1. WORK AND ENERGY Another Way to Look at Motion

2. The most important concept in science! The most important concept in science!

3. What’s so Great About Energy? It’s a scalar; forget those vector headaches It’s a scalar; forget those vector headaches It’s useful in all of physics and in other sciences It’s useful in all of physics and in other sciences It’s conserved, meaning the total amount of it doesn’t change It’s conserved, meaning the total amount of it doesn’t change

4. What is energy? Difficult to define precisely. Difficult to define precisely. Exists in many different forms Exists in many different forms

5. Work The product of the magnitude of displacement times the component of force parallel to displacement The product of the magnitude of displacement times the component of force parallel to displacement W = Fd W = Fd F d

6. Work(more precisely) The product of the magnitude of displacement times the component of force parallel to displacement The product of the magnitude of displacement times the component of force parallel to displacement W = F p d cos W = F p d cos  F d 

7. Units of Work and Energy SI unit – newton-meter = joule SI unit – newton-meter = joule 1 J = 1 n –m 1 J = 1 n –m Obsolete units you might run across: Obsolete units you might run across: –In cgs system unit is erg = dyne-cm –In British system ft-lb –1 J = 10 7 ergs = 0.7376 ft-lb

8. Who Does More Work? A weightlifter holding up 200Kg A weightlifter holding up 200Kg (Force, no displacement) (Force, no displacement) A baby lifting a feather (Small force, some displacement)

9. Who Does More Work? A weightlifter holding up 200Kg A weightlifter holding up 200Kg (Force, no displacement) (Force, no displacement) No Work! No Work! A baby lifting a feather (Small force, some displacement) Some work

10. Work or no work? Lifting force is up, but displacement is horizontal; therefore…… No work is done on refrigerator

11. Work or No Work A mass circles at constant speed, held by a string Force is along string, toward center Force is perpendicular to motion Therefore, no work is done

12. Calculate the work 20 Kg crate is pulled 50m horizontally by a 100N force 20 Kg crate is pulled 50m horizontally by a 100N force W = Fd = 100N x 50m = 5000Joules W = Fd = 100N x 50m = 5000Joules F = 100N mg FNFN

13. Work to Climb a Mountain How much work is How much work is required for a 70 Kg person to climb 1000 m up a peak? Hint: use F = mg Answer : 6.86 x 10 5 J Work = force x distance Only up component of displacement contributes

14. Work Done By Sun on Earth How much is there? How much is there? v FGFG NONE!

15. ENERGY The ability to do work (an imperfect definition) The ability to do work (an imperfect definition) Many types exist: mechanical (potential, kinetic), heat, light, electrical, magnetic, nuclear Many types exist: mechanical (potential, kinetic), heat, light, electrical, magnetic, nuclear They can change from one to another They can change from one to another The sum of all of them (total energy)is conserved The sum of all of them (total energy)is conserved

16. Energy Conversion Example What form of energy comes into the projector? What form of energy comes into the projector? What forms are produced? What forms are produced? Answer: electrical Answer: light, heat, sound, kinetic, magnetic

17. Common Forms of Energy Kinetic – energy of motion Kinetic – energy of motion Potential – energy of position Potential – energy of position A pendulum converts energy back and forth from potential to kinetic. Mechanical

18. Law of Conservation of Energy In any process total energy is neither decreased nor increased In any process total energy is neither decreased nor increased It can change from one form to another It can change from one form to another It can be transferred from one body to another, but It can be transferred from one body to another, but IT CAN NOT BE CREATED NOR DESTROYED IT CAN NOT BE CREATED NOR DESTROYED

19. Kinetic Energy Energy of Motion Energy of Motion Translational and rotational Translational and rotational TRANSLATIONAL: KE = ½ m v 2 TRANSLATIONAL: KE = ½ m v 2

20. Derivation of ½ mv 2 Consider a mass accelerated uniformly from rest to velocity v Consider a mass accelerated uniformly from rest to velocity v Work done = W = F x d Work done = W = F x d F = ma F = ma W = mad W = mad v 2 = v 0 2 + 2ad; v 2 = v 0 2 + 2ad; W = m d (v 2 – v 0 2 )/2d W = m d (v 2 – v 0 2 )/2d = ½ mv 2 (v 0 = 0) a = (v 2 – v 0 2 )/2d

21. Derivation of ½ mv 2 Consider a mass accelerated uniformly from rest to velocity v Consider a mass accelerated uniformly from rest to velocity v Work done = W = F x d Work done = W = F x d F = ma F = ma W = mad W = mad v 2 = v 0 2 + 2ad; v 2 = v 0 2 + 2ad; W = m d (v 2 – v 0 2 )/2d W = m d (v 2 – v 0 2 )/2d = ½ mv 2 (v 0 = 0) a = (v 2 – v 0 2 )/2d

