WESBURY COLLEGE OF SCIENCE 2013 GR 12 PHYSICAL

WESBURY COLLEGE OF SCIENCE 2013 • GR 12 PHYSICAL SCIENCES INTERVENTION FOR SCIENCE LEARNERS • SCIENCE DEPARTMENT PROJECT FOUNDATIONS OF LEARNING 2013 -09 -01 1

KNOWLEDGE AREAS • MECHANICS • CHEMICAL CHANGE • WAVES, LIGHT, SOUND • MATTER AND MATERIALS • ELECTRICITY AND MAGNETISM • CHEMICAL SYSTEMS 2

KNOWLEDGE AREA MECHANICS THEMES • FORCE, MOMENTUM AND IMPULS (GR 11 MECHANICS) • MOMENTUM (GR 12 MECHANICS) • VERTICAL PROJECTILE MOTION (GR 12 MECHANICS) • FRAMES OF REFERENCE (GR 12 MECHANICS) • WORK, POWER AND ENERGY (GR 12 MECHANICS) 3

KNOWLEDLEDGE AREA MECHANICS GR 11 MECHANICS THEME • FORCE, • MOMENTUM AND • IMPULSE 4

FORCE, MOMENTUM AND IMPULSE FORCE TWO TYPES OF FORCES-PUSHING AND PULLING FORCE 5

FORCE, MOMENTUM AND IMPULSE FORCE CONTACT AND NON-CONTACT FORCES 6

FORCE, MOMENTUM AND IMPULSE INTERACTION BETWEEN TWO BODIES TYPES OF FORCES 7

FORCE, MOMENTUM AND IMPULSE FREE BODY DIAGRAM FORCE DIAGRAM FREE BODY DIAGRAMS • OBJECT REPRESENT A DOT • FORCES ARE DRAWN AS ARROWS POINTING AWAY FROM THE DOT • LENGTH OF ARROW REPRESENTS SIZE OF FORCE • POINT OF ARROW INDICATES THE DIRECTION OF THE FORCE 8

FORCE, MOMENTUM AND IMPULSE FORCES WORK IN PAIRS – NEWTON’S THIRD LAW OF MOTION NEWTONS THIRD LAW OF MOTION WHEN A BODY (A) EXERTS A FORCE ON A SECOND BODY (B), THE SECOND BODY (B) EXERTS A FORCE EQUAL IN MAGNITUDE, BUT OPPOSITE IN DIRECTION ON THE FIRST BODY (A) 9

FORCE, MOMENTUM AND IMPULSE FORCES WORK IN PAIRS THE FORCE OF THE GROUND ON YOUR FOOT PUSHES YOU FORWARD 10

FORCE, MOMENTUM AND IMPULS FORCES WORK IN PAIRS NEWTON’S THIRD LAW OF MOTION EXPLAINS THE MOVEMENT OF THE BALLOON ROCKET 11

FORCE, MOMENTUM AND IMPULSE FORCES WORK IN PAIRS NEWTON’S THIRD LAW OF MOTION EXPLAINS THE 12 MOVEMENT OF THE BALLOON ROCKET

FORCE, MOMENTUM AND IMPULSE FORCES WORK IN PAIRS NEWTON’S THIRD LAW BOOK ON TABLE 13

FORCE, MOMENTUM AND IMPULSE FORCES WORK IN PAIRS ANALYSE THE SCIENTIFIC CORRECTNESS OF THE FOLLOWING STATEMENT ABOUT A HORSE PULLING A CART: “WHEN A HORSE PULLS A CART, THE CART PULLS THE HORSE WITH AN EQUAL BUT OPPOSITE FORCE, ……. . CONSEQUENTLY THE FORCES CANCEL EACH OTHER OUT AND THE CART IS UNABLE TO MOVE” 14

