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

Work The product of force and the amount of displacement along the line of action of that force. Units: ft . lbs (horsepower) Newton•meter (Joule) e

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

Calculate Work During 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 Work Table of Variables: Force = +1000 N Displacement = +0.8 m Force is positive due to pushing upward Displacement is positive due to moving upward

Calculate Work Table of Variables: Force = +1000 N Displacement = +0.8 m Select the equation and solve:

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

Calculate Work During 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 Work Table of Variables Force = +1000 N Displacement = -0.8 m Force is positive due to pushing upward Displacement is negative due to movement downward

Calculate Work Table of Variables Force = +1000 N Displacement = -0.8 m Select the equation and solve:

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

Contemplate During 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 180 90 On elbow

Work performed climbing stairs Work = Fd Force Subject weight From 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 stepper Work = Fd Force Displacement “Work” per step Push on the step ???? Displacement Step Height 8 inches “Work” per step ???N x .203 m = ???Nm

Work on a cycle ergometer Work = Fd Force belt friction on the flywheel mass (eg 3 kg) Displacement revolution of the pedals Monark: 6 m “Work” per revolution

Work on a cycle ergometer Work = Fd Force belt friction on the flywheel mass (eg 3 kg) Displacement revolution of the pedals Monark: 6 m “Work” per revolution 3kg x 6 m = 18 kgm

Similar principle for wheelchair

…and for handcycling ergometer

Energy Energy (E) is defined as the capacity to do work (scalar) Many forms No more created, only converted chemical, sound, heat, nuclear, mechanical Kinetic Energy (KE): energy due to motion Potential Energy (PE): energy due to position or deformation

KE = 1/2 mv2 Kinetic Energy Energy due to motion reflects the mass the velocity of the object KE = 1/2 mv2

Kinetic Energy Units: reflect the units of mass * v2 Units KE = Units work

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

Calculate Kinetic Energy Table of Variables Mass = 145 g  0.145 kg Velocity = 35.8 m/s

Calculate Kinetic Energy Table of Variables Mass = 145 g  0.145 kg Velocity = 35.8 m/s Select 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

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

Calculate Kinetic Energy Table of Variables 150 lbs = 68.18 kg of mass -3.2 m/s Select 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

Calculate Kinetic Energy 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 momentum of each player

Calculate Kinetic Energy Table of Variables m = 100 Kg v = 4.0 m/s Select the equation and solve: KE = ½ m v2 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 v2 KE = ½ (175)(3.75)2 KE = 1230 Nm or J

Calculate Momentum 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 = 656.25

Potential Energy Two forms of PE: Gravitational PE: Strain PE: energy due to an object’s position relative to the earth Strain PE: due to the deformation of an object

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

Take a look at the energetics of a roller coaster 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

Calculate GPE Trampoline mat is 1.25 m above the ground 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

Calculate GPE More on this GPE relative to mat Table of Variables m = 45 kg g = -9.81 m/s/s h = 4 m PE = mgh PE = 45kg * -9.81 m/s/s * 4 m PE = - 1765.8 J GPE relative to ground Table of Variables m = 45 kg g = -9.81 m/s/s h = 5.25 m PE = mgh PE = 45m * -9.81 m/s/s * 5.25 m PE = 2317.6 J

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

Strain PE Affected by the object’s amount of deformation stiffness greater deformation = greater SE x2 = change in length or deformation of the object from its undeformed position stiffness resistance to being deformed k = stiffness or spring constant of material SE = 1/2 kx2

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

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

Strain Energy When a fiberglass vaulting pole bends, strain energy is stored in the bent pole Bungee jumping Hockey sticks

Strain Energy Plyometrics 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 Relationship The work done by an external force acting on an object causes a change in the mechanical energy of the object

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

Work - Energy Relationship 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

Work - Energy Relationship 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

Work - Energy Relationship Of critical importance Sport and exercise =  velocity increasing and decreasing kinetic energy of a body similar to the impulse-momentum relationship Ft = m (vf-vi)

Work - Energy Relationship If more work is done, greater energy greater average force greater displacement Ex. Shot put technique (121-122). If displacement is restricted, average force is __________ ? (increased/decreased) “giving” with the ball landing hard vs soft

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

Calculate & compare power 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 seconds Lifter B: 0.75 seconds

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

Power on a cycle ergometer Work = Fd Force: 3kg Displacement: 6m /rev “Work” per revolution 3kg x 6 m = 18 kgm 60 rev/min

Power on a cycle ergometer Work = Fd Force: 3kg Displacement: 6m /rev “Work” per revolution 3kg x 6 m = 18 kgm 60 rev/min 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 step 60s/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

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