chapter 7 torque, equillibrium, angular momentum

8/19/2019 Chapter 7 Torque, Equillibrium, Angular Momentum

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CHAPTER 7

WORK, POWER & ENERGYContents:1. WORK AND UNITS.

2. GRAVITATIONAL FIELD IS CALLED COSERVATIVE FIELD.

3. POWER AND UNITS.

4. ENERGY AND KINDS OF ENERGY

5. KINETIC ENERGY.

6. POTENTAL ENERGY.

7. ABSOLUTEVPOTENTIAL ENERGY.

8. INTERCINVERSION OF ENERGY

9. LAW OF CONSERVATION OF ENERGY

10. EQUATIONS

11. DIMENSIONS

12. SHORT QUESTIONS AND ANSWERS.

DESCRIPTIVE PART

1: Work:

The work o!e "# $! o"%e&' w('h $ &o!)'$!' *or&e () 'he o' +ro,&' o* 'he *or&e F

$! 'he ()+-$&ee!' .

Work / F.

Ex!"n"t#on:

S,++o)e $! o"%e&' ,!er0oe) $ ()+-$&ee!' $-o!0 $ )'r$(0h' -(!e wh(-e $&'e o! "# $ &o!)'$!' *or&e F 'h$'

$ke) $! $!0-e 12 (') $0!(',e 0(3e! "#4 Work / F Co) θTh() )how) 'h$' work () $ )&$-$r 5,$!'('#. The ,!(' o* work () 67o,-e8 (! S.I. or (! M.K.S. $! 6er08 (! C.G.S. )#)'e4

h$3e (e!)(o!9 :9M L T .

Se$#"! $"ses:

C"se %1

Whe!4 θ / ;<4 For&e $! ()+-$&ee!' $re (! 'he )$e (re&'(o!.

The!4 Work / F Co) ;<

Work / F =>?

Work / F Th() )how) 'h$'4 work () +o)('(3e.

C"se%

Whe!4 θ / @;<4 For&e $! ()+-$&ee!' $re +er+e!(&,-$r 'o o!e $!o'her.

The!4 Work / F Co) @;<

Work / F =;?

Work / ;Th() )how) 'h$'4 !o work () 'o "e o!e.

C"se%'

Whe!4 θ />;<4 For&e $! ()+-$&ee!' $re (! o++o)('e (re&'(o!.

The!4 Work / F Co) >;< Work / F =:>?

Work / : F

Th() )how 'h$'4 work () !e0$'(3e.

(o)!e:

A &o!)'$!' *or&e o* o!e New'o! $&') +$r$--e- 'o $ ()+-$&ee!' o* o!e e'er2 'he work () &$--e 6O!e 7o,-e8.Work / F

> 7o,-e / >N.>

Er*:

A &o!)'$!' *or&e o* o!e #!e $&') +$r$--e- 'o $ ()+-$&ee!' o* o!e &e!'(e'er2 'he work () &$--e 6O!e Er08.Work / F

> Er0 / >#!e .>&Con+ers#on et-een .o)!e "n/ Er*:

We k!ow 'h$'4 Work / F

Work / >N.>

Prof: Najeeb Mughal, Composed by Tarvesh Kumar Page >



:9> N.> / >k0.> )e& .>

> N.> / >;;; 0.>;; & )e&:9 =>;; &?> N.> / >; 0. & )e&:9 =&?

> N.> / >;: #!e) .&

> 7o,-e / >;: Er0

> %o,-e / >;: er0/ ;. *oo' +o,!

E!e$tron +o!t:

A! e-e&'ro! 3o-' () $ e$),re o* e!er0#. A! e-e&'ro! 3o-' () 'he k(!e'(& e!er0# 0$(!e "# $! e-e&'ro! +$))(!0 'hro,0h

$ +o'e!'($- (**ere!&e o* o!e 3o-' 6A! e-e&'ro! 3o-' =eV? () 'he e!er0# 'h$' $! e-e&'ro! 0$(!) whe! (' 'r$3e-) 'hro,0h $ +o'e!'($- o* o!e 3o-'8.

