Ch#4 Work and Energy

8/12/2019 Ch#4 Work and Energy

http://slidepdf.com/reader/full/ch4-work-and-energy 1/16

Unit # 4

Work and energy Abrar Ahmad

(ZAAS Academy 0333-5307019)

Q1 (a) Define WORK and e !"ain #he $%r& d%ne by c%n'#an# f%rce(b) Di'c '' differen# ca'e' %f $%r& d%ne by c%n'#an# f%rce(c) Define S* ni#' %f #he $%r& .

Ans.(a) WORK

Def 1+ Work done by a constant force on a body is defined as the product of magnitudes of displacementand the component of force in the direction of displacement.

Def ,+ Work by a constant force on a body is defined as the dot product of force with displacement.

d )c%'- ( W

-d.%'W

d - W

===

Where the quantity of ( c%'- ) is the component of the force - in the direction of the displacement d

the work is a scalar quantity because it is dot product of force and displacement EXPLANATION

Consider a body initially resting on horizontal surface at position A.Suppose a constant force acts on the body parallel to itsdirection of motion and mo!es it to a new position " suchthat the displacement is d as shown in ig (a). #hen work done

by this constant force for this case is simply equal to the magnitudesof the constant force and displacement that is $

W / d (1)%f& howe!er& the direction of application of force makes anangle with that of the displacement d & as shown in ig(b)&then in eq(') the magnitude of the force is replaced by itshorizontal component / c%' along displacement d& as$

d )c%'- ( W

d - W

=→

b) DIFFERENT CASES OF WORK DONE BY CONSTANT FORCE

CASE I POSITIVE WORK (OR MAXIMUM WORK%f force and displacement are in the same direction then positi!e work and ma imum work is done. %n thiscase theta is /02 & so that $

W / d c%'02 W/ d (a' c%'02 / 1)

EXAMPLES:') When railway engine pulls a train then work done is positi!e.) When horse pulls a #onga along the roadside then work done is positi!e.*) When an electric field mo!es a positi!ely charged particle like +,-#- then work done is positi!e.

CASE II ZERO WORK%f force and displacement are at right angle to each other& then zero work is done. %n this case so that$

W / d cos01W/ 2 (as cos 321/2)

EXAMPLE:

'





nnn

nn

.%'d -

d - =

=n

n

W

W

#he total work done from point a to point b along the cur!ilinear path in y4plane is equal to sum of worksdone along all n displacement inter!als i.e

W #%#a" / W 1 W , W i ------ W n

+utting !alues of W ' &W&.........Wi&4444444& Wn in abo!e equation& we get$

nnn .%'d - .%'d - .%'d - .%'d - ----W 3133222111total

∑=

n

i i i i )( .%'d -

1total 1W

;q (') gi!es the work done by !ariable force.

Q3 (a) Define #he :ra6i#a#i%na" fie"d %f #he ear#h .(b) Define #he c%n'er6a#i6e fie"d and !r%6e #ha# #he :ra6i#a#i%na" fie"d %f #he ear#h i' c%n'er6a#i6e fie"d

Ans. GRAVITATIONAL FIELD OF T,E EART, Def+ “ #he space or region around the earth within which a body can e perience the gra!itational pull ofthe earth is called its gra!itational field. ”NOTE:

'4 #heoretically& the gra!itational field of the earth e tended up to infinity.4 :ike earth all other hea!enly bodies (planets and stars) do ha!e their gra!itational fields.

(-. CONSERVATIVE FIELDDe ! A field is said to be conser!ati!e if$<W%r& d%ne i' inde!enden# % f #he !a#h f%""%$ed %r $%r& d%ne a"%n: a c"%'ed !a#h i' ;er% .<

EXAMPLES$ #he following fields are conser!ati!e fields.

'. 7ra!itational field.. ;lectric field.

"#T$! The magnetic field is not conservative field (why?)

