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Work, Power & Energy

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

2. 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

3. 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

4. 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?

5. 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

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

7. - & + 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

8. 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

9. 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

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

11. - & + 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

12. 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?

13. EMG during the Bench Press 180 90 On elbow

14. 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

15. 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

16. 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

17. 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

18. Similar principle for wheelchair

19. …and for handcycling ergometer

20. 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

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

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

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

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

25. 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

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

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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?)

33. 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

34. 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

35. 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

36. Conversion of KE to GPE and GPE to KE and KE to GPE and …

37. 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 kx2

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

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

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

41. 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

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

43. 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?

44. 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

45. 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

46. 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)

47. 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

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

49. 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

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