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Work, Power & EnergyWork, Power & Energy
Chapter 7
Explaining the Causes Explaining the Causes of Motion Without of Motion Without NewtonNewton
(sort of)(sort of)
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
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
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?
Calculate WorkCalculate Work
Table of Variables:Force = +1000 NDisplacement = +0.8 m
Calculate WorkCalculate Work
Table of Variables:Force = +1000 NDisplacement = +0.8 mSelect the equation and solve:
JJouleNmWork
mNWork
ntdisplacemeForceWork
800800800
8.01000
- & + Work- & + WorkPositive work is performed
when the direction of the force and the direction of motion are the sameascent phase of the bench press throwingpush off phase of a jump
- & + Work- & + WorkPositive work is performed when
the direction of the force and the direction of motion are the same
Negative work is performed when the direction of the force and the direction of motion are the opposite
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
How much work did the lifter do to the barbell?
Calculate WorkCalculate Work
Table of VariablesForce = +1000 NDisplacement = -0.8 m
Calculate WorkCalculate Work
Table of VariablesForce = +1000 NDisplacement = -0.8 mSelect the equation and solve:
JJouleNmWork
mNWork
ntdisplacemeForceWork
800800800
8.01000
- & + 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
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?
EMG during the Bench PressEMG during the Bench Press
Work on a cycle ergometerWork on a cycle ergometer
Work = FdForce
belt friction on the flywheelmass ie 3 kg
Displacement revolution of the pedals
Monark: 6 m
“Work” per revolution3kg x 6 m = 18 kgm
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
EnergyEnergyEnergy (E) is defined as the capacity to
do workMany 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
Kinetic EnergyKinetic EnergyEnergy due to motion reflects
the mass the velocity
of the object
KE = 1/2 mv2
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
Calculate Kinetic Calculate Kinetic EnergyEnergy
How much KE in a 5 ounce baseball (145 g) thrown at 80 miles/hr (35.8 m/s)?
Calculate Kinetic Calculate Kinetic EnergyEnergy
Table of VariablesMass = 145 g 0.145 kgVelocity = 35.8 m/s
Calculate Kinetic Calculate Kinetic EnergyEnergy
Table of VariablesMass = 145 g 0.145 kgVelocity = 35.8 m/sSelect the equation and solve:
JKE
smkgKE
mvrgyKineticEne
9.92
)]/8.35)([145.0(2
12
1
2
2
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?
Calculate Kinetic EnergCalculate Kinetic EnergyyCompare 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
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
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?)
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
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
Calculate GPECalculate GPE
GPE relative to mat Table of Variables m = 45 kgg = -9.81 m/s/sh = 4 m
GPE relative to ground
Table of Variablesm = 45 kgg = -9.81 m/s/sh = 5.25 m
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
Strain EnergyStrain Energy When a fiberglass vaulting pole bends, strain
energy is stored in the bent pole 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
.
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
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?
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
) (i vv v m Ft
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
PowerPowerThe rate of doing work
Work = Fd
Units: Fd/s = J/s = watt
velocityForcePower
tFdPower
timeWorkPower
/
/
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
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
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
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 (How so??)
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
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
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