T,E GRAVITAYIONAL FIELD OF T,E EART, IS CONSERVATIVE FIELD#he gra!itational field of the earth is conser!ati!e field. %t can be pro!ed as follows$

CASE (!. WORK DONE IS INDEPENDENT OF T,E PAT, FOLLOWEDConsider two points A and " in the gra!itational field of earth.A body of mass m can mo!e from point A to " through se!eral

paths only three of which are shown in the figure(a) where$• +ath (%) is A to 8 to ".• +ath (%%) is A to C to ".• +ath (%%%) is cur!ed path.

ow work done along these three paths is to be calculatedseparately. When body mo!es along any of these three pathsat constant speed& then magnitude of the e ternal force on itwill be equal to its weight that is$ / WWORK DONE ALONG PAT, I: #he path % consists of two parts as A8 and 8". =ence the total work done along path % is$

W AD< / W AD W D< ------------(1)

=%$ W A>D / d / d c%' / (m:) (AD) c%'90/ 0 ( c%' 90 /0)

And W D>. / d

*



/ d c%' /(m:) (D<) c%'1 0/ m:h (-1) ( c%'1 0 / -1)/ - m:h

With these !alues of W A>C and W ">C & the eq(') becomes$W AD< / 0 ? m:hW AD< / - m:h 444444444444444444444444( )

WORK DONE ALONG PAT, II:+ath %% consists of two parts as AC and C". =ence& the total work done along path %% is gi!en by$

W A.< / W A>. W .>< -------------(3) =%$ W A>. / d

/ d c%' W A>. / (m:) (A.) c%'1 0

/ m:h(-1) ( c%'1 0 / -1)/ -m:h

And W .>< / d / d c%'

/ (m:) (.<) c%'90 ( c%'90 / 0)/ 0

With these !alues the eq (*) gi!es$W A.< / - m:h ------------------------(@)

WORK DONE ALONG PAT, III: #o calculate the work done along cur!ed path %%%& di!ide it into horizontal and !ertical elements as shownin the ig b. %t can be pro!ed that the work done along the horizontal elements is zero because for each ofthem 0/ 32 and cos32 / 2. =owe!er& the work done along !ertical elements is not zero. :et y 1 8 y , 8y 3 8 8 y n are lengths of the !ertical elements 18,838 8n. #hus& the total work done along path %%% is$

W A< / y 1 y , y n

W A< / y 1 c%' 1 y , c%' , y n c%' n

or each of !ertical component& the angle between and ?y i is 0 i / '@2& that is $ 1 / , / 3/ -------/ i /-----/ n/ 1 02 W A< / y 1c%'1 02 y , c%'1 0 y n c%'1 0 / - y - y , - y 3 - y n

W A< / - ( y 1 y , y n )=ere /m: & the weight of body and y 1 y , y n / h

W A< /-m:h ----------------------- (5)#he comparison of eqs & and B gi!es$

W A.< / W AD< / W A< -------------- ( )

CONCLUSION: #he eq shows that the work done in gra!itational field of the earth is independent ofthe path followed by the body. =ence& the gra!itational field of earth is conser!ati!e field.

CASE (-. WORK DONE ALONG CLOSED PAT, IS ZERO:Consider a closed path A"CA in the gra!itational field of the earth. Suppose a body of mass m is mo!edalong this closed path A"CA at constant speed. #hen force required for mo!ing body all along this path isequal to its weight mg i.e.

/ W / m: As shown in the ig that$ A< / d 1B <. / d , B .A / d 3

ow the total work done along the closed path A"CA is$

W A<.DA / W A>< W <>. W .>A ---------(1)

=%$ W A>< / A<



/ W d 1 (a' A< /d 1 )W A>< / Wd 1 c%'

/ Wd 1 c%'0 0 beca 'e W and d 1 are a"%n: #he 'ame direc#i%n/ Wd 1 ( c%'0 0 / 1)

Simi"ar"yW <>. / <.

/ W d , (a' <./d , )/ Wd , c%' / Wd , c%'90 0 beca 'e W and d 1 are !er!endic "ar #% each %#her / 0 ( c%'90 0 / 0)

A"'% W .>A / .A/ W d 3 (.A/d 3 )/ Wd 3 c%' / W(-d 1 ) ( d 3c%' / -d 1 )/ -Wd 1

Wi#h #he'e 6a" e' %f W A>< 8 W <>. and W .>A 8 #he eC (1) :i6e'+

W A<.DA / W A>< W <>. W .>AW A<.DA / Wd 1 0 - Wd 1

W A<.DA / 0

CONCLUSION: #he work done along a closed path in the gra!itational field of the earth is zero. =ence&the gra!itational field of the earth is conser!ati!e field.