22. Examples Find the kinetic energy of a 70 kg person walking at 1.0 m/s. Find the kinetic energy of a 70 kg person walking at 1.0 m/s. KE = 1/2mv 2 = 35kg x (1m/s) 2 = 35J KE = 1/2mv 2 = 35kg x (1m/s) 2 = 35J Find the kinetic energy of a 0.01 kg bullet traveling at 1000 m/s. Find the kinetic energy of a 0.01 kg bullet traveling at 1000 m/s. KE = 1/2mv 2 = 0.5 x 0.01 x (1000m/s) 2 KE = 1/2mv 2 = 0.5 x 0.01 x (1000m/s) 2 KE = 5000J KE = 5000J

23. Why is it so dangerous to get shot? Bullet deposits lots of energy in small area Bullet deposits lots of energy in small area What about momentum (mv)? What about momentum (mv)? Find momentum of man Find momentum of man 70 kg m/s Find momentum of bullet Find momentum of bullet 10 kg m/s 10 kg m/s

24. Why is a comet or asteroid crash on Earth so dangerous? Find the kinetic energy of a 10 14 Kg asteroid whose speed is 50 km/sec. Find the kinetic energy of a 10 14 Kg asteroid whose speed is 50 km/sec. KE = ½ mv 2 = 0.5 x 10 14 x (5 x 10 4 m/s) 2 = KE = ½ mv 2 = 0.5 x 10 14 x (5 x 10 4 m/s) 2 = 12.5 x 10 22 J = 1.25 x 10 23 J 12.5 x 10 22 J = 1.25 x 10 23 J

25. Work-Energy Principle The net work done on an object equals the change in its kinetic energy The net work done on an object equals the change in its kinetic energy W net =  KE W net =  KE Work that increases KE is positive Work that increases KE is positive Work that decreases KE is negative Work that decreases KE is negative

26. How Much Work? Is needed to give a car of mass 1000kg a speed of 10 m/s? Is needed to give a car of mass 1000kg a speed of 10 m/s? W = Kinetic Energy gained W = Kinetic Energy gained W= ½ mv 2 W= ½ mv 2 W = 0.5 x 1000kg x (10m/s) 2 W = 0.5 x 1000kg x (10m/s) 2 W = 50,000 J = 5 x 10 4 J W = 50,000 J = 5 x 10 4 J

27. Force Required What average force is needed to do this if the distance is 100m? What average force is needed to do this if the distance is 100m? W = F x D W = F x D F = W/D = KE/D = 50,000 / 100 = 500N F = W/D = KE/D = 50,000 / 100 = 500N

28. How Much Work… is required to accelerate a 1000Kg car from 30 to 40 m/s? is required to accelerate a 1000Kg car from 30 to 40 m/s? Use W = 1/2mv 2 2 - 1/2mv 1 2 Use W = 1/2mv 2 2 - 1/2mv 1 2 Answer: 3.5 x 10 5 joules Answer: 3.5 x 10 5 joules

29. Gravitational Potential Energy An object held high has the potential to do work An object held high has the potential to do work PE grav = mgy PE grav = mgy Reference level of zero PE is arbitrary Reference level of zero PE is arbitrary

30. How Much PE? How much PE does a 100kg crate get when raised 100m? How much PE does a 100kg crate get when raised 100m? PE = mgh use g = 10 N/kg PE = mgh use g = 10 N/kg PE = 100kg x 10N/kg x 100m PE = 100kg x 10N/kg x 100m PE = 100,000 J PE = 100,000 J PE = 1.0 x 10 5 J PE = 1.0 x 10 5 J

31. Roller Coaster What speed will a frictionless roller coaster have at the bottom of a 40m high hill assuming zero speed at the top of the hill? What speed will a frictionless roller coaster have at the bottom of a 40m high hill assuming zero speed at the top of the hill? PE lost = KE gained PE lost = KE gained mgh = ½ mv 2 mgh = ½ mv 2 2gh = v 2 2gh = v 2 v = (2gh) 1/2 v = (2gh) 1/2 v = (2 x 10 x 40) 1/2 = (800) 1/2 v = (2 x 10 x 40) 1/2 = (800) 1/2 Answer v = 28 m/s

32. Law of Conservation of Energy In any process total energy is neither decreased nor increased In any process total energy is neither decreased nor increased It can change from one form to another It can change from one form to another It can be transferred from one body to another, but It can be transferred from one body to another, but IT CAN NOT BE CREATED NOR DESTROYED IT CAN NOT BE CREATED NOR DESTROYED

33. Conservation of Mechanical Energy In absence of friction or other non- conservative forces In absence of friction or other non- conservative forces KE + PE = constant KE + PE = constant

