mechanicaal energyal energy, work and...

MechanicaMechanicaWork an

D. Gordon E. Robertson,

Biomechanics LaboratoryBiomechanics Laboratory,School of Human Kinetics,University of Ottawa, Ottaw

Biomechanics La

al Energyal Energy,d Power

PhD, FCSB

,wa, Canada

1ab, U. of Ottawa

Ene

• Ability to do work• Measured in joulesMeasured in joules• One joule is the wo

newton force movenewton force moveone metre

• 1 Calorie = 1000 ca• 1 Calorie = 1000 ca• Can take many for

Biomechanics La

ergy

s (J)s (J)ork done when a one es an object throughes an object through

als = 4 186 kJals = 4.186 kJrms

2ab, U. of Ottawa

Forms of

• Mass (E = mc2)• Solar or Light (solar

battery)• Electricity (electron f• Chemical (fossil fuels• Thermal or Heat• Mechanical energy

Biomechanics La

f Energy

panels, photovoltaic

flux, magnetic induction)s, ATP, food)

3ab, U. of Ottawa

Types of Mech

• Translational Kineti– v2 = vx

2 + vy2 (+ vz

2)x y ( z )– this is usually the lar

• Rotational Kinetic =Rotational Kinetic– this is usually the sm

• Gravitational Potent• Gravitational Potent• Elastic Potential = ½

– Assumed to be zero fBiomechanics La

hanical Energy

ic = ½ m v2

rgest type in biomechanics= ½ I ω2 ½ I ωmallest type in biomechanicstial m g ytial = m g y

½ k (x12 – x2

2)for rigid bodies

4ab, U. of Ottawa

Laws of Ther

Z th l• Zeroth law– When two quantities are in therma

thermal balance with each other. temperaturetemperature.

• First Law (Law of Conservatio– Energy is conserved (remains con

E t b t d d t– Energy cannot be created or dest

• Second Law (Law of Entropy)– When energy is transformed from

a loss of usable energy.– All processes increase the entrop

• Third Law– Absolute zero (absence of all atom

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rmodynamics

al balance to a third they are in I.e., they have the same

n of Energy)nstant) within a “closed system.”t dtroyed.

m one form to another there is always

py of the universe.

mic motion) cannot be achieved.5ab, U. of Ottawa

Law of ConsLaw of ConsMechanic

• If the resultant fora conservative forcmechanical energy

• Resultant force wilexternal forces are

• A force is conservaaround a closed pa

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servation ofservation of cal Energy

rce acting on a body is ce then the body’s total y will be conserved.ll be conservative if all

e conservative.ative if it does no work ath (motion cycle).

6ab, U. of Ottawa

ExampExampConservat

• Gravitational force

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ples ofples ofive Forces

es

gravityg y

7ab, U. of Ottawa

ExampExampConservat

• Gravitational force• Normal force of a fNormal force of a f

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esfrictionless surfacefrictionless surface

frictionless surface

8ab, U. of Ottawa

ExampExampConservat

• Gravitational force• Normal force of a fNormal force of a f• Elastic collisions

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elastic collision

9ab, U. of Ottawa

ExampExampConservat


P d l• Pendulum

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pendulum

10ab, U. of Ottawa

ExampExampConservat


P d l• Pendulum• Ideal spring

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ideal springp g

11ab, U. of Ottawa

ExampExampConservat


P d l• Pendulum• Ideal spring• Lever system

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force load

lever

fulcrumfulcrum12ab, U. of Ottawa

ExampExampConservat

Simple machines:• PulleysPulleys• Block & tackle

G• Gears• Cams• Winch• ……

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13ab, U. of Ottawa

ExampExampNonconserv

• Dry friction• Air (fluid) resistanAir (fluid) resistan• Viscous forces

Pl ti lli i• Plastic collisions• Real pendulums• Real springs

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ples ofples ofative Forces

ncence

14ab, U. of Ottawa

Direct Er

Treadmill Ergometry• External work =

m g t v sin θ• where, m = mass,

9 81 t tig = 9.81, t = time, v = treadmill velocity, and θ = treadmill’s angle of incline

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rgometry

15ab, U. of Ottawa

Direct Er

Cycle Ergometry• External work =

6 n L g6 n L g• where, n = number of

pedal revolutions, p ,L = load in kiloponds and g = 9.81Note each pedal c cle• Note, each pedal cycleis 6 metres motion of flywheel

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rgometry

ee

16ab, U. of Ottawa

Direct Er

Gjessing Rowing Ergometry

• External work = n L g

h b• where, n = number of flywheel cycles, L = workload in kiloponds and g = 9.81