Q@ (a) Define #he f%""%$in: (i) %$er (ii) A6era:e !%$er (iii) *n'#an#ane% ' !%$er(b) ind #he re"a#i%n be#$een !%$er and 6e"%ci#y(c) Wha# i' .%mmercia" ni# %f !%$er

Ans. ( . POWERDe%: +ower is defined as the time rate of doing work.NATURE: +ower is a scalar quantity.SYMBOL$ +ower is denoted by .FORMULA$ %fW work is done in time inter!al # then power is gi!en by$

#

W D

=

SI UNITS $ #he S% units of power are watt denoted by W.

#

W D

=

1W = 1%&1secDEF OF /W: %f '5 work is done in one sec then power generated is said to be 'W

'mW / '2 4*W'DW / '2E W'FW / '2 W'7W / '2GH W

( . AVERAGE POWER:De%: %t is defined as the ratio of total work done and total time.SYMBOL: #he a!erage power is denoted by a6.

FORMULA: %f ?Wtotal is the total work done in total time total then a!erage power is gi!en by$

#%#a"

#%#a" a6 #

W D

=

( . INSTANTENEOUS POWER

B



De%: %t is defined as the power at particular instant.SYMBOL: %t is denoted by in' .FORMULA: #he instantaneous power is equal limiting !alue of the ratio WIt when t approaches to zero i.e

(-. RELATION BETWEEN POWER AND VELOCITY%f Work W is done in time t then power is gi!en by$

#

W D =

%f is force and d is displacement then work W / .d so that$

-E D

# d

- D

# d -

D

=

=

=

=ence& the power is equal to dot product of force and !elocity. Since& power is the dot product of force and!elocityJ therefore& it is a scalar quantity.

(0. COMMERCIAL UNIT OF POWER:#he commercial unit of power is Dilowatt =our (DWh). %t is defined as$‘If power is supplied or consumed at the rate of 1KW per hour then power is said to 1KWh. %n other words it means that if sum of all power consumed (or supplied) is equal to '222 W and total timeelapsed in consuming (or supplying) this power becomes * 22sec& then it is called 'DWh and also calledthat one unit is consumed.

' DWh / 'DW K 'h / '222W K * 22s / *. K '2 W4sec

/ *. K '2 5 -#;.

'5/ .L@ K '2 4L DWh

Q5 a) Define ener:y and n mera#e i#' 6ari% ' #y!e' (f%rm') b) Define+ (1) Kine#ic ener:y and deri6e i#' f%rm "a

(,) %#en#ia" ener:y and deri6e i#' f%rm "aAns. A. ENERGY:

!The capa"ility of doing wor# is called energy.$

;nergy and matter are inter con!ertible by equation ;/mc;nergy has !arious forms for e ample$Fechanical energy ;lectric energySolar energy 7eothermal energyWind energy Sound energy=eat energy uclear energyChemical energy #idal energy

-. KINETIC ENERGY F It is defined as the energy possessed "y a "ody due to its motion$ OR

F The a"ility of a "ody to do wor# due to its motion is called its #inetic energy.$

SYMBOL: #he Dinetic energy is abbre!iated as D.;.

FORMULA: %f m is mass of a body mo!ing at linear speed ! then its translational D.; is gi!en by$



D.;/ )

)

'm%

DERIVATION OF FORMULAConsider a body of mass m and initially at rest. Suppose a constant force of magnitude acts on it up todistance d& where its final !elocity has magnitude M.

E i / 0 B E f / E B Acce"era#i%n / a B S / d B %rce /

ow the motion of body is go!erned by the third equation of motion gi!en as$,aS / E f , -E i ,

+utting !alues& we ha!e$ ,ad /E , - 0 ,ad / E , (1)

According to ewtonNs nd law of motion$ a / GmWith this !alue of a& the eq. ' becomes$

,( Gm)d/E ,

d/ )

)

'm%

%t is the work W / d done by force on the body that appears as its D.; so that$

d / K H K H /

)

)

'm%

%f M is !elocity of the body then E , / E E so that&

K H /→→

).('

% % m

rom abo!e equation notes that the D.;& being self dot product& is a scalar quantity.

