Linear Kinetics – Relationship between force and motion

• Sources:– Kinetics – Hamill, Ch 10 & 11, secondarily Adrian Ch 6)– Measurement – Kreighbaum pp 555-558; Adrian pp 145-149– Research methods – Robertson Ch 4

• Classification of forces• Types of forces encountered by humans• Force and motion relationships

– Instantaneous effect – Newton’s law of acceleration (F=ma)– Force applied through time (Impulse-momentum)

• Conservation of Momentum

– Force applied through distance (work-energy) • Conservation of Energy

Classification of Forces

• Action vs reaction

• Internal vs external

• Motive vs resistive

• Force resolution – horizontal and vertical components

• Simultaneous application of forces - vector summation

Types of external forces encountered by humans

• Gravitational force (weight = mg)• Ground Reaction Force (GRF)

– Vertical

– Horizontal (frictional)

• Frictional force (coefficient of friction) • Elastic force (coefficient of restitution)

• Centripetal force (mv2/r) • Buoyant force • Free body diagram - force graph

Ground reaction forces

Ground reaction forces whilewalking

Cfr = Frf /Nof

Centripetal & Centrifugal forces

Cf = mv2/r

Free body diagrams:

Free body diagrams

Instantaneous Effect of Force on an Object

• Remember the concept of net force?

• Need to combine, or add forces, to determine net force

• Newton’s third law of motion (F = ma)

• Inverse dynamics – estimating net forces from the acceleration of an object

Force Applied Through a Time: Impulse-Momentum Relationship

• Force applied through a time• Impulse - the area under the force-time curve• Momentum - total amount of movement (mass x velocity)• An impulse applied to an object will cause a change in its

momentum (Ft = mv)• Conservation of momentum (collisions, or impacts)

– in a closed system, momentum will not change

– what is a closed system?

Impulse: areaunder force-time curve

Impulse produces a change in momentum (mV)

Vertical impulse While Running: Area underForce-timecurve

Anterioposterior(frictional) component of GRF: impulseIs area under Force-time curvePositive andNegative impulseAre equal ifHorizontal compOf velocity isconstant

Conservation of momentum: when net impulse is zero (i.e. the system is closed), momentum does not change

Conservation of momentum: is this a closed system?

Force Applied Through a Distance: Work, Power, Energy

• Work - force X distance (Newton-meters, or Joules)– On a bicycle: Work = F (2r X N)– On a treadmill: Work = Weightd X per cent grade

• Power - work rate, or combination of strength and speed (Newton-meters/second, or watts)– On a treadmill: P = Weightd X per cent grade/ time– On a bicycle: P = F (2r X N) / time

• What about kilogram-meters/min?• Energy - capacity to do work

– kinetic, the energy by virtue of movement (KE = 1/2 mv2 ) – gravitational potential, energy of position (PE = Weight x height)– elastic potential, or strain, energy of condition (PE = Fd)

Work while pedaling on bicycle:

From McArdle and Katch.Exercise Physiology

Work while running on treadmill:

Note that %grade = tan θ X 100,and tan θ and sin θ are very similar below 20% grade

From McArdle and Katch. Exercise Physiology

Calculating Power on a Treadmill• Problem: What is workload (power) of a 100 kg man running on a

treadmill at 10% grade at 4 m/s?• Solution:

– Power = force x velocity– Force is simply body weight, or 100 x 9.8 = 980 N– Velocity is vertical velocity, or rate of climbing

• Rate of climbing = treadmill speed x percent grade = 4 m/s x .1 = .4 m/s

– Workload, workrate, or power = 980N X .4 m/s = 392 Watts• Note: 4 m/s = 9 mph, or a 6 min, 40 sec mile

• Homework: Calculate your workload if you are running on a treadmill set at 5% grade and 5 m/s.– Answer for 200 lb wt is: 223 Watts

Power running up stairs: Work rate = (weight X vertical dist) ÷ time

Conservation of Energy• In some situations, total amount of mechanical energy

(potential + kinetic) does not change– Stored elastic energy converted to kinetic energy

• diving board

• bow (archery)

• bending of pole in pole vault

• landing on an elastic object (trampoline)

– Gravitational potential energy converted to kinetic energy• Falling objects

Energy conservation – Case I : elastic potential (strain) and kinetic

Potential energy (FD) + Kinetic energy (1/2mv2) remains constant

Energy conservation – Case II : gravitational potential and kinetic

Potential energy(Wh) + kineticenergy (1/2mv2) remains constant

Electronic Load Measurement

• Sensor or transducer - the heart & soul of the measurement system– Properties of transducer often sets limits on the usefulness of the

measurement system– Electrodes for EMG – polarity between them– Strain gauge – bonded to an elastic material, such as steel beam, it

transforms bending into resistance– Piezoelectric – transforms force into electrical charge– Piezoresistive – transforms pressure into electrical resistance

(shoulder pad study)– Capacitance – transforms load into electrical energy storage

• Signal conduction– Telemetry or wired

Electronic load measurement (cont’d)

• Signal conditioning – converts output from transducer into an analog signal +10 VDC– Amplifier– Cutoff filters to eliminate noise (low frequency cutoff, high

frequency cutoff, notch filters)– Electric circuitry to change resistance to current– Balance potentiometer

• Analog-digital conversion, acquisition and analysis board and software

• Output– Visual display of data, graphs, charts– Hard copy of data, graphs, chartgs

Measurement of Muscle Action Potentials

Measuring ground Reaction forces

Measuring forces on bat handle using strain gages

Measuring forces on bat handle using strain gages

Using strain gages to measureBat bending and vibration

Begin swing: 183 ms PC

Bat Vibrations During Swing & Impact

-4

-3

-2

-1

0

1

2

3

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Time (s)

Str

ain

(v

)

Horiz DirVert DirMagnitudeHoriz DirVert DirMagnitude

Begin Swing 233ms PC

Peak 41 ms PC

Horiz Pk 38 ms PC

Bending Direction During Swing & Impact

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Time (s)

Dir

ec

tio

n (

de

g)

Beg Sw - 233 ms PC

O0 is horiz & back - 21 ms PC

Approximate position when peak bending andPeak torque occurs ~ 40 ms PC

Using strain gages to measure force onHammer during hammer throw

Pressure under shoulder pads using piezoresistive transducers

Pressure under shoulder pads

using piezoresistive transducers

Pressure under shoulder pads using piezoresistive transducers

Capacitance and piezoresistive transducers