Work, Power & Energy

1. Work, Power & Energy

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

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

12. 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

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

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

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

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

17. 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

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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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?)

25. 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

26. 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

27. 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

28. 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

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

30. 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

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

32. 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?

33. 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

34. 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

35. 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)

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

37. Newton’s Laws of Motion • 1st Law– An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity, unless acted upon by an unbalanced force. • 2nd Law – Force equals mass times acceleration. • 3rd Law – For every action there is an equal and opposite reaction.

38. 1st Law of Motion (Law of Inertia) An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity, unless acted upon by an unbalanced force.

39. 1st Law • Inertia is the tendency of an object to resist changes in its velocity: whether in motion or motionless. These pumpkins will not move unless acted on by an unbalanced force.

40. What is this unbalanced force that acts on an object in motion? Friction! • There are four main types of friction: • Sliding friction: ice skating • Rolling friction: bowling • Fluid friction (air or liquid): air or water resistance • Static friction: initial friction when moving an object

41. 2nd Law The net force of an object is equal to the product of its mass and acceleration, or F=ma.

42. 2nd Law • When mass is in kilograms and acceleration is in m/s/s, the unit of force is in newtons (N). • One newton is equal to the force required to accelerate one kilogram of mass at one meter/second/second.

43. 3rd Law • For every action, there is an equal and opposite reaction.

44. 3rd Law According to Newton, whenever objects A and B interact with each other, they exert forces upon each other. When you sit in your chair, your body exerts a downward force on the chair and the chair exerts an upward force on your body.