Mechanicaal Energyal Energy, Work and...
Transcript of Mechanicaal Energyal Energy, Work and...
MechanicaMechanicaWork an
D. Gordon E. Robertson,
Biomechanics LaboratoryBiomechanics Laboratory,School of Human Kinetics,University of Ottawa, Ottaw
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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
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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
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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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ples ofples ofive Forces
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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ples ofples ofive Forces
esfrictionless surfacefrictionless surface
elastic collision
9ab, U. of Ottawa
ExampExampConservat
• Gravitational force• Normal force of a fNormal force of a f• Elastic collisions
P d l• Pendulum
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ples ofples ofive Forces
esfrictionless surfacefrictionless surface
pendulum
10ab, U. of Ottawa
ExampExampConservat
• Gravitational force• Normal force of a fNormal force of a f• Elastic collisions
P d l• Pendulum• Ideal spring
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ples ofples ofive Forces
esfrictionless surfacefrictionless surface
ideal springp g
11ab, U. of Ottawa
ExampExampConservat
• Gravitational force• Normal force of a fNormal force of a f• Elastic collisions
P d l• Pendulum• Ideal spring• Lever system
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ples ofples ofive Forces
esfrictionless surfacefrictionless surface
force load
lever
fulcrumfulcrum12ab, U. of Ottawa
ExampExampConservat
Simple machines:• PulleysPulleys• Block & tackle
G• Gears• Cams• Winch• ……
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ples ofples ofive Forces
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
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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
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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
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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