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Work and Energy

Learn about the different forms of energy, including work, kinetic energy, and potential energy. Understand how to calculate work and energy using force, displacement, and other variables. Explore the concept of conservation of energy.

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Work and Energy

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  1. Work and Energy Dr. Robert MacKay Clark College

  2. Introduction • What is Energy? • What are some of the different forms of energy? • Energy = $$$

  3. Overview • Work (W) Kinetic Energy (K) Potential Energy (U) • All Are measured in Units of Joules (J) • 1.0 Joule = 1.0 N m W K U

  4. Overview • Work Kinetic Energy Potential Energy Heat Loss W K U Heat Loss Heat Loss

  5. Work and Energy • Work = Force x displacement • W = F d • Actually • Work = Force x displacement parallel to force Dr =4.0 m W= F Dr = 6.0 N (4.0m) = 24.0 J F= 6.0 N

  6. Work and Energy • Work = Force x Displacement parallel to force Dr = 8.0 m F= - 6.0 N W= F Dr = -6.0 N (8.0m) =-48 J

  7. Work and Energy • Work = Force x Displacement parallel to force Dr = 6.0 m F= ? N W= 60 J

  8. Work and Energy • Work = Force x Displacement parallel to force Dr = ? m F= - 50.0 N W= 200 J

  9. Work and Energy • Work = Force x Displacement parallel to force Dr = 8.0 m F= + 6.0 N W= 0 (since F and d are perpendicular

  10. Fig. 7.2, p.184

  11. Work and Energy • Work = FDr • Dot product W = F Dr cos (40) Dr = 8.0 m F= + 6.0 N 40° W= (6.0N) [8.0m cos(40) ]= 36.8 J

  12. Work and Energy • Work = F Dr • Dot product W = F Dr cos(40) Dr = 8.0 m F= + 6.0 N 40° W= (6.0N cos(40) ) [8.0m]= 36.8 J

  13. Total Area ~S (DA) Work ~ S (FxDx) ~ ~ Fig. 7.7a, p.189

  14. Fig. 7.7b, p.189

  15. Work Variable Force (q=0) • Work = F Dr cosq = FavgDx

  16. Springs 101 • Spring Constant k, stiffness = 50 N/m

  17. Work Variable Force (q=0) • Work = F D cosq = F D

  18. Work Variable Force (q=0) • Work = “Area” units of N m (Joules) W= 0.5*(100N)(4m) - 0.5(50N)2m) = +200 J-50 J = 150 J

  19. Potential Energy, U • Gravitational Potential Energy • Springs • Chemical • Pressure • Mass (Nuclear) • Measured in Joules

  20. Potential Energy, U The energy required to put something in its place (state) • Gravitational Potential Energy • Springs • Chemical • Pressure • Mass (Nuclear)

  21. Potential Energy • Gravitational Potential Energy = weight x height U=(mg) h m = 2.0 kg 4.0 m

  22. Potential Energy U=(mg) h U=80 J m = 2.0 kg 4.0 m K=?

  23. Potential Energy to Kinetic Energy U=(mg) h m = 2.0 kg K E= 0 J PE=40 J 2.0 m 1.0 m KE=?

  24. Potential Energy of a spring x 1 kx2 U= 2

  25. Potential Energy of a spring x 1 kx2 U= 2 For a spring with stiffness k= 80 N/m, what is its potential energy when stretched 0.1m? How about 0.2 m?

  26. Potential Energy of a spring x 1 1 U= kx2 = 80 N/m (0.1m)2 2 2 = 0.40 J For a spring with stiffness k= 80 N/m, what is its potential energy when stretched 0.1m? How about 0.2 m?

  27. Potential Energy of a spring x 1 1 U= kx2 = 80 N/m (0.2m)2 2 2 = 1.60 J For a spring with stiffness k= 80 N/m, what is its potential energy when stretched 0.1m? How about 0.2 m?

  28. Potential Energy of a spring x 1 kx2 U= 2

  29. Kinetic Energy K=1/2mv2 Table 7.1, p.194

  30. Kinetic Energy, K • K =1/2 m v2 m=2.0 kg and v= 5 m/s K= ?

  31. Kinetic Energy m=2.0 kg and v= 5 m/s K= 25 J • K =1/2 m v2 m=4.0 kg and v= 5 m/s K= ? m=2.0 kg and v= 10 m/s K= ?

  32. Kinetic Energy • K =1/2 m v2 • if m doubles KE doubles • if v doubles KE quadruples • if v triples KE increases 9x • if v quadruples KE increases ____ x

  33. Work Energy Theorm • K =1/2 m v2 • F = m a

  34. Work Energy Theorm • K =1/2 m v2 • F = m a • F d = m a d

  35. Work Energy Theorm • K =1/2 m v2 • F = m a • F d =m a d • F d = m (v/t) [(v/2)t]

  36. Work Energy Theorm • K =1/2 m v2 • F = m a • F d = m a d • F d = m (v/t) [(v/2)t] • W = 1/2 m v2

  37. Work Energy Theorm • KE =1/2 m v2 • F = m a • F d = m a d • F d = m (v/t) [(v/2)t] • W = 1/2 m v2 • W = ∆ KE

  38. Work EnergyW = ∆K • How much work is required to stop a 2000 kg car traveling at 20 m/s (45 mph)?

  39. Work EnergyW = ∆K • How much work is required to stop a 2000 kg car traveling at 20 m/s (45 mph)? • W= ∆K =-1/2 m v2 • =-1/2(2000 kg)(20 m/s)2 • = - 1000kg (400 m 2 /s 2) • = - 400,000 Joules

  40. Work EnergyW = ∆K • How much work is required to stop a 2000 kg car traveling at 20 m/s? If the friction force equals its weight, how far will it skid? • W= ∆K = - 400,000 Joules • F=weight=mg=-20,000 N • W=F d d=W/F=-400,000 J/-20,000N • = 20.0 m

  41. Work EnergyW = ∆K v = 20 m/s d=? m Same Friction Force v = 10 m/s d= 15 m

  42. Conservation of Energy Energy can neither be created nor destroyed only transformed from one form to another Total Mechanical Energy, E = U +K In the absence of friction or other non-conservative forces the total mechanical energy of a system does not change E f=Eo

  43. Conservation of Energy U=100 J K = 0 J m = 1.02 kg (mg = 10.0 N) Constant E {E = K + U} Ef = Eo U = 75 J K = 25 J 10.0 m U = 50 J K = 50 J U = 25 J K= ? No friction No Air resistance U = 0 J K = ?

  44. Conservation of Energy U=100 J m = 2.0 kg K=0 J Constant E {E = K + U} Constant E {E = K + U} Ef=Eo 5.0 m No friction U = 0 J K = ?

  45. Conservation of Energy U =100 J m = 2.0 kg K = 0 J Constant E {E = K + U} Constant E {E = K + U} Ef=Eo 5.0 m No friction v = ? K = 100 J

  46. Conservation of Energy Constant E {E = K + U} Ef=Eo Ef=Eo+Wother Kf +Uf=Ko+Uo +Wother

  47. Example 8.8

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