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## Work, Power & Energy

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**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 • 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**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**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**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 Kinetic Energy**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: • 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 • weight • mg • elevation (height) above reference point • ground or some other surface • h GPE = mgh Units = Nm or J (why?)**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**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**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 Calculate GPE More on this**Strain PE**Affected by the object’s • amount of deformation • 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 kx2**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**• 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**Lifter A**Table of Variables F = 1000 N d = 0.8 m t = 0.50 s Lifter B Calculate & compare power