Re!"t#on et-een e!e$tron +o!t 0eV "n/ .o)!e:

We k!ow 'h$'4Work

V /5

E!er0# =Work? / V5

> e-e&'ro! 3o-' =eV? / +o'e!'($- (**ere!&e × &h$r0e o* $! e-e&'ro!.

>eV / V =>. × >;:>@ C?

>eV/7

C=>.×>;:>@ C?

>eV / >. × >;:>@ 7

: Work /one 2 " +"r#"!e 3or$e 0one /#4ens#on"! $"se?:Le' ,) &o!)(er $ )(',$'(o! where 'he *or&e () $&'(!0 $-o!0 'he :$() $! 'he $0!(',e o*

'he *or&e () 3$r#(!0 w('h +o)('(o! . Th,)4 $) 'he "$-- o3e)4 'he $0!(',e o* 'he work h$)

o!e "# 'he *or&e4 o! 'he "$--4 &h$!0e). The $%$&e!' 0r$+h )how) 'he +-o' o* $ o!e(e!)(o!$- 3$r($"-e *or&e.

Le' ,) &$-&,-$'e 'he work o!e o! 'he "$-- "# 'h() *or&e. We (3(e 'he $re$ ,!er 'he 0r$+h

(!'o !,"er o* !$rrow )'r(+) o* w('h D. I' () )$-- e!o,0h 'o $)),e 'h$' F =? (),!(*or (! 'h$' r$!0e. Le' F %$ "e 'he $3er$0e 3$-,e o* F =? w('h(! 'he %'h (!'er3$-. There*ore4

Dw % () 'he work o!e (! 'he %'h (!'er3$- '(e2 Dw % / F %$D To'$- work4 W / Dw % / F %$D

I ;

Work / -( FI→ ∑( )Work / F ∫

Geoe'r(&$--#4 'he work () e5,$- 'o 'he $re$ "e'wee! 'he F=? &,r3e $! 'he :$() "e'wee! 'he -((') ( $! .

': S5o- t5"t Gr"+#t"t#on"! 3#e!/ #s "!so $"!!e/ Conser+"t#+e 3#e!/:Gr"+#t"t#on"! 3#e!/:

A 0r$3('$'(o!$- *(e- () 'he *or&e *(e- &re$'e $ro,! $))(3e "o(e) 'h$' &$,)e) $''r$&'(o! o* o'her $))(3e "o(e).

Conser+"t#+e 3#e!/:

A 0r$3('$'(o!$- *(e- o* *or&e (! wh(&h 'he work o!e () o3(!0 $ "o# *ro o!e +o(!' 'o $!o'her () (!e+e!e!' 'o

'he +$'h '$ke!. A! o'her () 'he 'o'$- $o,!' o* work o!e (! 'he &-o)e +$'h4 (! 'he 0r$3('$'(o!$- *(e- () e5,$- 'o

Jero. S,&h 0r$3('$'(o!$- *(e- () &$--e4 6Co!)er3$'(3e F(e-8.

The *or&e re5,(re 'o o3e 'he "o# "e'wee! 'he)e +o(!') (! $ &o!)er3$'(3e *(e- () &$--e $ &o!)er3$'(3e *or&e.

Proo3 o3 6#rst P"rt:

Work /one #s #n/een/ent o3 "t5 3o!!o-e/ et-een t-o o#nts:

Co!)(er $ "o# o* we(0h' W (!('($--# $' re)' () 'o "e -o&$'e $' +o)('(o! P (! 'he 0r$3('$'(o!$-

*(e-. The )$e () 'o "e4 o3e 'hro,0h ()+-$&ee!' > 'o +o)('(o! Q. The we(0h' $!

