Work, Power & EnergyWork, Power & Energy

Chapter 7Explaining 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 dTo 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 WorkTable of Variables:Force = +1000 NDisplacement = +0.8 m

Calculate WorkCalculate WorkTable of Variables:Force = +1000 NDisplacement = +0.8 mSelect the equation and solve:

JJouleNmWork

mNWorkntdisplacemeForceWork

8008008008.01000

- & + 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

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

Calculate WorkCalculate WorkTable of VariablesForce = +1000 NDisplacement = -0.8 m

Calculate WorkCalculate WorkTable of VariablesForce = +1000 NDisplacement = -0.8 mSelect the equation and solve:

JJouleNmWork

mNWorkntdisplacemeForceWork

8008008008.01000

- & + 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?

Or even…

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?

SteveMcCaw1981

EMG during the Bench PressEMG during the Bench Press

On elbow180

90

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 = 1300 Nm Multiply by the number of steps

Work on a stair stepperWork on a stair stepperWork = FdForce

Push on the step????

Displacement Step Height

8 inches“Work” per step

???N x .203 m = ???Nm

Work on a cycle ergometerWork on a cycle ergometerWork = FdForce

belt friction on the flywheelmass ie 3 kg

Displacement revolution of the pedals

Monark: 6 m“Work” per revolution

Work on a cycle ergometerWork on a cycle ergometer Work = Fd Force

belt friction on the flywheelmass ie 3 kg

Displacement revolution of the pedals

Monark: 6 m “Work” per revolution

3kg x 6 m = 18 kgm

Similar principle for Similar principle for wheelchairwheelchair

……and for handcycling and for handcycling ergometerergometer

EnergyEnergy Energy (E) is defined as the capacity to do

work 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

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

21

)//(21

//21

)/)((2121

2

2

Calculate Kinetic Calculate Kinetic EnergyEnergyHow much KE in a 5 ounce baseball (145 g) thrown at 80 miles/hr (35.8 m/s)?

Calculate Kinetic Calculate Kinetic EnergyEnergyTable of VariablesMass = 145 g 0.145 kgVelocity = 35.8 m/s

Calculate Kinetic Calculate Kinetic EnergyEnergyTable of Variables

Select the equation and solve:

Calculate Kinetic Calculate Kinetic EnergyEnergyHow 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 EnergyTwo 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 GPEHow 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 GPEHow 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 GPEGPE relative to mat Table of Variables m = 45 kgg = -9.81 m/s/sh = 4 m

GPE relative to ground

Table of Variables

More on this

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 ……

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 EnergyWhen a fiberglass vaulting pole

bends, strain energy is stored in the bent pole

.

Strain EnergyStrain EnergyWhen a fiberglass vaulting pole

bends, strain energy is stored in the bent pole

Bungee jumping.

Strain EnergyStrain EnergyWhen a fiberglass vaulting pole

bends, strain energy is stored in the bent pole

Bungee jumpingHockey sticks.

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

Work - Energy RelationshipWork - Energy RelationshipThe work done by an external force

acting on an object causes a change in the mechanical energy of the object

)(21 2

ifif rrmgvvmFd

PEKEFdEnergyFd

Click here fora website

Work - Energy RelationshipWork - Energy RelationshipThe 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 RelationshipRelationshipOf critical importanceSport and exercise = velocity

increasing and decreasing kinetic energy of a body

similar to the impulse-momentum relationship )(

21 2

vivfif rrmgvvmFd

PEKEFdEnergyFd

) (i vv v m Ft

Work - Energy RelationshipWork - Energy RelationshipIf 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 = wattvelocityForcePower

tFdPowertimeWorkPower

//

Calculate & compare Calculate & compare powerpowerDuring 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 powerpowerLifter ATable of VariablesF = 1000 Nd = 0.8 mt = 0.50 s

Lifter B

wsJPower

smNPower

tFdPower

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/""/""

kgmPowerkgmPowerrevFdPowertFdPower

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/""/""

kgmPowerkgmPowerrevFdPowertFdPower

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

smFPowersmFPower

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

smFPowersmFPower

vFPower

inch

inch

/122.0/121.0

10

5

Results: VO2 similar fast/short steps vs slow/deep steps