34. Conservative Force Work done does not depend on path taken Work done does not depend on path taken Potential energy can be defined Potential energy can be defined Example: lifting an object against gravity Example: lifting an object against gravity

35. Non Conservative or Dissipative Force Work done depends on path Work done depends on path No potential energy function can be defined No potential energy function can be defined Example: pushing an object against friction Example: pushing an object against friction W = Fd =  F N d =  mgd W = Fd =  F N d =  mgd

36. Power The rate that work is done The rate that work is done P = work/time = Fd/time = Fv P = work/time = Fd/time = Fv Unit joules/sec = watt Unit joules/sec = watt 746 watts = 1 horsepower 746 watts = 1 horsepower

37. Power The rate that work is done The rate that work is done P = work/time = Fd/time = Fv P = work/time = Fd/time = Fv Unit joules/sec = watt Unit joules/sec = watt 746 watts = 1 horsepower 746 watts = 1 horsepower

38. Simple Machines Machines that make work easier by increasing force or increasing distance Machines that make work easier by increasing force or increasing distance All simple machines trade force for distance; they can’t increase both

39. Examples of Simple Machines Lever Lever Inclined Plane Inclined Plane Screw Screw Gear Gear Wheel and Axle Wheel and Axle Pulley Pulley

40. Lever See saw See saw Pry bar Pry bar Screw driver used to pry Screw driver used to pry Fork, pencil Fork, pencil Paint brush Paint brush Which of these increase force? Which of these increase force? Courtesy www.lkwdpl.org/schools/elempath/ simplemachines

41. Inclined Plane Ramp Ramp Knife Knife Road up hill Road up hill Screwdriver pushed in Screwdriver pushed in Courtesy www.disabled.driverinfo.btinternet.co.uk / acctocar.html

42. Screw Inclined plane wrapped around a cylinder Inclined plane wrapped around a cylinder Courtesy www.uen.org/.../ view_activity.cgi?activity_id=6528 Q: Is a screwdriver an example of a screw?

43. Gear Wheel with teeth that mesh Wheel with teeth that mesh Changes speeds Changes speeds Increases or decreases force Increases or decreases force Used in auto and marine transmissions Used in auto and marine transmissions

44. Wheel and Axle A lever wrapped in a circle A lever wrapped in a circle Axle is normally fixed to wheel Axle is normally fixed to wheel

45. Pulley Axle turns freely Axle turns freely Types: Types: –Single fixed –Single moveable –One fixed one moveable –Block and tackle Courtesy www.conductortrain.com/.../apprentice/ skills/doc9.shtml

46. Work In = Work Out In absence of friction the work you put into a simple machine equals the work that comes out In absence of friction the work you put into a simple machine equals the work that comes out F in D in = F out D out F in D in = F out D out F out / F in = D in / D out F out / F in = D in / D out Illustrates the trade-off between force and distance Illustrates the trade-off between force and distance You can’t get “something for nothing without violating conservation of energy You can’t get “something for nothing without violating conservation of energy

47. Mechanical Advantage F out / F in is called “mechanical advantage,” actual mechanical advantage(AMA) to be exact. F out / F in is called “mechanical advantage,” actual mechanical advantage(AMA) to be exact. D in / D out is called ideal mechanical advantage (IMA) D in / D out is called ideal mechanical advantage (IMA) In a real machine AMA is always less than IMA because of friction In a real machine AMA is always less than IMA because of friction

48. Small and Large Mechanical Advantage Machines that increase force greatly are said to have large mechanical advantage Machines that increase force greatly are said to have large mechanical advantage –Example – pry bar Machines that increase distance and decrease force have mechanical advantage less than one Machines that increase distance and decrease force have mechanical advantage less than one –Example – paint brush

49. Efficiency AMA =  x IMA AMA =  x IMA  is called efficiency  is called efficiency All machines have an efficiency less than one so as not to violate? All machines have an efficiency less than one so as not to violate? Energy Conservation!

50. Lever Example A certain lever lifts a weight of 20N with an effort force of only 5N. Assuming ideal efficiency, over what distance will the effort force act to lift the weight by 0.1 meter? A certain lever lifts a weight of 20N with an effort force of only 5N. Assuming ideal efficiency, over what distance will the effort force act to lift the weight by 0.1 meter? Answer: 0.4m

51. Pulley Example A pulley system has an ideal mechanical advantage of 2. A pulley system has an ideal mechanical advantage of 2. –(a) What effort force will be required to lift 500N? –(b) if the efficiency is only 80%, would more force be required or less? 250 N more

52. Review Why can’t a simple machine have an efficiency greater than 1 (100%) ? Why can’t a simple machine have an efficiency greater than 1 (100%) ? It would violate the law of conservation of energy.

53. Compound Machines Many real machines are combinations of simple machines Many real machines are combinations of simple machines