Download - Chapter 06 Work, Energy, Power
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CAMBRIDGE A LEVEL
PHYSICS
WORK, ENERGY,
POWER
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L EA R N I N G O U TC O M E SNO. LEARNING OUTCOME
i Understand the concept of work
ii What is kinetic energy?
iii Look at the relationship between gravitational forces and
gravitational potential energy
iv Apply the principle of conservation of energy
v What is internal energy?
vi What is power?
vii Learn efficiency and concept of useful work
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CONCEPT OF WORK
Definition:
Work is defined as displacement
times force in the direction of the
displacement.
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CONCEPT OF WORK
w h e r e
= m a g n i t u d e o f f o r c e , N . = d i s p l a c e m e n t o f m a s s , m . = a n g l e b e t w e e n f o r c e a n d
d i s p l a c e m e n t v e c t o r s .
,
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CONCEPT OF WORK
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CONCEPT OF WORK
Example 6.4, Chapter 6: WORK AND KINETIC ENERGY, page 178; SEARS AND ZEMANSKYS
UNIVERSITY PHYSICS (WITH MODERN PHYSICS); YOUNG, FREEDMAN, BHATHAL; Pearson ,
Australia 2011.
Work is positive since component of F that is co - linear to
displacement vector and displacement vector are in the
same direction.
Positive work increases the total mechanical energy (kinetic
+ gravitational potential) energy of the mass.
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CONCEPT OF WORK
Example 6.4, Chapter 6: WORK AND KINETIC ENERGY, page 178; SEARS AND ZEMANSKYS
UNIVERSITY PHYSICS (WITH MODERN PHYSICS); YOUNG, FREEDMAN, BHATHAL; Pearson ,
Australia 2011.
Work is negative since component of F that is co - linear to
displacement vector and displacement vector are in the
opposite direction.
Negative work decreases the total mechanical energy
(kinetic + gravitational potential) energy of the mass.
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CONCEPT OF WORK
Example 6.4, Chapter 6: WORK AND KINETIC ENERGY, page 178; SEARS AND ZEMANSKYS
UNIVERSITY PHYSICS (WITH MODERN PHYSICS); YOUNG, FREEDMAN, BHATHAL; Pearson ,
Australia 2011.
No work is done since there is no component of F that is
parallel to displacement vector.
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E X A M P L E S
Answers:
a. 3.60 J; b. 0.90 J; c. 0 J; d. 0 J; e. 2.70 J
Exercise 6.1: Work, page 198, Chapter 6: Work and Kinetic Energy from Sears
and Zemanskys University Physics with Modern Physics, 13th edition, by
Young, Freedman and Ford ; Addison Wesley, 2012, San Francisco.
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C O N C E P T O F W O R K
( A D D E N D U M )
C O N C E P T O F W O R K
( A D D E N D U M )Q: What happens if the work producing the force is not
W dx
Q: What happens if the work producing the force is not constant?
Ans: Use W
dxwhere W workdoneF componentofFinx ' directionx( finalpositionx, initialposition
or in other words,
find the area under the graph of force in direction of displacement versus displacement .
Equation 6.7, Chapter 6: WORK AND KINETIC ENERGY, page 178; SEARS AND
ZEMANSKYS UNIVERSITY PHYSICS (WITH MODERN PHYSICS); YOUNG, FREEDMAN,
BHATHAL; Pearson , Australia 2011.
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KINETIC ENERGYKINETIC ENERGY
Every moving object has this form of mechanical energy
Formula : -. /
0120
where:
3 = mass of object, kg4 = speed of object , m s-1
A scalar quantity
Work must be done on/by object or conversion of energy must
occur if objects kinetic energy is to be changed (either increased
or decreased)
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KINETIC ENERGYKINETIC ENERGY
Derivation:
5 3 6 3 4( ' 7(
2
,
(3 94( ' 7(: =
,
(34( when 7 0 i.e. if object starts from
rest.
Assumptions:
i. F is the resultant external force in direction of s.
ii. All work done on object is positive work.
iii. There is no change in height of object.
iv. Recall 0? from KINEMATICS chapter
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EXAMPLESEXAMPLESOct/Nov 2009 Paper 11, Question 14.
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EXAMPLESEXAMPLESOct/Nov 2009 Paper 11, Question 15.
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EXAMPLESEXAMPLESMay/Jun 2011 Paper 12, Question 19.
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EXAMPLESEXAMPLESOct/Nov 2011 Paper 12, Question 15.
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POTENTIAL ENERGY
POTENTIAL ENERGYPOTENTIAL ENERGY
ELASTIC
POTENTIAL ENERGY
ELASTIC
POTENTIAL ENERGY
GRAVITATIONAL
POTENTIAL ENERGY
GRAVITATIONAL
POTENTIAL ENERGY
ELECTRICAL
POTENTIAL ENERGY
ELECTRICAL
POTENTIAL ENERGY
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A L I T T L E B I T A B O U T
G R AV I TAT I O N A L F I E L D S
A L I T T L E B I T A B O U T
G R AV I TAT I O N A L F I E L D S
GRAVITATIONAL FIELDS
How they occur? Gravitational fields exist around ALL objects that have
mass.