()+-$&ee!' $re $k(!0 $! $!0-e α w('h e$&h o'her.

There*ore4 >P Q

Work / F. →

>P Q

Work / W Co) K→

>P Q

B$)e

Work / W H#+.→

>P Q

>

Work / W

→

Prof: Najeeb Mughal, Composed by Tarvesh Kumar Page 9



P QWork / W

→

A0$(!4 'he "o# () 'o "e o3e *ro +o)('(o! Q 'o S4 (! 'he 0r$3('$'(o!$- *(e-4 'hro,0h ()+-$&ee!' 9 $' $!

$!0-e @;< $e w('h 'he we(0h'.

9Q

Work / W. S →

o

9Q S

Work / W Co) @;→

( )9Q S

Work / W ;→

Q SWork / ;→

A!4 !ow $0$(! $ "o# () 'o "e o3e *ro 'he (!('($- +o)('(o! P 'o )$e *(!$- +o)('(o! S4 (! 'he 0r$3('$'(o!$- *(e-4

'hro,0h ()+-$&ee!' $' $! $!0-e β w('h 'he we(0h'.

P S

Work / W. →

P S

Work /W Co) L→

P S

B$)eWork / W

H#+.→

P S

Work / W

→

P SWork / W

→

Th,)4 P P Q Q SWork / Work Work

S → → →

W / W ;

Or W / W 4

Th() )how) 'h$'2

6The work o!e "e'wee! 'wo +o)('(o! +o(!') (! 'he 0r$3('$'(o!$- *(e- () (!e+e!e!' o* +$'h *o--owe 'he +o(!')8.

Proo3 o3 se$on/ T-o:

Work /one #n $!ose/ "t5 or !oo #s e)"! to 8ero:

Co!)(er $ "o# o* we(0h' W (!('($--# -#(!0 $' re)' $&'e 3er'(&$--# ow! w$r4 whe! +-$&e $' +o)('(o! P (! 'he

0r$3('$'(o!$- *(e-. I' () o3e 'ow$r Q 'hro,0h ()+-$&ee!' > $k(!0 $! $!0-e α w('h 'he we(0h' o* $ "o#.

We k!ow 'h$'4 >P Q

Work / F. →

>P Q

Work / W Co) K→

>P Q

B$)eWork / W

H#+.→

>P Q

>

Work / W

→

P QWork / W

→

Now $ "o# () 'o "e o3e hor(Jo!'$--# *ro +o)('(o! Q 'o S 'hro,0h ()+-$&ee!' 9

$' r(0h' $!0-e 'o we(0h'.

9Q

Work / W. S →

o

9Q S

Work / W Co) @;→

( )9Q S

Work / W ;→

Q SWork / ;

→

I! 'he -$)' $ "o# () 'o "e o3e *ro +o)('(o! S 'o (') *(!$- +o)('(o! P *ro wh(&h (' )'$r') (') o'(o!4 ,+w$r (! 'he

0r$3('$'(o!$- *(e-4 'hro,0h ()+-$&ee!' $k(!0 $! $!0-e =>;< : β? w('h 'he we(0h'.

S P

Work / W. →

( ) S P

Work /W Co) >; : L→

Prof: Najeeb Mughal, Composed by Tarvesh Kumar Page



( )o

S P

Work / W Co)>;< Co)L S(! >; S(! L→

( )S P

Work / W :> Co) L ;→

×

( )S P

Work / W :Co) L→

S P

Work / : W Co) L→

S P

"$)eWork / : W

h#+.→

S P

Work / : W →

S PWork / : W

→

P Q S P P Q Q S S PTo'$- Work o!e/ work work work

→ → → → → →

( ) ( ) ( )P Q S P

To'$- Work o!e/ W ; : W → → →

+

( ) ( )P Q S P

To'$- Work o!e/ W : W → → →

To'$- Work o!e / ; Th() )how) 'h$'4

6To'$- work o!e (! $ &-o)e +$'h or -oo+ (! 'he 0r$3('$'(o!$- *(e- () e5,$- 'o Jero8.

