Work, Power & Energy

1. Work, Power & Energy 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 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

8. Input Force FI Force applied to a machine Output Force FO Force applied by a machine Simple machines and work--Forces involved:

9. Work Input work done on a machine =Input force x the distance through which that force acts (input distance) Work Output Work done by a machine =Output force x the distance through which the resistance moves (output distance) Two forces, thus two types of work

10. Mechanical Advantage (MA) – expressed in a ratio WITH NO UNITS!! • The number of times a machine multiplies the input force. MA = output force/input force

11. Efficiency • Efficiency can never be greater than 100 %. Why? • Some work is always needed to overcome friction. • A percentage comparison of work output to work input. • work output (WO) / work input (WI)

12. Mechanical advantage of levers. • Ideal = input arm length/output arm length • input arm = distance from input force to the fulcrum • output arm = distance from output force to the fulcrum

13. 2. The Wheel and Axle • A lever that rotates in a circle. • A combination of two wheels of different sizes. • Smaller wheel is termed the axle. • IMA = radius of wheel/radius of axle.

14. 3. The Inclined Plane • A slanted surface used to raise an object. • Examples: ramps, stairs, ladders • IMA = length of ramp/height of ramp • Can never be less than one.

15. 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

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

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

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

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

20. 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

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

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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?)

28. 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

29. 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

30. 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

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

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

33. 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?

34. 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

35. 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

36. 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)

37. 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

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

39. 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

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