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rgometry

17ab, U. of Ottawa

Biomechanic

Point M M th dPoint Mass Method– Simplest, least accurate

• Mechanical Energy =• Mechanical Energy =• External work = Efina

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cal Methods

e, ignores rotational energy

= E = m g y + ½ m v2= E = m g y + ½ m v

al – Einitial

18ab, U. of Ottawa

Biomechanic

Single Rigid Body Method– Simple, usually planar,

includes rotational energyincludes rotational energy

• Mechanical Energy = gyE= mgy + ½mv2 + ½Iω2

• External Work = Efinal – Einitial

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cal Methods

Carriage loadCarriage load

19ab, U. of Ottawa

Biomechanic

Multiple Rigid Body Method

Difficult usually planar– Difficult, usually planar, more accurate, accuracy increases with number of segments

• External Work = Efinal – Einitialfinal initial

• E = sum of segmental total energies (kinetic plus potential energies)

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cal Methods

20ab, U. of Ottawa

Biomechanic

Inverse Dynamics Method

M t diffi lt ll– Most difficult, usually planar, requires force platforms

E t l W k• External Work = Σ ( Σ Μj ωj ∆t )

• Sum over all joint moments and over duration of movementduration of movement

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cal Methods

21ab, U. of Ottawa

Biomechanic

Absolute Power Method– similar to previous method

• Total Mechanical Work• Sum over all joint mom

d ti f tduration of movement• Notice positive and nega

powers do not cancel (abpowers do not cancel (ab• Internal Work =

Total mechanical workTotal mechanical work –Biomechanics La

cal Methods

d

k = Σ ( Σ | Μj ωj | ∆t )ents and over

ative moment bsolute values)bsolute values)

External work– External work22ab, U. of Ottawa

Physiologic

• Oxygen Uptake– Difficult, accurate,

expensive invasiveexpensive, invasive

• Physiological Work =c (VO2)( 2)

• Where, c is the energyreleased by metabolizing O2 and VO2 is the volume of O2 consumedO2 consumed

Biomechanics La

cal Methods

=

y

23ab, U. of Ottawa

Mechanical

• Measure both mechanical and physiological costsphysiological costs

• ME = mechanical cost divided bycost divided by physiological cost times 100%

Monark ergometer used to measure mechanical work done

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Mouthpiece for collecting expiredl Efficiency collecting expired gases and physiological costs

24ab, U. of Ottawa

Mechanical

Internal work +ME = ———————

Physiologi

Internal work is measudone by all the joint mresearchers ignore th

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l Efficiency

+ External work———————— × 100 %

ical cost

ured by adding up the work moments of force. Most e internal work done.

25ab, U. of Ottawa

Work of

Work of a Force is producdisplacement (s) when Fdirection.direction.

Work = F s (w= F s cos φ (wφ (

an= F . s = Fx sx + Fy syx x y y= Ef – Ei (c= P t (p

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a Force

ct of force (F) and F and s are in the same

when F is parallel to s)when F is not parallel to spnd is φ angle between F and s)y + Fz sz (dot product)y z z ( p )

change of energy)power times time)

26ab, U. of Ottawa

Work of a Mom

Work of a Moment of Fmoment of force (M) (θ)(θ).

Work = M θF ( i φ) θ (φ= r F (sin φ) θ (φ

= P t (p= Σ (M ω ∆t) (t

po

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ment of Force

Force is product of and angular displacement

φ i l b d F)φ is angle between r and F)power times time)time integral of moment ower)

27ab, U. of Ottawa

Average

Power is the rate of doin– measured in watts (W),

Power = work / time= (Ef – Ei) / time (Ef Ei) / time

= (F s) / t = F v= (F s) / t = F v= (M θ) / t = M ω

Biomechanics La

e Power

ng work.1 watt = 1 joule per second (J/s)

(work rate)(change in energy over(change in energy over time)(force times velocity)(force times velocity)(moment of force timesangular velocity)

28ab, U. of Ottawa

Instantaneous PInstantaneous Por Momen

Power = F v (w= F v cos φ (w F v cos φ (w

ananan

= F . v = Fx vx + FM (= M ω (m

Biomechanics La

Power of a ForcePower of a Force nt of Force

when F is parallel to v)when F is not parallel to vwhen F is not parallel to vnd is φ angle between Fnd v)nd v)

Fy vy + Fz vz (dot product)i lmoment times angular

velocity)

29ab, U. of Ottawa

Isokinetic Dy

• Controls speed of motion therefore lever has constantlever has constant angular velocity (ω)

• Measures force i t lagainst a lever arm

• Moment = force times lever armlever arm

• Instantaneous Power= moment times

l l itangular velocityBiomechanics La

ynamometersKinCom 500HKinCom 500H

hydraulically controlled motion

lever arm

controlled motion

force sensor

30ab, U. of Ottawa

mechanicaal energyal energy, work and...

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