FORCE, MOMENTUM AND IMPULSE FORCES WORK IN PAIRS “… WHEN A HORSE PULLS A CART, THE CART PULLS THE HORSE WITH AN EQUAL BUT OPPOSITE FORCE, …” ACCORDING TO NEWTON’S THIRD LAW THIS PART OF THE STATEMENT TRUE!!!! THE CART PULLS THE HORSE WITH AN EQUAL BUT OPPOSITE FORCE THAN WHAT THE HORSE IS PULLING THE CART. CONSEQUENTLY THE FORCES CANCEL EACH OTHER OUT AND THE CART IS UNABLE TO MOVE” THIS PART OF THE STATEMENT IS NOT TRUE!!!!!! THE TWO FORCES ACT ON DIFFERENT OBJECTS AND CAN THEREFOR NOT CANCEL EACH OTHER OUT. ONLY THE FORCES THAT ACT IN ON THE CART – 1 APPLIED FORCE OF THE HORSE 2 FRICTION OF CART WILL DETEMINE IF THE CART WILL MOVE. 15

FORCE, MOMENTUM AND IMPULSE NEWTONS LAW OF MOTION (ESA) 16

FORCE, MOMENTUM AND IMPULSE UNDERSTANDING OF NEWTON’S THIRD LAW OF MOTION • THE TWO FORCES WORK SIMULTANEOUSLY AND HAVE THE SAME MAGNITUDE • THE TWO FORCES HAVE OPPOSITE DIRECTIONS • THE TWO FORCES ARE THE SAME - BOTH FRICTIONAL OR NORMAL FORCES • IF TWO FORCES ACT ON DIFFERENT OBJECTS AND CAN THEREFORE NOT CANCEL EACH OTHER OUT • ONLY FORCES ACTING ON THE SAME OBJECT CANCEL EACH OTHER OUT 17

FORCE, MOMENTUM AND IMPULSE MOMENTUM – AMOUNT OF MOTION ANY MOVING OBJECT HAS MOMENTUM 18

FORCE, MOMENTUM AND IMPULSE WHAT IS LINEAR MOMENTUM? LINEAR MOMENTUM (MOMENTUM IN A STRAIGHT LINE) CAN BE DEFINED AS THE PRODUCT OF MASS AND 19 VELOCITY

FORCE, MOMENTUM AND IMPULSE CHANGE IN MOMENTUM A NET FORCE ON AN OBJECT CAUSES A CHANGE IN MOMENTUM - A TACKLE IN RUGBY CHANGES THE MOMENTUM OF THE OPPONENT 20

FORCE, MOMENTUM AND IMPULSE NEWTONS SECOND LAW OF MOTION IN TERMS OF MOMENTUM THE NET (OR RESULTANT) FORCE EXERTED ON AN OBJECT IS EQUAL TO THE RATE OF CHANGE OF MOMENTUM 21

FORCE, MOMENTUM AND IMPULSE CHANGE IN MOMENTUM THROWING AN EGG TO STOP THE EGG, THE MOMENTUM OF THE EGG MUST BE CHANGED TO ZERO THE CONTACT TIME IS THE ONLY SOLUTION TO ENSURE THAT THE EGG EXPERIENCE AS SMALL A FORCE AS POSSIBLE 22

FORCE, MOMENTUM AND IMPULSE CHANGE IN MOMENTUM CATCH A WATER BALLOON TO STOP THE WATER BALLOON, THE MOMENTUM MUST BE CHANGED TO ZERO THE CONTACT TIME IS THE ONLY SOLUTION TO ENSURE THAT BALLOON EXPERIENCE AS SMALL A FORCE A POSSIBLE 23

FORCE, MOMENTUM AND IMPULSE CHANGE IN MOMENTUM CRICKET PLAYER CATCHING A BALL THE CONTACT TIME IS THE ONLY SOLUTION TO ENSURE THAT CRICKET PLAYER EXPERIENCE A SMALL FORCE 24

FORCE, MOMENTUM AND IMPULSE CHANGE IN MOMENTUM A BATSMAN HITTING A CRICKET BALL THE MAGNITUDE OF THE NET FORCE, AS WELL AS THE CONTACT TIME , WILL THE DETERMINE THE SUCCESS OF THE SHOT 25

FORCE, MOMENTUM AND IMPULSE CHANGE IN MOMENTUM SUMMARY 26

FORCE, MOMENTUM AND IMPULSE THE PRODUCT OF THE NET FORCE AND THE CONTACT TIME IS CALLED THE IMPULSE (N. s) OF THE FORCE 27

FORCE, MOMENTUM AND IMPULSE THE CONCEPT OF IMPULSE AND SAFETY CONSIDERATIONS IN EVERYDAY LIFE AIRBAGS INCREASES THE CONTACT TIME AND THE PASSENGER EXPERIENCE A SMALLER FORCE 28

