chapter 06 work, energy, power

CAMBRIDGE A LEVEL

PHYSICS

WORK, ENERGY,

POWER

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

CONCEPT OF WORK

Definition:

Work is defined as displacement

times force in the direction of the

displacement.

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 .

,

CONCEPT OF WORK

,

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.

CONCEPT OF WORK



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.

CONCEPT OF WORK



Australia 2011.

No work is done since there is no component of F that is

parallel to displacement vector.

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.

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.

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)

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

EXAMPLESEXAMPLESOct/Nov 2009 Paper 11, Question 14.

EXAMPLESEXAMPLESMay/Jun 2011 Paper 12, Question 19.

POTENTIAL ENERGY

POTENTIAL ENERGYPOTENTIAL ENERGY

ELASTIC

POTENTIAL ENERGY

ELASTIC

POTENTIAL ENERGY

GRAVITATIONAL

POTENTIAL ENERGY

GRAVITATIONAL

POTENTIAL ENERGY

ELECTRICAL

POTENTIAL ENERGY

ELECTRICAL

POTENTIAL ENERGY

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.

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


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





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.

EXAMPLESEXAMPLESMay/Jun 2008 Paper 1, Question 18

C O N S E R VAT I O N O F

E N E R G Y


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

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

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.


E N E R G Y


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


E N E R G Y


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:


E N E R G Y


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:

HOMEWORK1. May/June 2008, Paper 1, question 17.1. May/June 2008, Paper 1, question 17.

2. Oct/Nov 2008, Paper 1, question 15.




6. May/June 2011, Paper 11, question 9.




10.Oct/Nov 2011, Paper 11, question 16.


12.Oct/Nov 2011 Paper 12, question 16.

13.Oct/Nov 2011 Paper 22, question 2.



16.May/June 2012, Paper 21, question 2.

HOMEWORK17.May/June 2012, Paper 21, question 2.







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.

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

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.

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

]

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

EXAMPLESEXAMPLESMay/June 2010, Paper 11, question 16.

EXAMPLESEXAMPLESOct/Nov 2010, Paper 11, question 18.

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%

EFFICIENCY We can also measure efficiency in terms of

power.

GFFBBGDZ % [GF[ENXG

BDN[CNXG /ee%

HOMEWORK1. Oct/Nov 2008, Paper 1, question 18.1. Oct/Nov 2008, Paper 1, question 18.

2. May/Jun 2009 Paper 1, Question 14.







HOMEWORK17.May/June 2012, Paper 11, question 18.17.May/June 2012, Paper 11, question 18.








HOMEWORK25.Oct/Nov 2012, Paper 23, question 3.

chapter 06 work, energy, power

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