1. POTENTIAL ENERGYF It is defined as the energy possessed "y a "ody due to its position in gravitational field of the earth$.

OR!The a"ility of a "ody to do wor# due to its position in gravitational field of the earth is called gravitational potential energy.$

SYMBOL: #he potential energy is abbre!iated as +.;.FORMULA: %f m is mass of body laying at height h from the surface of earth then its gra!itational

potential energy is gi!en by$ H / m:h

DERIVATION OF FORMULA

Consider a body of mass m and initially placed on the surface of earth. Suppose it is raised !erticallyupward at constant speed to height h from the surface of the earth. ow the work done on the body in raising it at constant speed from the surface of the earth is gi!en by$

W/ d (1)#he force required by the body to go up to height h is equal to its weight i.e.

/ m: B d / hWith these !alues eq.' becomes$ W / m:h%t is this work W that is done in raising the body from surface of the earth up to height h at constant speedis stored in it as its gra!itational +.; i.e. W / H so that$

H / m:h ote that the gra!itational +.; of the body depends on three forces as$

"#T$ $1. +.; is always measured with respect to some reference le!el. %t may be the surface of the earth or a

point at infinity (i.e a far of point at which !alues of g almost reduces to zero).

L



2. %n the formula of potential energy i.e +.;/mgh& the h is always the !ertical height from referencele!el (usually the surface of the earth).

'. ;lastic potential energy of stretched or compressed spring is. H / 1G,& ,

. ;lectric potential energy of a system of two point changes is& H/KC1 C1Gr ,

Q Define #he ab'%" #e :ra6i#a#i%na" H and deri6ed i#' e !re''i%n . Ans. ABSOLUTE GRAVITATIONAL POTENTIAL

F The a"solute gravitational potential energy is defined as the wor# done in moving a "ody against the gravitational field of the earth at constant speed up to point of infinity.$

SYMBOL: #he absolute gra!itational potential energy is denoted by I : FORMULA! %f m is mass of the body and , is radius of the earth then

R

Jm I : Where F is mass of the earth.

DERIVATION OF MAT,EMATICAL EXPRESSIONConsider a body of mass m that is mo!ed !ertically upward at constant speed& from point ' to point inthe gra!itational field of the earth. As the !alue of gra!itational acceleration g !aries in!ersely with thesquare from the surface of the earth& therefore& it does not remain constant along the lengthy path from

point ' to point . #o o!er come this difficulty& di!ide the whole lengthy path from point ' to point intosmall inter!als of displacement such as1 #% ,B , #% 3B 3 #% @B (=-3) #% (=-,)B (=-,) #% (=-1)B ((=-1) #% = such that the !alue of g remainsconstant for each of them"y definition& the absolute gra!itational +.; is gi!en by$

* = W total -------- (1) =(+, ace /)

When body is mo!ed at constant speed from point ' to point & then total work done on it is gi!en by$W #%#a"/W 1>, W ,>3 W 3>@ W (=-3>=-,) W (=-,>=-1) W (=-1>=) ------- (,)

W #%#a"/W (1 > =)

CALCULATION OF W/ > 1 ::et the r ' and r are distances of point ' and point from the center of the earth. #hen magnitude of thedisplacement from point ' to point is gi!en by$

r / r , ?r 1 ------- (3)r , / r 1 r --------(@)

%f is the force required to mo!e the body at constant speed from point ' to point & then work done on itis gi!en by

W 1>, / r

W 1>, / r c%' %n this case 0 / '@2& so that$W 1>, / r.%'1 0

W 1>, / r(-1) W 1>, / - r

%f F is the mass of the earth then ewtonNs law of gra!itation& we ha!e

2r

Jm - =

So that )(221 r

r Jm W

∆

Where r is a!erage distance of mid point of the displacementinter!al ' to such that$

2

21 r r r

=

+utting !alue of 2 from eq & we get$

@



2

22

2

1

1

11

r r r

r r r

r r r r

∆

∆=

∆=

Square both sides to get &

r r

r r r

r r r

∆

∆

1

'2

12

2

12

'

2

Since ?r OO r & therefore& 0'

'