FORCE, MOMENTUM AND IMPULSE THE CONCEPT OF IMPULSE AND SAFETY CONSIDERATIONS IN EVERYDAY LIFE AIRBAGS 29

FORCE, MOMENTUM AND IMPULSE THE CONCEPT OF IMPULSE AND SAFETY CONSIDERATIONS IN EVERYDAY LIFE CRUMPLE ZONES INCREASES THE CONTACT TIME AND THE PASSENGER EXPERIENCE A SMALLER FORCE 30

FORCE, MOMENTUM AND IMPULSE THE CONCEPT OF IMPULSE AND SAFETY CONSIDERATIONS IN EVERYDAY LIFE ARRESTOR BEDS ARRESTER BEDS INCREASES THE CONTACT TIME FOR A RUNAWAY TRUCK TO BE STOPPED 31

FORCE, MOMENTUM AND IMPULSE WESBURY COLLEGE OF SCIENCE 32

KNOWLEDLEDGE AREA MECHANICS GR 12 MECHANICS THEME MOMENTUM 33

CONSERVATION OF MOMENTUM WHEN DOES MOMENTUM CHANGE? MOMENTUM CHANGES WHEN A NET FORCE ACTS ON AN OBJECT! WHEN IS MOMENTUM CONSERVED? WHEN THE NET FORCE THAT ACTS ON AN OBJECT IS ZERO, THE OBJECT DOES NOT EXPERIENCE AN ACCELERATION THEREFOR NO CHANGE IN VELOCITY. 34

CONSERVATION OF MOMENTUM DURING A COLLISION TWO VEHICLES EXPERIENCE EQUAL BUT OPPOSITE FORCES 35

CONSERVATION OF MOMENTUM THE CONTACT TIME DURING WHICH THE FORCES ACT ON THE TWO VEHICLES IS/ARE THE SAME THE VEHICLES EXPERIENCE THE SAME IMPULSE BUT IN OPPOSITE DIRECTIONS FA = -FB and t. A= t. B FAt. A = -FBt. B FAt. A + FBt. B = 0 36

CONSERVATION OF MOMENTUM THE TOTAL LINEAR MOMENTUM IN A CLOSED SYSTEM IS CONSERVED IN MAGNITUDE AND DIRECTION 37

CONSERVATION OF MOMENTUM THE TOTAL LINEAR MOMENTUM IN A CLOSED SYSTEM IS CONSERVED IN MAGNITUDE AND DIRECTION 38

CONSERVATION OF MOMENTUM COLLISIONS AND EXPLOSIONS MOMENTUM STAY CONSERVED IN A CLOSED SYSTEM 39

ELASTIC AND INELASTIC COLLISIONS ARE OFTEN CLASSIFIED ACCORDING TO THE CHANGE IN TOTAL KINETIC ENERGY ELASTIC COLLISIONS TOTAL KINETIC ENERGY OF THE SYSTEM BEFORE THE COLLISION IS EQUAL TO THE TOTAL KINETIC ENERGY AFTER THE COLLISION INELASTIC COLLISIONS TOTAL KINETIC ENERGY OF THE SYSTEM IS NOT THE SAME BEFORE AND AFTER THE COLLISION 40

ELASTIC AND INELASTIC COLLISIONS TOTAL KINETIC ENERGY BEFORE A COLLISION = TOTAL KINETIC ENERGY AFTER A COLLISION Ek BEFORE COLLISION = Ek AFTER COLLISION ½ mv 2 = ½ mv 2 41

ELASTIC AND INELASTIC COLLISIONS NEWTON’S CRADLE TOTAL KINETIC ENERGY BEFORE A COLLISION = TOTAL KINETIC ENERGY AFTER A COLLISION 42

ELASTIC AND INELASTIC COLLISIONS NEWTON’S CRADLE 43

ELASTIC AND INELASTIC COLLISIONS GIANT NEWTON’S CRADLE 44

MECHANICS NNEWTONS CRADLE – PENDULUM WAVES 45

ELASTIC AND INELASTIC COLLISIONS SUMMARY MOMENTUM WILL ALWAYS BE CONSERVED DURING COLLISIONS KINETIC ENERGY WILL ONLY BE CONSERVED DURING ELASTIC COLLISIONS 46

