chapter 06 work, energy, power

CAMBRIDGE A – LEVELPHYSICS

WORK, ENERGY, POWER

L E A R N I N G O U T C O M E SNUMBER LEARNING OUTCOME

i U n d e r s t a n d t h e c o n c e p t o f w o r k

ii W h a t i s k i n e ti c e n e r g y ?

iii L o o k a t t h e r e l a ti o n s h i p b e t w e e n g r a v i t a ti o n a l f o r c e s a n d g r a v i t a ti o n a l p o t e n ti a l e n e r g y

iv A p p l y t h e p r i n c i p l e o f c o n s e r v a ti o n o f e n e r g y

v W h a t i s i n t e r n a l e n e r g y ?

vi L e a r n e ffi c i e n c y a n d c o n c e p t o f u s e f u l w o r k

vii W h a t i s p o w e r ?

CONCEPT OF WORK

D e fi n i ti o n ( f o r a c o n s t a n t f o r c e ) : “ W o r k i s d e fi n e d a s f o r c e ti m e s d i s p l a c e m e n t i n t h e d i r e c ti o n o f t h e f o r c e .”

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 .

𝐖𝐨𝐫𝐤 ,𝐖=𝐅×𝐬𝐜𝐨𝐬𝛉

CONCEPT OF WORK

𝐖𝐨𝐫𝐤 ,𝐖=𝐅×𝐬𝐜𝐨𝐬𝛉

𝜽

𝑭

𝒔

𝑭 𝐜𝐨𝐬𝜽

CONCEPT OF WORK

Example 6.4, Chapter 6: WORK AND KINETIC ENERGY, page 178; SEARS AND ZEMANSKY’S 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


• 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


• 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 Zemansky’s University Physics with Modern Physics, 13th edition, by Young, Freedman and Ford ; Addison Wesley, 2012, San Francisco.

E X A M P L E S

Question 6, Set 18: WORK, KINETIC ENERGY AND POWER, page 42; PROBLEMS IN PHYSICS ; E.D GARDINER, B.L McKITTRICK; McGraw – Hill Book Company, Sydney 1985.

Answers:a. 24 Jb. 12 Jc. 0 J

E X A M P L E S


E X A M P L E S

Question 8 (cont’d), Set 18: WORK, KINETIC ENERGY AND POWER, page 42; PROBLEMS IN PHYSICS ; E.D GARDINER, B.L McKITTRICK; McGraw – Hill Book Company, Sydney 1985.

Answers:a. 400 Jb. 23 Nc. 2 m s-2

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 constant?Ans: Use where

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 ZEMANSKY’S UNIVERSITY PHYSICS (WITH MODERN PHYSICS); YOUNG, FREEDMAN, BHATHAL; Pearson , Australia 2011.

K I N E T I C E N E R GYKINETIC ENERGY

Every moving object has this form of mechanical energy

Formula : where:

= mass of object, kg = speed of object , m s-1

A scalar quantity

Work must be done on/by object or conversion of energy must occur if object’s kinetic energy is to be changed (either increased or decreased)

K I N E T I C E N E R GYKINETIC ENERGY

Derivation:

= when 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 from “KINEMATICS” chapter

Equation states that work done on object if 0

E X A M P L E S

Oct/Nov 2009 Paper 11, Question 14.

E X A M P L E S


E X A M P L E S


8 J

2.0 m s-1

E X A M P L E S


c. 32 J, 4 m s-1 ; d. 12 J

12 J

E X A M P L E S


8.0 N s

E X A M P L E S

May/Jun 2011 Paper 12, Question 19.

E X A M P L E S


H O M E WO R K


Answers:a. 10,000 Jb. 10,000 Jc. 2,000 N

H O M E WO R K

10 J

10 J

18 J28 J


3.74 m s-1

H O M E WO R K


H O M E WO R K


Answers:a. 1.33 m s-2

b. 5.0 Jc. 2.0 m s-1

H O M E WO R K


Answer:a. 0.4 kg m s-1

P OT E N T I A L E N E R GY

POTENTIAL ENERGY

ELASTIC POTENTIAL ENERGY

GRAVITATIONAL POTENTIAL ENERGY

ELECTRICAL POTENTIAL ENERGY

A L I T T L E B I T A B O U T G R A V I TAT I O N A L F I E L D S

GRAVITATIONAL FIELDSHow 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 = .”

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 Earth’s 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

GRAVITATIONAL POTENTIAL ENERGYStored 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 : where:

= mass of object, kg = gravitational field strength , N kg-1 = 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 of an object at the reference level is 0.

Equation only valid close to surface of object that “provides” gravitational field

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 and since gravitational force.• If we replace by we get .

hdirection of movement

F = m g

Points to note:• of object decreases when direction

of movement is the same as direction of gravitational force

• of object increases when direction of movement is opposite to direction of gravitational force.

