Work, Power & Energy

Explaining the Causes of Motion in a Different Way

WorkThe product of force and the amount

of displacement along the line of action of that force.

Units: ft . lbs (horsepower) Newton•meter (Joule)

ntdisplacemeForceWork

Work = 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 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 WorkTable of Variables:Force = +1000 NDisplacement = +0.8 m

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

upward

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

JJouleNmWork

mNWorkntdisplacemeForceWork

8008008008.01000

Work performed climbing stairs 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 Nm (Joules) Multiply by the number of steps

Work on a stair stepperWork = FdForce

Push on the step????

Displacement Step Height

8 inches“Work” per step

???N x .2m = ???Nm (Joules)

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

work (scalar) Many forms

No more created, only convertedchemical, sound, heat, nuclear, mechanical

Mechanical Energy Kinetic Energy (KE):

energy due to motion Potential Energy (PE):

energy due to position

Kinetic EnergyEnergy due to motion reflects

the mass the velocity

of the object

KE = 1/2 mv2

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

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

Calculate Kinetic EnergyTable 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

Gravitational 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 GPEHow much gravitational potential

energy in a 45 kg gymnast when she is 4m above the mat of the trampoline?

Calculate GPEGPE 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

Conversion of KE to GPE and GPE to KE and KE to GPE and …

Work - Energy RelationshipWork is the change in the

mechanical energy of the object

Fd KineticEnergyFd KE

Work - Energy Relationship If more work is done, greater

energy greater average forcegreater displacement

Extension…

PowerThe rate of doing work

Work = Fd

Units: Fd/s = J/s = wattvelocityForcePower

tFdPowertimeWorkPower

//

Calculate & compare powerDuring 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 powerLifter 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 ergometer 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 ergometer 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

Compare “power” in typical 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 typical 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 typical 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

- & + 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

- & + 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

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

Force is positive due to pushing upwardDisplacement is negative due to

movement downward

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

JJouleNmWork

mNWorkntdisplacemeForceWork

8008008008.01000

ContemplateDuring 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 Press

On elbow180

90

Extra Practice on KE

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

Calculate Kinetic EnergyTable 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