MECHANICS MOMENTUM VIDEO 47

MECHANICS WESBURY COLLEGE OF SCIENCE LEARNERS MODULE 1 p 45 -46 p 47 p 48 AKT 6. VRAE 1 -4 48

KNOWLEDLEDGE AREA MECHANICS GR 11 MECHANICS • NEWTON’S SECOND LAW OF MOTION • NEWTON’S FIRST LAW OF MOTION 49

NEWTON’S SECOND LAW OF MOTION MATHEMATICAL EXPRESSION OF NEWTON’S SECOND LAW OF MOTION 51

NEWTON’S SECOND LAW OF MOTION WHEN A RESULTANT FORCE ACTS ON A BODY, THE BODY ACCELARATES THE ACCELARATION IS DIRECTLY PROPORTIONAL TO THE NET FORCE AND INVERSELY PROPORTIONAL TO THE MASS OF THE BODY 52

NEWTON’S FIRST LAW OF MOTION 53

NEWTON’S FIRST LAW OF MOTION APPLICATIONS OF NEWTON’S FIRST LAW 54

KNOWLEDLEDGE AREA MECHANICS THEME VERTICAL PROJECTILE MOTION 55

PROJECTILE MOTION DIFFERENT TYPES OF PROJECTILE MOTION 56

PROJECTILE MOTION FREE-BODY DIAGRAM FOR A PROJECTILE MOTION A PROJECTILE HAS ONLY ONE FORCE ACTING UPON IT - THE FORCE OF GRAVITY 57

PROJECTILE MOTION FREE FALL FROM REST AN OBJECT THAT FALLS FREE FROM REST IS THE SIMPLEST FORM OF PROJECTILE 58

PROJECTILE MOTION FREE FALL FROM REST THE MOTION EQUATIONS CAN BE ADAPTED FOR FREE FALL AS FOLLOWS vf = vi + g Dt Dy = vi Dt + ½ g Dt 2 vf 2 = vi 2 + 2 g Dy 59

PROJECTILE MOTION FREE FALL FROM REST USEFUL TIPS FOR FREE FALL MOTION EQUATIONS • THE INITIAL VELOCITY OF A FALLING BODY IS ZERO • ALWAYS WRITE THE COMPLETE EQUATION FIRST AND SHOW ALL SUBSTITUTIONS, EVEN ZERO VALUES • PLACE A UNIT AFTER EVERY FINAL ANSWER 60

PROJECTILE MOTION FREE FALL FROM REST (DISPLACEMENT) POSITION-TIME GRAPH FOR A FREE FALLING OBJECT 61

PROJECTILE MOTION FREE FALL FROM REST VELOCITY-TIME GRAPH FOR A FREE FALLING OBJECT 62

PROJECTILE MOTION FREE FALL FROM REST ACCELERATION-TIME GRAPH FOR A FREE FALLING OBJECT 63

PROJECTILE MOTION VERTICAL PROJECTILE MOTION ANY OBJECT THAT IS THROWN, KICKED OR SHOT PERPENDICULARLY INTO THE AIR, IS A VERTICAL PROJECTILE 64

PROJECTILE MOTION VERTICAL PROJECTILE MOTION USEFUL TIPS • PROJECTILES FALL FREE AT 9, 8 m. s-2 • PROJECTILES EXPERIENCE A CONSTANT DOWNWARD ACCELERATION (9, 8 m. s-2) REGARDLESS WHETHER THEY MOVE UPWARDS OR DOWNWARDS • THE VELOCITY OF A PROJECTILE AT ITS FULCRUM IS ZERO • THE TIME FOR THE UPWARD MOTION OF A PROJECTILE FROM THE STARTING POINT, IS THE SAME AS THE TIME OF THE DOWNWARD MOTION TO THE SAME POINT • Vi UPWARD MOTION = Vf DOWNWARD MOTION 65

PROJECTILE MOTION VERTICAL PROJECTILE MOTION GRAPHIC REPRESENTATION TIME (s) POSITION (m) 0 0 1 15 2 20 3 15 4 0 (DISPLACEMENT) POSITION-TIME GRAPH FOR VERTICAL PROJECTILE MOTION 66

