Work, Power & Energy Work, Power & Energy Chapter 4 Explaining the Causes of Motion in a Different Way

Work, Power & EnergyWork, Power & Energy

Chapter 4

Explaining the Causes of Explaining the Causes of Motion in a Different WayMotion in a Different Way

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

Force is positive due to pushing upwardDisplacement is positive due to moving

upward


Table of Variables:Force = +1000 NDisplacement = +0.8 mSelect the equation and solve:

JJouleNmWork

mNWork


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 pressThrowing a ballpush off (upward) phase of a jump

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


Table of VariablesForce = +1000 NDisplacement = -0.8 m

Force is positive due to pushing upwardDisplacement is negative due to

movement downward


Table of VariablesForce = +1000 NDisplacement = -0.8 mSelect the equation and solve:

JJouleNmWork

mNWork


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

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 = 130.0 Nm

Multiply by the number of steps

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

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

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

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 (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

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)?


Table of VariablesMass = 145 g 0.145 kgVelocity = 35.8 m/s

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


How much KE possessed by a 150 pound female volleyball player moving downward at 3.2 m/s after a block?

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


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

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

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

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


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


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

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

Pole vault explosion



Bungee jumping



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 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


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

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


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


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)


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

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



constant setting


0.127 m vs 0.254 m


)08.2/254(.

)05.1/127(.

10

5

smFPower

smFPower

vFPower

inch

inch



constant setting


0.127 m vs 0.254 m


smFPower

smFPower

vFPower

inch

inch

/122.0

/121.0

10

5

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

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Work, Power & Energy Work, Power & Energy Chapter 4 Explaining the Causes of Motion in a Different Way