≈r so that

212

12112

11

2

12

12

)(

)(

r r r

r r r r r

r r r r

r r r r

= ∆

∆

+utting !alue of ?r from eq B we get&

∆

→

→

→

21

21

21

1221

221

11

)(

r r

JmW

r r r r Jm

W

r r Jm

W

Similarly preceding it can be pro!ed that$

→

→

→

= = = =

= = = =

= = = =

r r JmW

r r JmW

r r JmW

r r JmW

r r JmW

11

11

11

11

11

)1()1(

)1()2()1()2(

)2()3()2()3(

'3'3

3232

+utting !alues W 1>, 8W ,>3 8W 3>@ 8 W (=-3>=-,) 8W (=-,>=-1) 8W (=-1>=) &in eq. we get$

3



= #%#a"

= #%#a"

= = = = = = #%#a"

W W

r r mJ W

r r r r r r r r r r r r mJ W

→

=

1

1

)1()1()2()2()3('33221

)(11

111111111111

+, ose t at $') +oint ' goes to the surface of the earth then r 1 / R

) point goes to the point at infinity& then r = >L With these assumptions& the eq gi!es$

)(

)4(

11

∞

∞

' rface#%#a"

#%#a"

#%#a"

W W R

mJ W

RmJ W

Psing eq.L in eq' we get$

)5( R

Jm I :

;q.@gi!es the absolute gra!itational +.; of the body placed on the surface of the earth. #he minus sign ineq.@ indicates that is the body4earth system is closed system that is the body is bound to stay with the earth.

Q7 S#a#e #he $%r& ener:y !rinci!"e f%r K H and !r%6e i#M

Ans. WORK ENERGY PRINCIPLE

STATEMENT: %t states that work done on the body is equal to the change in its kinetic energy.

MAT,EMATICAL FORM: %fNW is work done on a body and K H is corresponding change in its D.;then work energy principle can be e pressed as$

W/ K H PROOF: Consider a body of mass m initially mo!ing with !elocity of magnitude E i Suppose a constantforce of magnitude Q acts on the body to accelerate it along the original direction of motion o!er distanceQd where the final !elocity of the body has magnitude E f .%fNa is the magnitude of the positi!e acceleration of the body then

222 i f E E a' =owe!er& here S / d & so that$

222 i f E E ad (1)According to ewtonNs nd law of motion& we ha!e$

a / Gm+utting this !alue of a in eq.' we get&

,( Gm)d/E f , -E i ,

)(2

1 22Ei E m-d f

22

2

1

2

1i f mE mE -d

=owe!er$ d / ( %rce)(di'#ance) /W%r &/ W & so that22

2

1

2

1i f mE mE W

=owe!er& i i f f H K mE H K mE .2

1and.

2

1 22 = so that$

'2



H K W

H K H K W i f

.

..

∆

#his is mathematical form of the work energy principle for K H

NOTE Phe $%r& ener:y !rinci!"e h%"d' e6en f%r !%#en#ia" ener:y e : .') or gra!itational +.;$ W/?mgh

) or elastic +.;$ ∆ 2

21

K W Where D is spring constant.

*) or eclectic +.;$ W / q?M Where ?M is potential difference through the point charge q accelerates.

Q Define #he e'ca!e 6e"%ci#y %f a b%dy fr%m #he ear#h and %b#ain i#' e !re''i%n .a"c "a#e #he e'ca!e'!eed %f #he b%dy fr%m #he ear#h .

Ans. ESCAPE VELOCITY! The initial velocity of an o"&ect with which it goes out of the earth s gravitational field is #nown as

escape velocity$

SYMBOL: #he escape speed of a body is denoted by E e'! .EXPRESSION: %f , is the radius of the earth then escape speed of the body is gi!en by.

:RE e'c 2

DERIVATION OF MAT,EMATICAL EXPRESSIONConsider a body of mass m that is initially lying on the surface of the earth of radius ,. When body is

pro6ected !ertically upward& it rises to some height and then falls to earth because of insufficient D.; tocross the gra!itational field of the earth. %f the !elocity of its pro6ection is increased& the height to which itraises also increases but it again falls to the earth due to the same reason. %f the !elocity of pro6ection isincreased continuously& there occurs the minimum !alue of the speed of pro6ection for which the body getsD.; enough to cross the gra!itational field of the earth. #his minimum !alue of the !elocity of pro6ectionfor which the body gets D.; sufficient to cross the gra!itational field of the earth is called escape !elocity.

or the escape of body& its D.; on the surface of the earth must be equal to the numerical absolutegra!itational +.;.

