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Work, Power & EnergyWork, Power & Energy
Chapter 4
Explaining the Causes of Explaining the Causes of Motion in a Different WayMotion in a Different Way
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WorkWorkThe product of force and the amount
of displacement along the line of action of that force.
Units: ft . lbs (horsepower) Newton•meter (Joule) e
ntdisplacemeForceWork
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Work = F x dWork = F x d
To calculate work done on an object, we need:
The ForceThe average magnitude of the force The direction of the forceThe DisplacementThe magnitude of the change of positionThe direction of the change of position
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Calculate WorkCalculate WorkDuring the ascent phase of a rep of
the bench press, the lifter exerts an average vertical force of 1000 N against a barbell while the barbell moves 0.8 m upward
How much work did the lifter do to the barbell?
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Calculate WorkCalculate Work
Table of Variables:Force = +1000 NDisplacement = +0.8 m
Force is positive due to pushing upwardDisplacement is positive due to moving
upward
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Calculate WorkCalculate Work
Table of Variables:Force = +1000 NDisplacement = +0.8 mSelect the equation and solve:
JJouleNmWork
mNWork
ntdisplacemeForceWork
800800800
8.01000
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- & + Work- & + WorkPositive work is performed
when the direction of the force and the direction of motion are the sameascent phase of the bench pressThrowing a ballpush off (upward) phase of a jump
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Calculate WorkCalculate WorkDuring the descent phase of a rep of
the bench press, the lifter exerts an average vertical force of 1000 N against a barbell while the barbell moves 0.8 m downward
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Calculate WorkCalculate Work
Table of VariablesForce = +1000 NDisplacement = -0.8 m
Force is positive due to pushing upwardDisplacement is negative due to
movement downward
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Calculate WorkCalculate Work
Table of VariablesForce = +1000 NDisplacement = -0.8 mSelect the equation and solve:
JJouleNmWork
mNWork
ntdisplacemeForceWork
800800800
8.01000
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- & + Work- & + WorkPositive work Negative work is performed when
the direction of the force and the direction of motion are the oppositedescent phase of the bench presscatching landing phase of a jump
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ContemplateContemplateDuring negative work on the bar,
what is the dominant type of activity (contraction) occurring in the muscles?
When positive work is being performed on the bar?
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EMG during the Bench PressEMG during the Bench Press
On elbow180
90
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Work performed climbing Work performed climbing stairsstairs
Work = Fd Force
Subject weightFrom mass, ie 65 kg
Displacement Height of each step
Typical 8 inches (20cm)
Work per step 650N x 0.2 m = 130.0 Nm
Multiply by the number of steps
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Work on a stair stepperWork on a stair stepper
Work = FdForce
Push on the step????
Displacement Step Height
8 inches
“Work” per step???N x .203 m = ???Nm
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Work on a cycle ergometerWork on a cycle ergometer
Work = FdForce
belt friction on the flywheelmass (eg 3 kg)
Displacement revolution of the pedals
Monark: 6 m
“Work” per revolution
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Work on a cycle ergometerWork on a cycle ergometer
Work = Fd Force
belt friction on the flywheelmass (eg 3 kg)
Displacement revolution of the pedals
Monark: 6 m
“Work” per revolution 3kg x 6 m = 18 kgm
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Similar principle for Similar principle for wheelchairwheelchair
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……and for handcycling and for handcycling ergometerergometer
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EnergyEnergy Energy (E) is defined as the capacity to do
work (scalar) Many forms
No more created, only convertedchemical, sound, heat, nuclear, mechanical
Kinetic Energy (KE): energy due to motion
Potential Energy (PE): energy due to position or deformation
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Kinetic EnergyKinetic EnergyEnergy due to motion reflects
the mass the velocity
of the object
KE = 1/2 mv2
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Kinetic EnergyKinetic EnergyUnits: reflect the units of mass * v2
Units KE = Units work
NmKE
mssmkgKE
ssmmkgKE
smkgKE
mvKE
2
1
)//(2
1
//2
1
)/)((2
12
1
2
2
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Calculate Kinetic Calculate Kinetic EnergyEnergy
How much KE in a 5 ounce baseball (145 g) thrown at 80 miles/hr (35.8 m/s)?