': Po-er:The work o!e "# $ "o#4 (! ,!(' '(e () &$--e 6Power8.

Work Power /

'(e

Th,)4 +ower o* $ "o# () 'he 6R$'e o* o(!0 work8.

F. Power /

' or

Power / F .

'

r

Power / F . 3

Power / F 3 Co) θThe +ower &$! "e e*(!e $)4

6The o' +ro,&' "e'wee! *or&e $! 3e-o&('#8. I' () )&$-$r 5,$!'('#4 h$3e ,!(' 6w$''8. I') (e!)(o! () 9 :M L T

W"tt:

Whe!4 O!e:%o,-e work () 'o "e o!e "# $ "o# (! o!e )e&o! 'he! +ower () &$--e 6O!e w$''8.work

Power /'(e

> %o,-eO!e w$'' /

>)e&

>hor)e:+ower / w$'')

A!4 >hor)e +ower / ; *oo' +o,! )e& :>.

Con+ert one k#!o-"tt95o)r #nto .o)!e:

We k!ow 'h$'4 Work / +ower ='(e?

>k(-ow$'' ho,r />;;; W$'' =;; )e&?

> k(-o w$'' ho,r / ×>; =7o,-e )e&? )e&

>k(-o w$'' : ho,r / . × >;7o,-e)

The k(-ow$'':ho,r () $ Coer&($- ,!(' o* e-e&'r(&$- e!er0#.

: Ener*2:A "o# wh(&h h$) 'he &$+$&('# 'o o work () )$( 'o +o))e)) e!er0#. Whe!e3er $ "o# +er*or) work (' () "# 3(r',e o*

e!er0#. No e!er0# !o work. E!er0# () )&$-$r 5,$!'('#. There $re !,"er o* k(!) o* )o,r&e) o* e!er0#4 *or

Ex"4!e:

;e$5"n#$"! ener*2: The )o,r&e o* 'h() '#+e o* e!er0# () )'e$ e!0(!e)4 wh(&h work) o! he$' e!er0#.

C5e4#$"! ener*2: The )o,r&e o* 'h() '#+e o* e!er0# () o,r *oo) wh(&h $ke) 0row $! $-)o 0(3e) ,)&,-$r e!er0#

'o o3e .The o'her )o,r&e () 'he ",r!(!0 &he(&$- +ro+e--$!'.




He"t ener*2: The )o,r&e o* 'h() '#+e o* e!er0# () &o(- or ),! or ",r!(!0 o* &he(&$- +ro+e--$!'.

<#*5t ener*2: The )o,r&e o* 'h() '#+e o* e!er0# () &o(- or e-e&'r(& )o,r&e).

So)n/ ener*2: The )o,r&e o* 'h() '#+e o* e!er0# () )o,! w$3e o'(o! o* -(3(!0 or !o!:-(3(!0 "o(e).

E!e$tr#$"! ener*2: The )o,r&e o* 'h() '#+e o* e!er0# () e-e&'r(& o'or.

H2/roe!e$tr#$ ener*2: The )o,r&e o* e!er0# *or 'he +ro,&'(o! o* e-e&'r(&('# "# 0e!er$'or) r(3e! "# w$'er ',r"(!e).

T5er4on)$!e"r ener*2:

The e!er0# o"'$(!e "# *,)(o! * h#ro0e! !,&-e( 'o *or he$3er !,&-e,). I' () &$--e 'hero!,&-e$r re$&'(o!.

Geo ener*2: The )o,r&e o* 'h() '#+e o* e!er0# () e$r'h.

So!"r ener*2: The )o,r&e o* 'h() '#+e o* e!er0# () $(!-# o!-# ),!.

Ato4#$ ener*2: The )o,r&e o* 'h() '#+e o* e!er0# () $'o).

