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