PROJECTILE MOTION VERTICAL PROJECTILE MOTION GRAPHIC REPRESENTATION TIME (s) VELOCITY (m∙s– 1) 0 + 20 1 + 10 2 0 3 - 10 4 - 20 VELOCITY-TIME GRAPH FOR VERTICAL PROJECTILE MOTION 67

PROJECTILE MOTION VERTICAL PROJECTILE MOTION GRAPHIC REPRESENTATION ACCELERATION-TIME GRAPH FOR VERTICAL PROJECTILE MOTION 68

PROJECTILE MOTION VERTICAL PROJECTILE MOTION SKETCH GRAPHS UPWARD THEN DOWNWARD MOTION 69

PROJECTILE MOTION VERTICAL PROJECTILE MOTION SKETCH GRAPHS DOWNWARD THEN UPWARD MOTION 70

PROJECTILE MOTION VERTICAL PROJECTILE MOTION-SKETCH GRAPHS BOUNCING BALL 71

KNOWLEDLEDGE AREA MECHANICS THEME FRAMES OF REFERENCE 72

WHAT IS A FRAMES OF REFERENCE? IN THIS PICTURE THE CAR IS TO THE RIGHT OF THE TREE. AFTER 2 SECONDS, THE CAR IS TO THE LEFT OF THE TREE. AS THE TREE DOES NOT MOVE, THE CAR MUST HAVE MOVED FROM ONE PLACE TO ANOTHEREFORE, HERE THE TREE IS CONSIDERED AS THE FRAME OF REFERENCE 73

WHAT IS A FRAME OF REFERENCE? IN FIG. 1, IS DIE KAR AAN DIE REGTERKANT VAN DIE BOOM! IN FIG. 2, NA 2 SEKONDES, IS DIE KAR AAN DIE LINKERKANT VAN DIE BOOM! DIE BOOM BEWEEG NIE, DIE KAR MOES VAN EEN PLEK NA ‘N ANDER PLEK BEWEEG HET! DUS KAN DIE BOOM AS DIE VERWYSINGSRAAMWERK GENEEM WORD. 74

FRAMES OF REFERENCE MAN STAAN STIL IN BUS · DIE BUS BEWEEG 120 km. h-1 NOORD. · DIE MAN IN DIE BUS STAAN STIL, MAAR BEWEEG OOK TEEN 120 km. h-1 NOORD · VIR DIE KIND WAT SIT, STAAN DIE MAN STIL · VIR DIE VROU OP DIE SYPAADJIE BEWEEG DIE MAN TEEN ‘N 120 km. h-1 NOORD 75

FRAMES OF REFERENCE 76

FRAMES OF REFERENCE 77

FRAMES OF REFERENCE 78

KNOWLEDGE AREA MECHANICS THEMES • FORCE, MOMENTUM AND IMPULS (GR 11 MECHANICS) • MOMENTUM (GR 12 MECHANICS) • VERTICAL PROJECTILE MOTION (GR 12 MECHANICS) • FRAMES OF REFERENCE (GR 12 MECHANICS) • WORK, POWER AND ENERGY (GR 12 MECHANICS) 79

KNOWLEDLEDGE AREA MECHANICS THEME WORK, POWER AND ENERGY 80

WORK THE CONCEPT “WORK” IN EVERY DAY LIFE 81

WORK THE CONCEPT “WORK” IN PHYSICS THE CONCEPT WORK RELATES TO MOTION 82

WORK THE CONCEPT “WORK” IN PHYSICS WORK (W) IS DONE WHEN A FORCE (F) CAUSES AN OBJECT TO UNDERGO DISPLACEMENT (Dx) 83

WORK WHEN IS WORK DONE? ONLY THE HORIZONTAL COMPONENT OF THE FORCE DOES WORK 84

WORK WHEN IS WORK DONE? A FORCE THAT IS PERPENDICULAR TO THE DISPLACEMENT DOES NO WORK THE FORCE DOES NOT HAVE A COMPONENT IN THE DIRECTION OF THE DISPLACEMENT 85

WORK MATHEMATICAL EXPRESSION OF WORK Wnet = Fnet D x Cosθ Wnet = ΣW (of each individual force that is exerted on the system ) Fnet = the size of the net force Δx = size of the displacement θ = angle between the force Fnet and the displacement Δx 86

