, power, energy
General Phases of Skill Performance
Ritual Phase Full of idiosyncrasies, useful for mental focus Does the ritual phase affect performance negatively,
positively? Preparation Phase
Wind up (force, velocity, accuracy, combination?) Is energy storage required?
Force Phase Is the force applied in the right direction? Is there enough force, too much?
Follow Through Phase Is there enough time to slow down body parts? Does the follow through promote correct application of force?
