Download mechanics - Wesbury College of Science

WESBURY COLLEGE
OF SCIENCE
2013
• GR 12 PHYSICAL SCIENCES
INTERVENTION FOR SCIENCE
LEARNERS
• SCIENCE DEPARTMENT PROJECT
FOUNDATIONS OF LEARNING
1
2013-09-01
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
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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
CAN CANCEL EACH OTHER OUT
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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 SHOT25
FORCE, MOMENTUM AND IMPULSE
CHANGE IN MOMENTUM
SUMMARY
26
FORCE, MOMENTUM AND IMPULSE
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
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
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 tA= tB
FAtA = -FBtB
FAtA + FBtB = 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
COLLISIONS ARE OFTEN CLASSIFIED ACCORDING TO THE
CHANGE IN TOTAL KINETIC ENERGY
ELASTIC COLLISIONS
TOTAL KINETIC ENERGY OF THE
SYSTEM BEFORE THE COLLISION
EQUAL TO THE TOTAL KINETIC
ENERGY AFTER THE COLLISION
INELASTIC COLLISIONS
IS
TOTAL KINETIC ENERGY OF THE
SYSTEM IS NOT THE SAME BEFORE
AND AFTER THE COLLISION
40
ELASTIC AND INELASTIC COLLISIONS
ELASTIC COLLISIONS
TOTAL KINETIC ENERGY BEFORE A COLLISION =
TOTAL KINETIC ENERGY AFTER A COLLISION
 Ek BEFORE COLLISION = Ek AFTER COLLISION
 ½ mv2 = ½ mv2
41
ELASTIC AND INELASTIC COLLISIONS
ELASTIC COLLISIONS
NEWTON’S CRADLE
TOTAL KINETIC ENERGY BEFORE A COLLISION =
TOTAL KINETIC ENERGY AFTER A COLLISION
42
ELASTIC AND INELASTIC COLLISIONS
ELASTIC COLLISIONS
NEWTON’S CRADLE
43
ELASTIC AND INELASTIC COLLISIONS
ELASTIC 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
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MECHANICS
MOMENTUM VIDEO
47
MECHANICS
WESBURY COLLEGE OF SCIENCE
LEARNERS
MODULE 1
p45-46
p47
p48 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 Dt2
vf2 = vi2 + 2 g Dy
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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
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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 ANOTHER.
THEREFORE, 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
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 CosQ
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
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
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
ENERGY IS REQUIRED TO DO WORK!!!!
THIS FORCE MUST HAVE SOME FORM OF ENERGY
94
ENERGY
95
ENERGY
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
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 mv2
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= ½mvf2 - ½mvi2
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//DxCosq+ FNDxCosq + Fg┴ DxCosq
= mgSin30°DxCos0° + 0 + 0
 Wnet = mgSin30°DxCos0°
111
MECHANICS
WORK DONE ON A OBJECT MOVING UP A FRICTIONLESS
SURFACE
Wnet = WFg// + WFN + WFg┴
= Fg//DxCosq+ FNDxCosq + Fg┴ DxCosq
= mgSin30°DxCos180° + 0 + 0
 Wnet = mgSin30° Dx Cos180°
112
MECHANICS
WORK DONE ON A OBJECT MOVING DOWN
A SURFACE WITH FRICTION
Wnet = WFg// + Wf + WFN + WFg┴
= Fg//DxCosq+ f DxCosq+ FNDxCosq + Fg┴ DxCosq
= mgSin30°DxCos0° + fDxCos180° + 0 + 0
 Wnet = mgSin30°DxCos0° + fDxCos180°
113
MECHANICS
114
MECHANICS
WORK DONE ON A OBJECT MOVING UP
A SURFACE WITH FRICTION
Wnet = WFg// + Wf + WFN + WFg┴
= Fg//DxCosq+ f DxCosq+ FNDxCosq + Fg┴ DxCosq
= mgSin30°DxCos180° + fDxCos180° + 0 + 0
 Wnet = mgSin30°DxCos180° + fDxCos180°
115
WORK AND ENERGY
SUMMARY
………. IF THERE ARE NO FRICTIONAL 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
= ½mvf2 - ½mvi2
……….. IF THERE ARE FRICTIONAL FORCES
USE THE WORK ENERGY PRINCIPLE:
Wnet = ΔK
= Ekf – Eki
= ½mvf2 - ½mvi2
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
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