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Calculate Kinetic Calculate Kinetic EnergyEnergy
Table of VariablesMass = 145 g 0.145 kgVelocity = 35.8 m/s
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Calculate Kinetic Calculate Kinetic EnergyEnergyTable of VariablesMass = 145 g 0.145 kgVelocity = 35.8 m/sSelect the equation and solve:KE = ½ m v2
KE = ½ (0.145 kg)(35.8 m/s)2
KE = ½ (0.145 kg)(1281.54 m/s/s)KE = ½ (185.8 kg m/s/s)KE = 92.9 kg m/s/s, or 92.9 Nm, or 92.9J
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Calculate Kinetic Calculate Kinetic EnergyEnergy
How much KE possessed by a 150 pound female volleyball player moving downward at 3.2 m/s after a block?
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Calculate Kinetic EnergyCalculate Kinetic Energy
Table of Variables 150 lbs = 68.18 kg of mass -3.2 m/sSelect the equation and solve:KE = ½ m v2
KE = ½ (68.18 kg)(-3.2 m/s)2
KE = ½ (68.18 kg)(10.24 m/s/s) KE = ½ (698.16 kg m/s/s) KE = 349.08 Nm or J
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Calculate Kinetic Calculate Kinetic EnergyEnergy
Compare KE possessed by: a 220 pound (100 kg) running back
moving forward at 4.0 m/s a 385 pound (175 kg) lineman
moving forward at 3.75 m/s
Bonus: calculate the momentumof each player
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Calculate Kinetic EnergyCalculate Kinetic Energy
Table of Variablesm = 100 Kgv = 4.0 m/sSelect the equation
and solve:KE = ½ m v2
KE = ½ (100 kg)(4.0 m/s)2
KE = 800 Nm or J
Table of Variablesm = 175 kgv = 3.75 m/sSelect the equation
and solve:KE = ½ m v2
KE = ½ (175)(3.75)2
KE = 1230 Nm or J
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Calculate Momentumomentum
Momentum = mass times velocity
Player 1 = 100 kg * 4.0 m/sPlayer 1 = 400 kg m/s
Player 2 = 175 * 3.75 m/sPlayer 2 = 656.25
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Potential EnergyPotential Energy
Two forms of PE:Gravitational PE:
energy due to an object’s position relative to the earth
Strain PE:due to the deformation of an object
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Gravitational PEGravitational PEAffected by the object’s
weight mg
elevation (height) above reference point ground or some other surfaceh
GPE = mgh
Units = Nm or J (why?)
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Calculate GPECalculate GPE
How much gravitational potential energy in a 45 kg gymnast when she is 4m above the mat of the trampoline?
Take a look at the energetics of a roller coaster
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Calculate GPECalculate GPE
How much gravitational potential energy in a 45 kg gymnast when she is 4m above the mat of the trampoline?
Trampoline mat is 1.25 mabove the ground
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Calculate GPECalculate GPE
GPE relative to mat Table of Variables m = 45 kgg = -9.81 m/s/sh = 4 mPE = mghPE = 45kg * -9.81
m/s/s * 4 mPE = - 1765.8 J
GPE relative to groundTable of Variablesm = 45 kgg = -9.81 m/s/sh = 5.25 mPE = mghPE = 45m * -9.81
m/s/s * 5.25 mPE = 2317.6 J
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Conversion of KE to GPE and Conversion of KE to GPE and GPE to KE and KE to GPE and GPE to KE and KE to GPE and ……
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Strain PEStrain PEAffected by the object’samount of deformation
greater deformation = greater SE x2 = change in length or deformation of the
object from its undeformed positionstiffness
resistance to being deformedk = stiffness or spring constant of material
SE = 1/2 kx2
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Strain EnergyStrain EnergyWhen a fiberglass vaulting pole
bends, strain energy is stored in the bent pole
Pole vault explosion
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Strain EnergyStrain EnergyWhen a fiberglass vaulting pole
bends, strain energy is stored in the bent pole
Bungee jumping
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Strain EnergyStrain EnergyWhen a fiberglass vaulting pole
bends, strain energy is stored in the bent pole
Bungee jumpingHockey sticks
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Strain EnergyStrain Energy When a fiberglass vaulting pole bends, strain energy is
stored in the bent pole Bungee jumping When a tendon/ligament/muscle is stretched, strain
energy is stored in the elongated elastin fibers (Fukunaga et al, 2001, ref#5332) k = 10000 n /m x = 0.007 m (7 mm), Achilles tendon in
walking When a floor/shoe sole is deformed, energy is stored in
the material
.