What effect do they
cause?
Gravitational fields exert a gravitational force on ANY
object that has mass. The value of the gravitational
force = 1@
A@2BC@CBD@EFBGEHCGDACI.
How is it
measured?
All gravitational fields have a gravitational field
strength. This value depends on the mass of object and
distance.
Any examples? The gravitational field that exists around the Earth
exerts a gravitational force on ALL objects that have
mass. The Earths gravitational field strength has a
value of 9.81 N kg-1 close to or on its surface.
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G R AV I TAT I O N A L
P O T E N T I A L E N E R G Y
G R AV I TAT I O N A L
P O T E N T I A L E N E R G YGRAVITATIONAL POTENTIAL ENERGY
Stored in an object with mass when the object is in the gravitational
field of another object, e.g when an apple is placed on the ground.
Formula : -J 1AIwhere:
1 = mass of object, kgK = gravitational field strength , N kg-1
L = height above reference level (altitude), m
A scalar quantity
Reference level is chosen arbitrarily. However, the lowest level is
almost always set as reference level to avoid negative values.
The MN of an object at the reference level is 0.
Equation only valid close to surface of
object that provides gravitational field
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G R AV I TAT I O N A L
P O T E N T I A L E N E R G Y
G R AV I TAT I O N A L
P O T E N T I A L E N E R G Y
Derivation:
Recall O P and QK since gravitational force. If we replace R by S we get O QKL.
hdirection of
movement
F = m g
PointstonotePointstonotePointstonotePointstonote: VW of object decreases when
direction of movement is the same
as direction of gravitational force
VWof object increases when direction of movement is opposite to direction
of gravitational force.
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EXAMPLESEXAMPLESMay/Jun 2008 Paper 1, Question 18
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EXAMPLESEXAMPLESOct/Nov 2008 Paper 1, Question 16.
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C O N S E R VAT I O N O F
E N E R G Y
C O N S E R VAT I O N O F
E N E R G Y
Recall: Energy cannot be created nor
destroyed, only transformed.
For closed systems; i.e. where energy cannot
be transferred in or out of system:
If only mechanical energy is considered, then
the equation becomes:
MBDBCB@E MFBD@E
M,BDBCB@E >MN,BDBCB@E M,FBD@E >MN,FBD@EM,BDBCB@E >MN,BDBCB@E M,FBD@E >MN,FBD@E
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EXAMPLESEXAMPLES
Question 3, Set 19: GRAVITATIONAL POTENTIAL ENERGY IN A UNIFORM FIELD, page
45; PROBLEMS IN PHYSICS ; E.D GARDINER, B.L McKITTRICK; McGraw Hill Book
Company, Sydney 1985.
Answers:
a. 200 J, b. C, c. 78.5 J, d. 122 J, e. 14.1 m s-1
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EXAMPLESEXAMPLES
Question 3, Set 19: GRAVITATIONAL POTENTIAL ENERGY IN A UNIFORM FIELD, page
45; PROBLEMS IN PHYSICS ; E.D GARDINER, B.L McKITTRICK; McGraw Hill Book
Company, Sydney 1985.
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C O N S E R VAT I O N O F
E N E R G Y
C O N S E R VAT I O N O F
E N E R G Y
What happens when there is friction?
The frictional force acting on a moving object
does work on that object.
or:
MFBD@E MBDBCB@E ' XHDGYZFBCBD
M,FBD@E > MN,FBD@EM,BDBCB@E >MN,BDBCB@E ' XHDGYZFBCBD
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C O N S E R VAT I O N O F
E N E R G Y
C O N S E R VAT I O N O F
E N E R G Y
What happens when there is:
manual effort, or
animal effort, or
effort due to a machine / engine?
or,
MFBD@E MBDBCB@E > 9XHDGYZGFFC:
M,FBD@E >MN,FBD@EM,BDBCB@E > MN,BDBCB@E> 9XHDGYZGFFC:
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C O N S E R VAT I O N O F
E N E R G Y
C O N S E R VAT I O N O F
E N E R G Y
If we combine both situations, we obtain:
M,FBD@E >MN,FBD@E M >M
> 9XHDGYZGDABDG1@D[@EGFFC:
M,FBD@E >MN,FBD@E M,BDBCB@E >MN,BDBCB@E' XHDGYZFBCBD> 9XHDGYZGDABDG1@D[@EGFFC:
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EXAMPLESEXAMPLESOct/Nov 2010 Paper 12, Question 14.
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EXAMPLESEXAMPLESMay/Jun 2011 Paper 11, Question 15.
