Momentum & Energy conservation

1. Momentum & Energy conservation

2. Momentum

3. Newton’s 2nd law (shorthand version) F= ma change in v time a = change in v time F= m

4. Car truck collision Fc Ft Ft = mt change in vt time Fc = mc change in vc time Fc t = mc change in vc Ft t = mt change in vt Fc t +Ft t= mc change in vc+mt change in vt (Fc+Ft)t=change in mcvc+change inmtvt (Fc+Ft)t=change in(mcvc+mtvt)

5. Car truck collision Fc Ft (Fc+Ft)t=change in(mcvc+mtvt) Newton’s 3rd law: Fc= -Ft (Fc+Ft)t= 0 0 = change in(mcvc+mtvt) mcvc+mtvt stays constant!

6. Momentum = mv mcvc = momentum of car this changes this changes Mtvt= momentum of thruck mcvc+mtvt = total momentum this stays constant Before = -40 After = -40 Momentum is conserved!

7. True for all collisions before =+20 after =+20 visit www.physicsclassroom.com/mmedia/index.html

8. Revisit the canoe at the dock Initial momentum canoe = 0 boy = 0 Total = 0 final momentum canoe = mcvc boy = mbvb Total = 0

9. Momentum is a vector: mvcollision in 2 dimensions

10. eating Finding nemo

11. Billiard balls 2 before after ptot 2 ptot 1 1

12. Conservation of momentumon a sub-atomic level before p p ptot proton after p ptot p p- meson p- meson

13. Rocket travel before P0 after P0 + p exhaust p

14. Rifle recoil mV mV

15. Machine-gun granny

16. Work and Energy

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

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

19. 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

20. 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

21. Concept of Kinetic Energy Emilie du Châtelet (1706-1749) Brilliant mathematician One of Voltaire’s lovers

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

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

24. 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

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

26. 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

27. 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

28. 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

29. 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

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

31. Pendulum conserves energy Etot=mghmax Etot=mghmax hmax Etot=1/2 m(vmax)2

32. Roller coaster

33. 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

34. 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 potential energy in the spring

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

36. example grav PE KineticE Spring PE

37. 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

38. (-)Work done by frictionheat

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

40. 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)

41. 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

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

43. 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

44. 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

45. 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

46. 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

47. 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

48. about 300 won In Hawaii electrical energy costs about 25cents/kW-hr What is the cost in Seoul?