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

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Work lThe product of force and the amount of displacement along the line of action of that force. Units: ft. lbs (horsepower) Newtonmeter (Joule) e

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Work = F x d To calculate work done on an object, we need: The Force ¬The average magnitude of the force The direction of the force The Displacement ¬The magnitude of the change of position The direction of the change of position

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Calculate Work lDuring 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 lHow much work did the lifter do to the barbell?

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Calculate Work Table of Variables: Force = N Displacement = +0.8 m Force is positive due to pushing upward Displacement is positive due to moving upward

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Calculate Work Table of Variables: Force = N Displacement = +0.8 m Select the equation and solve:

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- & + Work lPositive work is performed when the direction of the force and the direction of motion are the same l ascent phase of the bench press l Throwing a ball l push off (upward) phase of a jump

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Calculate Work lDuring 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

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Calculate Work Table of Variables Force = N Displacement = -0.8 m Force is positive due to pushing upward Displacement is negative due to movement downward

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Calculate Work Table of Variables Force = N Displacement = -0.8 m Select the equation and solve:

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- & + Work lPositive work lNegative work is performed when the direction of the force and the direction of motion are the opposite l descent phase of the bench press l catching l landing phase of a jump

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Contemplate lDuring negative work on the bar, what is the dominant type of activity (contraction) occurring in the muscles? lWhen positive work is being performed on the bar?

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EMG during the Bench Press On elbow

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Work performed climbing stairs lWork = Fd lForce l Subject weight lFrom mass, ie 65 kg lDisplacement l Height of each step lTypical 8 inches (20cm) lWork per step l 650N x 0.2 m = Nm lMultiply by the number of steps

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Work on a stair stepper lWork = Fd lForce l Push on the step l???? lDisplacement l Step Height l8 inches l“Work” per step l ???N x.203 m = ???Nm

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Work on a cycle ergometer lWork = Fd lForce l belt friction on the flywheel lmass (eg 3 kg) lDisplacement l revolution of the pedals lMonark: 6 m l“Work” per revolution

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Work on a cycle ergometer lWork = Fd lForce l belt friction on the flywheel lmass (eg 3 kg) lDisplacement l revolution of the pedals lMonark: 6 m l“Work” per revolution l 3kg x 6 m = 18 kgm

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Similar principle for wheelchair

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…and for handcycling ergometer

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Energy lEnergy (E) is defined as the capacity to do work (scalar)Energy l Many forms lNo more created, only converted lchemical, sound, heat, nuclear, mechanical lKinetic Energy (KE): l energy due to motion lPotential Energy (PE): l energy due to position or deformation

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Kinetic Energy Energy due to motion reflects l the mass l the velocity of the object KE = 1/2 mv 2

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Kinetic Energy Units: reflect the units of mass * v 2 lUnits KE = Units work

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

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Calculate Kinetic Energy Table of Variables Mass = 145 g kg Velocity = 35.8 m/s

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Calculate Kinetic Energy Table of Variables Mass = 145 g kg Velocity = 35.8 m/s Select the equation and solve: KE = ½ m v 2 KE = ½ (0.145 kg)(35.8 m/s) 2 KE = ½ (0.145 kg)( 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

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

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Calculate Kinetic Energy Table of Variables l150 lbs = kg of mass l-3.2 m/s Select the equation and solve: KE = ½ m v 2 lKE = ½ (68.18 kg)(-3.2 m/s) 2 lKE = ½ (68.18 kg)(10.24 m/s/s) lKE = ½ ( kg m/s/s) lKE = Nm or J

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Calculate Kinetic Energy Calculate Kinetic Energy Compare KE possessed by: l a 220 pound (100 kg) running back moving forward at 4.0 m/s l a 385 pound (175 kg) lineman moving forward at 3.75 m/s Bonus: calculate the momentum of each player

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Calculate Kinetic Energy Calculate Kinetic Energy Table of Variables m = 100 Kg v = 4.0 m/s Select the equation and solve: KE = ½ m v 2 KE = ½ (100 kg)(4.0 m/s) 2 KE = 800 Nm or J Table of Variables m = 175 kg v = 3.75 m/s Select the equation and solve: KE = ½ m v 2 KE = ½ (175)(3.75) 2 KE = 1230 Nm or J

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omentum Calculate Momentum Calculate M Momentum = mass times velocity Player 1 = 100 kg * 4.0 m/s Player 1 = 400 kg m/s Player 2 = 175 * 3.75 m/s Player 2 =

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Potential Energy Two forms of PE: lGravitational PE: l energy due to an object’s position relative to the earth lStrain PE: l due to the deformation of an object

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Gravitational PE lAffected by the object’s l weight lmg l elevation (height) above reference point l ground or some other surface lh GPE = mgh Units = Nm or J (why?)