WORK MATHEMATICAL EXPRESSION OF WORK 87

WORK EXAMPLES OF WORK THE WORK DONE BY THE FORCE “F” ON THE LAWNMOWER IS F Dx Cos. Q 88

WORK EXAMPLES OF WORK A PERSON HOLDING A SUITCASE IS DOING NO WORK ON THE SUITCASE BECAUSE THERE IS NO MOTION D x = 0 W = 0 89

WORK EXAMPLES OF WORK WHEN F IS EXERTED PERPENDICULAR TO Δx, THEN Cos Θ = Cos 90º = 0, AND THEN THE FORCE IS NOT DOING WORK ON THE SUITCASE 90

WORK EXAMPLES OF WORK WILL BE DONE IF A PERSON CARRY A SUITCASE UP A STAIRCASE BECAUSE AND CosΘ WILL BE BETWEEN 0 AND 1 W = FΔx CosΘ 91

WORK EXAMPLES OF WORK WILL BE DONE BY “f” ON THE SUITCASE THAT IS DISPLACED OVER A FLOOR WITH Δx. BUT “f” IS PARALLEL AND IN THE OPPOSITE DIRECTION AS Δx, SO: CosΘ = Cos 180º = -1 92

WORK EXAMPLES OF WORK FORCE F THAT THE ELECTRIC MOTOR EXERTS ON THE SUITCASE IS DOING WORK. BUT F IS PARALLEL AND IN THE OPPOSITE DIRECTION TO Δy, SO: CosΘ = Cos 180º = -1 93

ENERGY IS REQUIRED TO DO WORK!!!! THIS FORCE MUST HAVE SOME FORM OF ENERGY 94

ENERGY 95

ENERGY IS REQUIRED TO DO WORK WHEN WORK IS DONE, OBJECTS EXCHANGE ENERGY THE OBJECT ON WHICH WORK IS DONE GAINS ENERGY, WHILE THE OBJECT THAT DOES WORK LOSES ENERGY 96

ENERGY LAW OF CONSERVATION OF ENERGY CANNOT BE DESTROYED OR CREATED BUT CAN ONLY BE TRANSFERRED FROM ONE TO THE OTHER 97

ENERGY WHAT IS POTENTIAL ENERGY? POTENTIAL ENERGY IS THE ENERGY THAT AN OBJECT POSSESSES AS RESULT OF ITS POSITION 98

ENERGY WHAT IS GRAVITATIONAL POTENTIAL ENERGY? U = Ep = mgh IS THE ENERGY THAT AN OBJECT WITH A MASS (m) POSESSES AS RESULT OF ITS POSITION (h) RELATIVE TO THE SURFACE OF THE EARTH 99

ENERGY WHAT IS KINETIC ENERGY? K = Ek = ½ mv 2 THE ENERGY RESULTING FROM MOTION 100

ENERGY WHAT IS MECHANICAL ENERGY? THE ENERGY A OBJECT RECEIVES WHEN WORK IS DONE ON IT IS CALLED MECHANICAL ENERGY, AND CONSISTS OF… POTENTIAL ENERGY AND KINETIC ENERGY 101

ENERGY MECHANICAL ENERGY IN TERMS OF POTENTIAL AND KINETIC ENERGY 102

ENERGY MECHANICAL ENERGY IN TERMS OF POTENTIAL AND KINETIC ENERGY 103

ENERGY LAW OF THE CONSERVATION OF MECHANICAL ENERGY THE TOTAL MECHANICAL ENERGY OF A MOVING OBJECT IN A CLOSED SYSTEM STAYS CONSTANT IF NO WORK IS DONE BY EXTERNAL FORCES MECHANICAL ENERGY (i) = MECHANICAL ENERGY (f) (Ep + Ek)i = (Ep + Ek)f 104

ENERGY LAW OF THE CONSERVATION OF MECHANICAL ENERGY 105

ENERGY LAW OF CONSERVATION OF MECHANICAL ENERGY WHAT IS A CLOSED SYSTEM? NO EXTERNAL FORCES (LIKE FRICTION) HAS AN EFFECT ON THE SYSTEM. WHAT IS AN EXTERNAL FORCE? - NET APPLIED FORCE - FRICTIONAL FORCE - ATMOSPHERIC RESISTANCE - NORMAL FORCE 106