R

mJ mE

I H K

e'!

: e'!

=

=

2

2

1

).(

=ere F is the mass of the earth.

)1(2

R

J E e'! =

#he gra!itational pull of the earth on the body is gi!en by ewtonNs law of gra!itation as$

2 R

Jm - =

"y definition the force equals the weight m: - = of the body& therefore$

2

2

R

J :

R

Jm m:

=

=

Fultiply both sides by F to get$

''



)2( R

J :R =

Psing eq in eq' we get$)3(2 :RE e'c =

;q* gi!es the escape !elocity of the body lying on the surface of the earth. ote that the escape !elocity ofthe body is independent of the mass of the body as well as that of the earth .%t means that the escape

!elocity for a molecule and a hea!y space !ehicle is the same.

CALCULATION: or the earth g / 3.@mIs and , / . K'2 m.+utting the !alues in equation in eq * we get

sec& 2.11

10'.5.62

&mE

E

e'!

e'!

×

#he escape !elocity for some other planets are gi!en below$

,EAVENLY BODY ESCAPE SPEED (K23$.Foon .Fercury .*

Fars B eptune B.

Q9 r%6e #he "a$ %f c%n'er6a#i%n %f ener:y f%r b%dy fa""in: #% ear#h nder #he inf" ence :ra6i#y in #he+(a) Ab'ence %f air (b) re'ence %f air

Ans. INTER CONVERSION OF P4E AND K4E

#he fact that +.; can be transformed into D.; and !ice !ersa is known as the inter con!ersion of +.; andD.;. #he inter con!ersion of +.; and D.; takes place according to the law of conser!ation of energy thatreads that the energy can neither be created or destroyed but can be transformed from one form toanother form such that the total energy remains constant.Consider a body of mass m and placed in gra!itational field at height h from the surface of the earth.%nitially the body rests at position A. When body is allowed to the earth under the action of gra!ity then its$1) +.; goes on the decreases due to decrease in height from the surface of the earth.2) D.; goes on increasing due to increase in its speed as it approaches to the ground.

ollowing two cases can be discussedC!$e ! FALL IN T,E ABSENCE OF AIR (FREE FALL.Suppose the body in falling to the earth in the absence of air then$

AT POSITION A#he gra!itational potential energy of the body at position A is gi!en by$

m:h H D =.

At position QA7 the body is at rest so E A/ 0 and hence the K H of the body at position 8A7 is also zero$

0.2

1. 2

=

=

H K

mE H K A

#hus& the total potential energy at position 8A7 is gi!en by$

)1(..

m:h H H K H D H

a

A

=

AT POSITION B

'



:et be the distance co!ered by the body on reaching position 897. #hen remaining height of the body at position 897 from the surface of earth is (h - )

2

2

1.

)(.

<mE H K

hm: H D

=

DETERMINATION OF V 1 At B

As the body starts its down word motion from rest at position 8A7& therefore&E i / 0 B S / B a / : B E f / E <

#he motion of the body is go!erned by the third equation of motion as$

m: H K

: m H K

'% : E

E :

E E aS

<

<

i f

×

.

22

1.

2

02

2

2

2

22

#hus total energy at point " is gi!en by$

)2(

)(..

m:h H

m: hm: H H K H D H

<

<

<

=

AT POSITION C#he position C is !ery closer to the ground. =ence& the height of the body at position C w.r.t the surface ofthe earth is almost zero& therefore&

0. = H D

=owe!er& on reaching position C the body has ma !elocity to2

. E therefore D.; at position C is2

2

1. AmE H K =

DETERMINATION OF2

. E As body starts its downward motion from the rest at position A& therefore

E i / 0 B S / h B a / : B E f / E .

#he motion of body is go!erned by the third equation by the third equation of motion is

'% :hE

E :

E E aS

<

.

i f

2

02

2

2

2

22

m:h H K

:hm H K

×

.

2

2

1.

#hus total energy at point 8:7 is gi!en by$

)3(

..

m:h H

H K H D H

.

.