E X A M P L E S

Question 3, Set 19: GRAVITATIONAL POTENTIAL ENERGY IN A UNIFORM FIELD, page 44; PROBLEMS IN PHYSICS ; E.D GARDINER, B.L McKITTRICK; McGraw – Hill Book Company, Sydney 1985.

Answer:3190 J

E X A M P L E SMay/Jun 2008 Paper 1, Question 18

E X A M P L E S


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:

𝐄𝐢𝐧𝐢𝐭𝐢𝐚𝐥=𝐄𝐟𝐢𝐧𝐚𝐥

E X A M P L E S


Answers:a. 200 J, b. C, c. 78.5 J, d. 122 J, e. 14.1 m s-1

E X A M P L E S



• What happens when there is friction?• The frictional force acting on a moving object

does work on that object.

or:𝐄𝐟𝐢𝐧𝐚𝐥=𝐄𝐢𝐧𝐢𝐭𝐢 𝐚𝐥− (𝐰𝐨𝐫𝐤𝐝𝐨𝐧𝐞𝐛𝐲 𝐟𝐫𝐢𝐜𝐭𝐢𝐨𝐧 )

𝐄𝐤 , 𝐟𝐢𝐧𝐚𝐥+𝐄𝐩 ,𝐟𝐢𝐧𝐚𝐥=𝐄𝐤 , 𝐢𝐧𝐢𝐭𝐢𝐚𝐥+𝐄𝐩 ,𝐢𝐧𝐢𝐭𝐢𝐚𝐥− (𝐰𝐨𝐫𝐤𝐝𝐨𝐧𝐞𝐛𝐲𝐟𝐫𝐢𝐜𝐭𝐢𝐨𝐧 )


• What happens when there is:– manual effort, or– animal effort, or– effort due to a machine / engine?

• or,𝐄𝐟𝐢𝐧𝐚𝐥=𝐄𝐢𝐧𝐢𝐭𝐢 𝐚𝐥+(𝐰𝐨𝐫𝐤𝐝𝐨𝐧𝐞 𝐛𝐲𝐞𝐟𝐟𝐨𝐫𝐭 )

𝐄𝐤 , 𝐟𝐢𝐧𝐚𝐥+𝐄𝐩 ,𝐟𝐢𝐧𝐚𝐥=𝐄𝐤 , 𝐢𝐧𝐢𝐭𝐢𝐚𝐥+𝐄𝐩 ,𝐢𝐧𝐢𝐭𝐢𝐚𝐥+(𝐰𝐨𝐫𝐤𝐝𝐨𝐧𝐞 𝐛𝐲𝐞𝐟𝐟𝐨𝐫𝐭 )


• If we combine both situations, we obtain:

E X A M P L E S


H O M E WO R K

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

H O M E WO R K

8. May/June 2011, Paper 11, question 17.9. 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.

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• 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 will be equal to increase in heat energy in the car’s tyres.

𝟎=∆𝐄𝐤+∆𝐄𝐩+∆𝐄𝐢𝐧𝐭𝐞𝐫𝐧𝐚𝐥

EFFICIENCY• The efficiency of a device or machine

measures how capable the device is in converting 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.

𝐞𝐟𝐟𝐢𝐜𝐢𝐞𝐧𝐜𝐲 (% )= 𝐮𝐬𝐞𝐟𝐮𝐥 𝐰𝐨𝐫𝐤𝐢𝐧𝐩𝐮𝐭 𝐞𝐧𝐞𝐫𝐠𝐲

×𝟏𝟎𝟎%

E X A M P L E S


POWER• 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 same amount of work done over a longer period of time.

• 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.

POWER

can be measured as:

POWER

POWER• Another way of expressing power is:

*(provided F is time independent / constant )

𝐏=𝐝𝐖𝐝𝐭

=𝐝 (𝐅𝐬)𝐝𝐭

=𝐅 𝐝𝐬𝐝𝐭

=𝐅 𝐯

Instantenous power ,𝐏𝐢𝐧𝐬𝐭=𝐅𝐯 𝐢𝐧𝐬𝐭

Average power ,𝐏𝐚𝐯𝐞=𝐅 𝐯𝐚𝐯𝐞

E X A M P L E S


Answers:a. 6.0 × 105 J; b. 1.5 × 104 J ; c. 1.5 × 104 W

E X A M P L E S

Questions 22 and 25, Set 18: WORK, KINETIC ENERGY AND POWER, page 44; PROBLEMS IN PHYSICS ; E.D GARDINER, B.L McKITTRICK; McGraw – Hill Book Company, Sydney 1985.

Answers:22. 7000 W; 25. 1.76 × 105 W

E X A M P L E S

May/June 2010, Paper 11, question 16.

E X A M P L E S

Oct/Nov 2010, Paper 11, question 18.

H O M E WO R K

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.

H O M E WO R K

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.

chapter 06 work, energy, power

Documents

positive work

negative work

levelphysics work

physics e

concept of work definitionfor

internal energy

modern physics young

zemanskys university