ENERGY 107

ENERGY WHAT IS THE WORK-KINETIC ENERGY THEOREM? THE NETTO WORK DONE ON AN OBJECT IS EQUAL TO THE CHANGE OF THE KINETIC ENERGY OF THE OBJECTS. OR THE WORK DONE ON AN OBJECT BY A NET FORCE IS EQUAL TO THE CHANGE IN THE KINETIC ENERGY OF THE OBJECT. OR WHEN AN EXTERNAL NET FORCE DOES WORK ON AN OBJECT, THE KINETIC ENERGY OF THE OBJECT CHANGES FROM AN INITIAL AN VALUE EKI, TO A FINAL VALUE, EKF. THE DIFFERENCE BETWEEN THESE VALUES IS EQUAL TO THE WORK DONE. Wnet = Δ K = ΔEk = Ekf – Eki 108

ENERGY WHAT IS THE WORK-KINETIC ENERGY THEOREM? Wnet = Δ K = ΔEk = Ekf – Eki but Wnet = Fnet Δx Cosθ therefore FnetΔx Cosθ = ΔK = Ekf – Eki Fnet Δx Cosθ= ½mvf 2 - ½mvi 2 REMEMBER Wnet = ΣW (OF EACH INDIVIDUAL FORCE 109 EXERTED ON THE SYSTEM)

MECHANICS DIFFERENT FORCES ACTING ON A BODY MOVING UP A SLOPE 110

MECHANICS WORK DONE ON A OBJECT MOVING DOWN A FRICTIONLESS SURFACE Wnet = WFg// + WFN + Ww┴ = Fg//Dx. Cosq + FNDx. Cosq + Fg┴ Dx. Cosq = mg. Sin 30°Dx. Cos 0° + 0 Wnet = mg. Sin 30°Dx. Cos 0° 111

MECHANICS WORK DONE ON A OBJECT MOVING UP A FRICTIONLESS SURFACE Wnet = WFg// + WFN + WFg┴ = Fg//Dx. Cosq + FNDx. Cosq + Fg┴ Dx. Cosq = mg. Sin 30°Dx. Cos 180° + 0 Wnet = mg. Sin 30° Dx Cos 180° 112

MECHANICS WORK DONE ON A OBJECT MOVING DOWN A SURFACE WITH FRICTION Wnet = WFg// + Wf + WFN + WFg┴ = Fg//Dx. Cosq + f Dx. Cosq + FNDx. Cosq + Fg┴ Dx. Cosq = mg. Sin 30°Dx. Cos 0° + f. Dx. Cos 180° + 0 Wnet = mg. Sin 30°Dx. Cos 0° + f. Dx. Cos 180° 113

MECHANICS 114

MECHANICS WORK DONE ON A OBJECT MOVING UP A SURFACE WITH FRICTION Wnet = WFg// + Wf + WFN + WFg┴ = Fg//Dx. Cosq + f Dx. Cosq + FNDx. Cosq + Fg┴ Dx. Cosq = mg. Sin 30°Dx. Cos 180° + f. Dx. Cos 180° + 0 Wnet = mg. Sin 30°Dx. Cos 180° + f. Dx. Cos 180° 115

WORK AND ENERGY SUMMARY ………. IF THERE ARE NO FRICTIONAL FORCES: FORCES USE THE LAW OF CONSERVATION OF MECHANICAL ENERGY: ME(i) = ME(f) (Ep + Ek)i = (Ep + Ek)f OR USE THE WORK ENERGY PRINCIPLE: Wnet = ΔK = Ekf – Eki = ½mvf 2 - ½mvi 2 ………. . IF THERE ARE FRICTIONAL FORCES USE THE WORK ENERGY PRINCIPLE: Wnet = ΔK = Ekf – Eki = ½mvf 2 - ½mvi 2 116

117

ENERGY 118

MECHANICS POWER WHAT IS POWER? POWER IS THE RATE AT WHICH WORK IS DONE OR ENERGY IS USED 119

MECHANICS POWER, FORCE AND VELOCITY INSTANTANEOUS POWER OR AVERAGE POWER IF A FORCE THAT IS EXERTED ON AN OBJECT MOVES THE OBJECT AT A CONSTANT VELOCITY, WE CAN CALCULATE THE INSTANTANEOUS POWER OR AVERAGE POWER BY USING: 120

END GR 12 MECHANICS 121