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Work and Energy

Work and Energy. Physics 100 Chapt 5. Physicist’s definition of “work”. dist ∥. A scalar (not a vector). dist. Work = F x dist ∥. Atlas holds up the Earth. But he doesn’t move, dist ∥ = 0. Work= F x dist ∥ = 0. He doesn’t do any work!. Garcon does work when he picks up the tray.

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Work and Energy

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  1. Work and Energy Physics 100 Chapt 5

  2. Physicist’s definition of “work” dist∥ A scalar (not a vector) dist Work = F x dist∥

  3. Atlas holds up the Earth But he doesn’t move, dist∥ = 0 Work= Fx dist∥ = 0 He doesn’t do any work!

  4. Garcon does work whenhe picks up the tray but not while he carries it around the room dist is not zero, but dist∥ is 0

  5. Why this definition? A vector equation Newton’s 2nd law: F=ma Definition of work + a little calculus A scalar equation Work= change in ½mv2 This scalar quantity is given a special name: kinetic energy

  6. Work = change in KE This is called: the Work-Energy Theorem

  7. Units again… Kinetic Energy = ½mv2 m2 s2 kg work = F x dist∥ same! =1Joule m s2 N m =kg m

  8. Work done by gravity end start dist dist∥ change in vertical height W=mg Work = F x dist∥ = -mg xchange in height = -change in mgh

  9. Gravitational Potential Energy Workgrav = -change in mgh This is called: “Gravitational Potential Energy” (or PEgrav) change in PEgrav = -Workgrav Workgrav = -change in PEgrav

  10. If gravity is the only force doing work…. Work-energy theorem: -change in mgh = change in ½ mv2 0 = change in mgh + change in ½ mv2 change in (mgh + ½ mv2) = 0 mgh + ½ mv2 = constant

  11. Conservation of energy mgh + ½ mv2 = constant Gravitational Potential energy Kinetic energy If gravity is the only force that does work: PE + KE = constant Energy is conserved

  12. Free fall(reminder) height t = 0s 80m V0 = 0 75m t = 1s V1 = 10m/s 60m t = 2s V2 = 20m/s t = 3s 35m V3 = 30m/s t = 4s 0m V4 = 40m/s

  13. m=1kg free falls from 80m mgh ½ mv2 sum t = 0s V0 = 0 h0=80m 800J 0 800J t = 1s 750J 50J V1 = 10m/s; h1=75m 800J t = 2s V2 = 20m/s; h2=60m 600J 200J 800J t = 3s V3 = 30m/s; h3=35m 350J 450J 800J t = 4s V4 = 40m/s; h4=0 0 800J 800J

  14. pendulum T W=mg Two forces: T andW T is always ┴ to the motion (& does no work)

  15. Pendulum conserves energy E=mghmax E=mghmax hmax E=1/2 m(vmax)2

  16. Roller coaster

  17. Work done by a spring Relaxed Position F=0 x F I compress the spring (I do + work; spring does -work) Work done by spring = - change in ½kx2

  18. Spring Potential Energy Workspring = -change in ½kx2 This is the: “Spring’s Potential Energy” (or PEspring) Workspring = -change in PEspring change in PEspring = -Workspring

  19. If spring is the only force doing work…. Work-energy theorem: -change in ½ kx2 = change in ½ mv2 0 = change in ½ kx2 + change in ½ mv2 change in ( ½kx2 + ½mv2) = 0 ½ kx2 + ½ mv2 = constant

  20. Conservation of energysprings & gravity mgh + ½kx2 + ½mv2 = constant Gravitational potential energy spring potential energy Kinetic energy If elastic force & gravity are the only force doing work: PEgrav + PEspring + KE = constant Energy is conserved

  21. example grav PE KineticE Spring PE

  22. Two types of forces: • “Conservative” forces • forces that do + & – work • Gravity • Elastic (springs, etc) • Electrical forces • … • “Dissipative” forces • forces that only do – work • Friction • Viscosity • …. -work  heat (no potential energy.) -work  change in PE

  23. (-)Work done by frictionheat

  24. Thermal atomic motion Air solid Heat energy= KE and PE associated with the random thermal motion of atoms

  25. Work-energy theorem(all forces) Workfric = change in (PE+KE) Work done dissipative Forces (always -) potential energy From all Conservative forces Kinetic energy -Workfric= change in heat energy Workfric= -change in heat energy -change inHeat Energy = change in (PE+KE)

  26. Work – Energy Theorem(all forces) 0 =change inHeat Energy + change in (PE+KE) 0 =change in (Heat Energy+PE+KE) Heat Energy + PE + KE = constant Law of Conservation of Energy

  27. Energy conversion while skiing Potential energy Potential energykinetic energy Friction: energy gets converted to heat

  28. Units again Heat units: 1 calorie = heat energy required to raise the temp of 1 gram of H2O by 1o C Kg m2/s2 1 calorie= 4.18 Joules

  29. Food Calories 1 Calorie = 1000 calories = 1Kcalorie The Calories you read on food labels 1 Calorie= 4.18x103 Joules 7 x 106 J 8 x 105 J 2 x 106 J

  30. Power amout of energy elapsed time Rate of using energy: Power = Joule second Units: 1 = 1 Watt A 100 W light bulb consumes 100 J of electrical energy each second to produce light

  31. Other units Over a full day, a work-horse can have an average work output of more than 750 Joules each second 1 Horsepower = 750 Watts

  32. Kilowatt hours energy time Power =  energy = power x time  power unit x time unit = energy unit Kilowatts (103 W) hours (3600s) Elec companies use: x 1 kilowatt-hour = 1kW-hr = 103W x 3.6x103s = 3.6x106 Ws J HECO charges us about 15cents/kW-hr

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