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Calculate 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

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Calculate 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 m above the ground

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Calculate GPE GPE relative to mat Table of Variables m = 45 kg g = m/s/s h = 4 m PE = mgh PE = 45kg * m/s/s * 4 m PE = J GPE relative to ground Table of Variables m = 45 kg g = m/s/s h = 5.25 m PE = mgh PE = 45m * m/s/s * 5.25 m PE = J More on this

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

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Strain PE Affected by the object’s lamount of deformation l greater deformation = greater SE l x 2 = change in length or deformation of the object from its undeformed position lstiffness l resistance to being deformed l k = stiffness or spring constant of material SE = 1/2 k x 2

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Strain Energy lWhen a fiberglass vaulting pole bends, strain energy is stored in the bent pole Pole vault explosion

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Strain Energy lWhen a fiberglass vaulting pole bends, strain energy is stored in the bent pole lBungee jumping

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Strain Energy lWhen a fiberglass vaulting pole bends, strain energy is stored in the bent pole lBungee jumping lHockey sticks

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Strain Energy lWhen a fiberglass vaulting pole bends, strain energy is stored in the bent pole lBungee jumping lWhen a tendon/ligament/muscle is stretched, strain energy is stored in the elongated elastin fibers (Fukunaga et al, 2001, ref#5332 ) l k = n /m x = m (7 mm), Achilles tendon in walking lWhen a floor/shoe sole is deformed, energy is stored in the material. Plyometrics

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Work - Energy Relationship lThe work done by an external force acting on an object causes a change in the mechanical energy of the object

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Work - Energy Relationship lThe work done by an external force acting on an object causes a change in the mechanical energy of the object l Bench press ascent phase linitial position = 0.75 m; velocity = 0 lfinal position = 1.50 m; velocity = 0 lm = 100 kg lg = -10 m/s/s lWhat work was performed on the bar by lifter? lWhat is GPE at the start & end of the press?

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Work - Energy Relationship lWhat work was performed on the bar by lifter? lFd = KE + PE lFd = ½ m(v f –v i ) 2 + mgh lFd = 100kg * - 10 m/s/s * 0.75 m lFd = 750 J lW = Fd lW = 100 kg *.75m lW = 75 kg m lW = 75 kg m (10) = 750 J

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Work - Energy Relationship lWhat is GPE at the start & end of the press? lEnd (ascent) lPE = mgh lPE = 100 kg * -10 m/s/s * 1.50 m lPE = 1500 J lStart (ascent) lPE = 100 kg * -10 m/s/s * 0.75m lPE = 750 J

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Work - Energy Relationship lOf critical importance lSport and exercise = velocity l increasing and decreasing kinetic energy of a body l similar to the impulse-momentum relationship Ft = m (v f -v i )

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Work - Energy Relationship lIf more work is done, greater energy l greater average force l greater displacement lEx. Shot put technique ( ). lIf displacement is restricted, average force is __________ ? (increased/decreased) l “giving” with the ball l landing hard vs soft

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Power lThe rate of doing work l Work = Fd Units: Fd/s = J/s = watt

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Calculate & compare power lDuring 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 lLifter A: 0.50 seconds lLifter B: 0.75 seconds

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Calculate & compare power Lifter A Table of Variables F = 1000 N d = 0.8 m t = 0.50 s Lifter B

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Power on a cycle ergometer lWork = Fd lForce: 3kg lDisplacement: 6m /rev l“Work” per revolution l 3kg x 6 m = 18 kgm l60 rev/min

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Power on a cycle ergometer lWork = Fd lForce: 3kg lDisplacement: 6m /rev l“Work” per revolution l 3kg x 6 m = 18 kgm l60 rev/min 1 Watt = 6.12 kgm/min

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Compare “power” in typical stair stepping lWork = Fd lForce: Push on the step lconstant setting lDisplacement l Step Height: 5” vs 10” l0.127 m vs m lstep rate l 56.9 /min vs 28.8 /min lTime per step l 60s/step rate Thesis data from Nikki Gegel and Michelle Molnar

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Compare “power” in typical stair stepping lWork = Fd lForce: Push on the step lconstant setting lDisplacement l Step Height: 5” vs 10” l0.127 m vs m lstep rate l 56.9 /min vs 28.8 /min

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Compare “power” in typical stair stepping lWork = Fd lForce: Push on the step lconstant setting lDisplacement l Step Height: 5” vs 10” l0.127 m vs m lstep rate l 56.9 /min vs 28.8 /min Results: VO 2 similar fast/short steps vs slow/deep steps

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