=

#he comparison of eqs'& R* shows that$ )'(. < A H H H =

CONCLUSION: #he downward motion of body takes place according to the law of conser!ation ofenergy such that the total amount of the energy at each point remains constant.

LOSS OF POTENTIAL ENERGY AND GAIN KINENTIC ENERGY( . FOR POSITIONS A AND B-n reaching portion "& the body looses its +.; and gains D.;

'*



Loss ;n <.$ at 9 = <.$ at A - <.$ at 9 / m:h ? m:(h- ) / mh -------------(5)

a;n ;n >.$ at 9 = >.$ at 9 ? >.$ at A / m:h - 0

/ m:h ----------- ( )#he comparison of eqsB and gi!es that$

LOSS IN P4E AT POINT B 5 GAIN IN K4E AT POINT B

( . FOR POSITIONS B AND C-n reaching portion C& the body looses almost all its H and gains ma K H

Loss ;n <.$ at : = <.$ at 9 - <.$ at : / m:(h- ) ? 0 / m:h ? m: ----------(7)

a;n ;n >.$ at : = >.$ at : ? >.$ at 9

/ m:h ? m: ----------( ) #he comparison of eqsL and @ gi!es that$

LOSS IN P4E AT POINT C 5 GAIN IN K4E AT POINT C

CONCLUSIONAbo!e discussion indicates that in the absence of air the motion of body under the action of gra!ity takes

place in such a way that at each point of the path$

L#++ @" <.$ = A@" @" >.$

CASE B: FALL IN T,E PRESENCE OF AIR

When body falls to the earth in the presence of air then its motion is opposed by air resisti!e force. =encea part of its total energy at its initial position is wasted in o!ercoming the air friction is N f then the totalwork done by force of gra!ity against air friction in the body pulling from initial position to the final

position$

#hen remaining +.; is gi!en by$,emaining +.; / +.; at point A Work done against frictional force

/ m:h ? f h#his remaining +.; is con!erted into D.;& hence

,emaining +.; / D.;

fhmE m:h

mE fhm:h

=

2

2

21

21

%n words the abo!e equation can be written as$LOSS IN P4E 5GAIN IN K4E 6WORK DONE AGAINST AIR FRICTION

Q10 S#a#e and e !"ain #he "a$ %f c%n6er'a#i%n %f ener:y (:enera" di'c ''i%n) Ans.

LAW OF CONVERSATION OF ENERGY

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STATEMENT: #his law states that the energy can neither created nor destroyed but it can be transformedfrom one form to another such that total energy remains constant.

EXPLANATION#he law of con!ersation of energy in one of the greatest facts& e!er unfolded by Science. #he creation anddestruction of energy is impossible& only transformation is possible. or e ample& when a body freely& the

gra!itational +.; con!erts into D.; such that at each and e!ery point of path$

L#++ @" <.$ = A@" @" >.$

T#TAL $"$ B = :#"+TA"T

When this body strikes the surface of earth its D.; changes to other forms of energy such as heat andsound Fechanical energy is sum of +.; and D.;. %t can be pro!ed that the sum of +.; and D.; of a bodyalways remains constant equal to mechanical energy pro!ided no transformation takes place into otherforms of energy.When transformation of energy from one form to other takes place& some energy con!ector is always

in!ol!ed e.g. to con!ert gra!itation +.; stored in water dams into electrical energy& an electric generator isneeded. +ractically during transformation of energy into is wasted in the form of heart or sound or both.#he wasted energy causes a rise in temperature of atmosphere.

Q10 Wri#e a n%#e n%n-c%n6en#i%na" '% rce' %f ener:y .

Ans. NON*CONVENTIONAL SOURCES OF ENERGY

#he non4con!entional sources of energy are un4common sources of energy. =owe!er& these sources aree pected to contribute a lot to meet the increasing demands of energy all o!er the world.

1) ENERGY FROM TIDES : #he gra!itational upward pull of the moon on the sea water gi!es rise to tidesin the sea. At the time of high tide& the water is trapped in a high dam. :ater on& at the time of low tide& thiswater stored in dam is released through spill ways to run the turbine of electric generator for production. Atthe time of ne t high tide& again sea water is stored in high dam and then released through the spill waysfor the production of electricity.