Plyometrics
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Work - Energy RelationshipWork - Energy Relationship
The work done by an external force acting on an object causes a change in the mechanical energy of the object
)(2
1 2ifif rrmgvvmFd
PEKEFd
EnergyFd
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Work - Energy RelationshipWork - Energy Relationship
The work done by an external force acting on an object causes a change in the mechanical energy of the objectBench press ascent phase
initial position = 0.75 m; velocity = 0final position = 1.50 m; velocity = 0m = 100 kgg = -10 m/s/sWhat work was performed on the bar by lifter?What is GPE at the start & end of the press?
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Work - Energy Work - Energy RelationshipRelationship
What work was performed on the bar by lifter? Fd = KE + PE Fd = ½ m(vf –vi)2 + mgh Fd = 100kg * - 10 m/s/s * 0.75 m Fd = 750 J W = Fd W = 100 kg * .75m W = 75 kg m W = 75 kg m (10) = 750 J
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Work - Energy Work - Energy RelationshipRelationship
What is GPE at the start & end of the press? End (ascent) PE = mgh PE = 100 kg * -10 m/s/s * 1.50 m PE = 1500 J Start (ascent) PE = 100 kg * -10 m/s/s * 0.75m PE = 750 J
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Work - Energy Work - Energy RelationshipRelationship
Of critical importanceSport and exercise = velocity
increasing and decreasing kinetic energy of a body
similar to the impulse-momentum relationship
)(2
1 2vivfif rrmgvvmFd
PEKEFd
EnergyFd
Ft = m (vf-vi)
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Work - Energy RelationshipWork - Energy Relationship
If more work is done, greater energy greater average forcegreater displacement
Ex. Shot put technique (121-122).
If displacement is restricted, average force is __________ ? (increased/decreased)
“giving” with the ball landing hard vs soft
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PowerPowerThe rate of doing work
Work = Fd
Units: Fd/s = J/s = watt
velocityForcePower
tFdPower
timeWorkPower
/
/
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Calculate & compare Calculate & compare powerpower
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 secondsLifter B: 0.75 seconds
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Calculate & compare Calculate & compare powerpower
Lifter ATable of VariablesF = 1000 Nd = 0.8 mt = 0.50 s
Lifter B
ws
JPower
s
mNPower
t
FdPower
160050.0
80050.0
8.01000
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Power on a cycle Power on a cycle ergometerergometer
Work = Fd Force: 3kg Displacement: 6m /rev “Work” per revolution
3kg x 6 m = 18 kgm
60 rev/min
min/1080""
min/6018""
min/""
/""
kgmPower
kgmPower
revFdPower
tFdPower
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Power on a cycle Power on a cycle ergometerergometer Work = Fd Force: 3kg Displacement: 6m /rev “Work” per revolution
3kg x 6 m = 18 kgm
60 rev/min
min/1080""
min/6018""
min/""
/""
kgmPower
kgmPower
revFdPower
tFdPower
1 Watt = 6.12 kgm/min
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Compare “power” in Compare “power” in typical stair steppingtypical stair stepping
Work = Fd Force: Push on the step
constant setting
Displacement Step Height: 5” vs 10”
0.127 m vs 0.254 m
step rate 56.9 /min vs 28.8 /min
Time per step60s/step rate
Thesis data from Nikki Gegel and Michelle Molnar
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Compare “power” in Compare “power” in typical stair steppingtypical stair stepping
Work = Fd Force: Push on the step
constant setting
Displacement Step Height: 5” vs 10”
0.127 m vs 0.254 m
step rate 56.9 /min vs 28.8 /min
)08.2/254(.
)05.1/127(.
10
5
smFPower
smFPower
vFPower
inch
inch
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Compare “power” in Compare “power” in typical stair steppingtypical stair stepping
Work = Fd Force: Push on the step
constant setting
Displacement Step Height: 5” vs 10”
0.127 m vs 0.254 m
step rate 56.9 /min vs 28.8 /min
smFPower
smFPower
vFPower
inch
inch
/122.0
/121.0
10
5
Results: VO2 similar fast/short steps vs slow/deep steps