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HOMEWORK1. May/June 2008, Paper 1, question 17.1. May/June 2008, Paper 1, question 17.
2. Oct/Nov 2008, Paper 1, question 15.
3. Oct/Nov 2008, Paper 1, question 17.
4. Oct/Nov 2010, Paper 12, question 15.
5. Oct/Nov 2010, Paper 12, question 16.
6. May/June 2011, Paper 11, question 9.
7. May/June 2011, Paper 11, question 14.
8. May/June 2011, Paper 11, question 17.
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HOMEWORK9. May/June 2011, Paper 21, question 2.9. May/June 2011, Paper 21, question 2.
10.Oct/Nov 2011, Paper 11, question 16.
11.Oct/Nov 2011, Paper 11, question 18.
12.Oct/Nov 2011 Paper 12, question 16.
13.Oct/Nov 2011 Paper 22, question 2.
14. May/June 2012, Paper 11, question 16.
15. May/June 2012, Paper 12, question 17.
16.May/June 2012, Paper 21, question 2.
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HOMEWORK17.May/June 2012, Paper 21, question 2.
18.May/June 2012, Paper 22, question 2.
19.Oct/Nov 2012, Paper 11, question 18.
20.Oct/Nov 2012, Paper 11, question 20.
21.Oct/Nov 2012, Paper 13, question 18.
22.Oct/Nov 2012, Paper 11, question 21.
23.Oct/Nov 2012, Paper 23, question 2.
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INTERNAL ENERGY
The internal energy of an object is the
total energy content of ALL its
molecules / atoms.
The internal energy of an object is also
the sum of the kinetic and potential
energies of ALL its molecules / atoms.
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INTERNAL ENERGY
M
We can rewrite our equation for conservation
of energy by including the internal energy
change as:
For example, when a car brakes, the
decrease in M will be equal to increase inheat energy in the cars tyres.
N BDCGD@E N BDCGD@E
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EXAMPLESEXAMPLESMay/Jun 2008 Paper 1, Question 19.
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POWER Definition: Power measures the rate at Definition: Power measures the rate at
which work is done. Work done in a shorter time period produces a
higher power output compared to the sameamount of work done over a longer period oftime.
Power could also refer to the rate at which energy is converted into another form.
Power measures the performance of a machine / equipment / person / animal.
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POWERPOWER
can be measured as:
POWER
INSTANTENOUS POWER
Power at a particular
time instant
AVERAGE POWER
Power output
over a given time
interval, ]
Formula: O
]
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POWER Another way of expressing power is:
*(provided F is time independent / constant )
^ H
HC
H9:
HC
H
HC 2
Instantenouspower, B^DC 2BDC
Averagepower, @^2G 2@2G
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EXAMPLESEXAMPLESMay/June 2010, Paper 11, question 16.
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EXAMPLESEXAMPLESOct/Nov 2010, Paper 11, question 18.
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EFFICIENCYThe efficiency of a device or machine The efficiency of a device or machinemeasures how capable the device is inconverting input energy into useful work.
These three quantities are related mathematically by:
The input energy that is not converted into useful work is wasted energy.
GFFBBGDZ % [GF[EX
BDN[CGDGAZ /ee%
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EFFICIENCY We can also measure efficiency in terms of
power.
GFFBBGDZ % [GF[ENXG
BDN[CNXG /ee%
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HOMEWORK1. Oct/Nov 2008, Paper 1, question 18.1. Oct/Nov 2008, Paper 1, question 18.
2. May/Jun 2009 Paper 1, Question 14.
3. May/June 2010, Paper 11, question 3.
4. May/June 2010, Paper 11, question 15.
5. May/June 2010, Paper 23, question 3.
6. Oct/Nov 2010, Paper 11, question 16.
7. Oct/Nov 2010, Paper 11, question 17.
8. Oct/Nov 2010, Paper 12, question 17.
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HOMEWORK9. May/June 2011, Paper 11, question 16.9. May/June 2011, Paper 11, question 16.
10.May/June 2011, Paper 12, question 18.
11.May/June 2011, Paper 22, question 3.
12.Oct/Nov 2011, Paper 11, question 19.
13.Oct/Nov 2011, Paper 12, question 17.
14.Oct/Nov 2011, Paper 22, question 2.
15.May/June 2012, Paper 11, question 14.
16.May/June 2012, Paper 11, question 17.
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HOMEWORK17.May/June 2012, Paper 11, question 18.17.May/June 2012, Paper 11, question 18.
18.May/June 2012, Paper 11, question 19.
19.May/June 2012, Paper 12, question 18.
20.May/June 2012, Paper 12, question 19.
21.Oct/Nov 2012, Paper 11, question 21.
22.Oct/Nov 2012, Paper 12, question 21.
23.Oct/Nov 2012, Paper 12, question 22.
24.Oct/Nov 2012, Paper 13, question 20.
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HOMEWORK25.Oct/Nov 2012, Paper 23, question 3.