2) ENERGY FROM WAVES: #he tidal mo!ement and winds blowing near sea produce ocean wa!es.;nergy of these wa!es can be utilized to produce electricity. -ne such de!ice is known as SalterNs duck(after the name of +rofessor Salter). %t consists of two parts as under$

D,cC Float 9alance Float

#he energy of water wa!es produces relati!e motion between the duck float and balance float. #he relati!emotion of duck and float is then used to run the electric generators.

3) ENERGY : #he earth recei!es huge amount of energy directly from the sun each day. Solar energy outsidethe earthNs atmosphere is about '. DWIm which is referred to as solar constant. While passing throughthe atmosphere& the total energy is reduced due to reflection& scattering and absorption by dust particles andother gases. -n clear day at noon& the intensity of the solar energy reaching the earth surface is ' DwIm .

#his energy can be used directly to heat water by using reflectors or thermal absorbers or be con!erted intoelectricity. %n one method flat plate collectors are used for heating water. A typical collector is shown inthe ig. %t has a black surface that absorbs energy directly from the solar radiation. Cold water passes o!erthe hot black and is heated to L2 degree centigrade. Fuch higher temperature can be achie!ed by

concentrating solar radiation on to small surface area by using huge reflectors (mirrors) or lenses to produce steam for running turbine.#he other method is the direct con!ersion of sun light into electricity through use of semi conductor de!icecalled solar cells also known as photo !oltaic cell. Solar cells are thin wafers made from silicon. ;lectronsin the silicone gain energy from sunlight to create a !oltage. #he !oltage produced by a single !oltaic cell

'B



is !ery low. %n order to get sufficient high !oltage for practical use& a large number of such cells allconnected in series forming solar panel. or cloudy days or nights electric energy can be stored during thesun light in ickel Cadmium batteries by connecting them to solar panels. #hese batteries can then pro!ide

power to electrical appliances at night or on cloudy days. Solar cells although& are e pensi!e but last a longtime and ha!e low running cost. Solar cells are used to power satellite ha!ing large solar panels which arekept facing the sun. -ther e amples of the use of solar cells are remote ground4based weather stations andrain forest communication systems. Soar calculators are also in use now a days.

') ENERGY FROM BIOMASS:"iomass is potential source of renewable energy. #his include all organicmaterials including crop residue& natural !egetation& trees& animal dung and sewage. "iomass energy isrefers to the use of biomass as fuel or its con!ersion into fuels.#here are many methods used for the con!ersion of biomass into fuels such as$

DIRECT COMBUSTION: %t is the method applied to get energy from the waste products knownas solid waste.

FERMENTATION: %t is the process of producing decomposition of biomass by enzymes and bacterial action in the absence of air (o ygen).#he rotting of biomass in closed tank called digester produces "iogas which can be piped out to usefor cooking and heating. #he waste material of biomass is good fertilizer. #hus& production of

biogas pro!ides the energy source and also sol!es the problem of organic waste disposal.) ENERGY FROM WASTE PRODUCTS: Waste products like wood waste& crop residue and particularly

municipal solid waste can be used to get energy by direct con!ersion. %t is most commonly used con!ersion process in which waste is directly burnt in a confined container. #he heat thus produced can be used to boilwater to steam that can run electric generator.

) GEOT,ERMAL ENERGY: #he interior of the earth is !ery hot. Psing P4shaped pipe cool water can be boiled to steam which runs the electric generator. #he geothermal energy within the earth is beinggenerated by three processes& as e plained under$

RADIOACTIVE DECAY: #he energy that heats up rocks is being constantly generated by theradioacti!e decay of radioacti!e elements present in the interior of the earth.

RESIDUAL ,EAT OF T,E EART,: At some places the igneous rocks at depth of '2 Dmfrom the ;arthNs surface in molten or semi molten state& they con!ert the energy from the earthNsinterior which is still !ery hot. #he temperature of the rock is about 22 oC or more.

COMPRESSION OF MATERIAL: #he compression of the material deep beneath the surface ofthe earth produces heat energy. #he heat boil the water to steam at high pressure. #his team can beused to run electric generator.

TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTby

Abrar Ahmad

(ZAAS Academy 0333-5307019)

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Ch#4 Work and Energy

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