W#n/ ener*2: The )o,r&e o* 'h() '#+e o* e!er0# () w(!.

T#/"! ener*2: The )o,r&e o* 'h() '#+e o* e!er0# () w$'er w$3e).

6oss#! ener*2: The )o,r&e o* 'h() '#+e o* e!er0# () o- "o!e) o* $!($-)

N)$!e"r ener*2: E!er0# re-e$)e (! !,&-e$r re$&'(o!). Whe! $ !e,'ro! )+-(') $! $'o) !,&-e,) (!'o )$--er +(e&e) ('

() &$--e *())(o!. Whe! 'wo !,&-e( $re %o(!e 'o0e'her *ewer 'h$! (--(o!) o* e0ree) o* he$' (' () &$--e *,)(o!

E!e$tr#$"! o-er: A!4 'here $re $!# o'her k(!) o* e!er0# *ro 'he Me&h$!(&$- e!er0# () o!e. I' () &-$))(*(e (!'wo +$r')2 o!e o* 'he () k(!e'(& $! o'her +o'e!'($- e!er0(e)

K#net#$ ener*2 The )o,r&e o* e!er0# () ,e 'o o'(o!.

Potent#"! ener*2: The )o,r&e o* e!er0# () ,e 'o he(0h' or -e3e-.

A-- 'he)e )o,r&e) o* e!er0# $re ,)e 'o +er*or work.

=: C"!$)!"t#on o3 k#net#$ ener*2:The e!er0# +o))e))e ,e 'o o'(o! () &$--e 6k(!e'(& e!er0#8.

Ex!"n"t#on: Le' ,) &o!)(er $ "o# o* $)) () 'hrow! ,+ w$r (! 'he o++o)('e (re&'(o! o* +,-- o* 0r$3('#4 (! 'he

0r$3('$'(o!$- *(e-4 w('h (!('($- 3e-o&('# 638 'o re$&h $' he(0h' 6h8. The work () 'o "e o!e "# 'he "o# () $0$(!)' 'he0r$3('$'(o!$- *or&e.

;"t5e4"t#$"! /er#+"t#on:

Work / F .

Work / W h Co) θWork / 0 h Co) ;<

Work / 0 h : : : : : : : : :: e5. =>?I* (!('($- 3e-o&('# o* $! o"%e&' ()8384 (') *(!$- 3e-o&('# "e&oe) Jero $' 'he he(0h' 6h8.

There*ore4 9 ( )9 9

* (0 h / 3 : 3

9 =:0? h / ; : 3

:9 0 h / : 3

> 3h /

9 0

B# +,''(!0 6h8 (! e5,$'(o! >4 we 0e'4> 3

Work / 09 0

( )>

Work / 3

9The $o,!' work o!e "# 3(r',e o* o'(o! o* $ "o#4 () &$--e 6k(!e'(& e!er0#8.

Work / k. E.




K. E. / ( )>

39

7: C"!$)!"t#on o3 Gr"+#t"t#on"! otent#"! ener*2:The e!er0# +o))e))e ,e 'o +o)('(o! () &$--e 6Gr$3('$'(o!$- +o'e!'($- e!er0#8.

Ex!"n"t#onA "o# o* $)) 68 () $' re)' o! 'he e$r'h) ),r*$&e. I' () 'he! r$()e $ 3er'(&$- ()'$!&e 6h8 $"o3e 'he ),r*$&e. The

work () 'o "e o!e o! 'o 'he "o# $0$(!)' 'he +,-- o* 0r$3('# (! 'he 0r$3('$'(o!$- *(e-. The e!er0#4 wh(&h )'ore (! 'he

"o#4 () &$--e 6Gr$3('$'(o!$- +o'e!'($- e!er0#.8 Whe! e'er!$- *or&e $&'e wh(&h e5,$- 'o 'he we(0h' o* $ "o# 'he!4

work) () o!e "# 'he e'er!$- *or&e () 0(3e! "#4

;"t5e4"t#$"! /er#+"t#on:

e'e'Work . / F . h

Work e'. / 0 h Co) ;<

Work e'. / 0 h

Work o!e "# 'he 0r$3('$'(o!$- *or&e4 Work G / : work e'

The work o!e o! 'o 'he "o# "# $! e'er!$- *or&e (! 'he 0r$3('$'(o! 'h$' )'ore (! 'he *or o* 60r$3('$'(o!$- +o'e!'($-e!er0#8

Th,)4 UG / work e'/ : Work G/ : =: 0h ?Or Gr$3('$'(o!$- +o'e!'($- e!er0# / UG / 0h

> : Aso!)te Potent#"! ener*2:The 6A")o-,'e +o'e!'($- e!er0#8 () 'he 'o'$- e!er0#4 wh(&h 'he "o# +o))e))e) $' $!# +o(!' (! 'he 0r$3('$'(o!$- *(e-.

;"t5e4"t#$"! /er#+"t#on:

For &$-&,-$'(!0 'he $")o-,'e +o'e!'($- e!er0# $' $!# +o(!' (! 'he 0r$3('$'(o!$- *(e-4 'he ()+-$&ee!' *ro 'he &e!'er

o* 'he e$r'h 'o ),&h $r"('r$r# +o(!' (3(e (! 'o )$--er e5,$- ()+-$&ee!' e-ee!') 6∆r8. A&&or(!0 'o 'he

New'o!) 0r$3('$'(o!$- *or&e4 9

MeF / G

r o! 'o "o# o* $)) 4 ,e 'o Me4 $' $ ()'$!&e 6r8.

⇒ ∆r / r 9 : r >

The *or&e4e

> 9

>

MF / G

r 4 () eer'e $' $ ()'$!&e r >

A!4e

9 9

9

MF / G

r 4 $' $ ()'$!&e r 9.

The work ,e 'o $3er$0e *or&e "e'wee! 'he)e 'wo +o(!') () 0(3e! "#4

$3eWork / F . r∆ Work / F$3e ∆r Co) θ Work / F$3e ∆r Co) ;< Be&$,)e4 Co) ;</>

Work / F$3e ∆r ::::::::::::::: e5. >

> 9

$3e

F F

F / 9

9 9

> 9$3e

G Me G Me

r r F /

9

$3e 9 9

> 9

> > >F / G Me

9 r r

9 9

9 >$3e 9 9

> 9

r r >F / G Me

9 r r

( )

9 9

> >

$3e 9 9

> 9

r r r >F / G Me

9 r r

∆

( )9 9 9

> > >

$3e 9 9

> 9

r 9 r r r r >F / G Me

9 r r

∆ ∆




( )( )9 9

9 > > > >

$3e 9 9

> 9

; 9 r : r r r r >F / G Me

9 r r

( )9 9 9

9 > > > >

$3e 9 9

> 9

9r r 9r r r >F / G Me

9 r r

−

( )9 9

9 > > >

$3e 9 9

> 9

9r r r r >F / G Me

9 r r

−

9 >$3e 9 9

> 9

9r r

F / G Me 9 r r

$3e

> 9

>F / G Me

r r

The work o!e *ro 'he +o)('(o! > 'o +o)('(o! 94 () 0(3e! "#4

> 9 > 9

> G Me r

r r Work

→

= ∆

Fro e5,$'(o! =>?

( )9 >> 9 > 9

> G Me r : r

r r Work

→

=

9 >

> 9 9 > 9 >

r r G Me :

r r r r Work

→

= ÷

> 9 > 9

> > G Me :

r r Work →

= ÷

S((-$r-#49 9

> > G Me :

r r Work

→

= ÷

: : : : : : : : :

: : : : : : :

N:> N N:> N

> > G Me :

r r Work

→

= ÷

> N > 9 9 N:> N

: : : To'$- Work Do!e Work work Work→ → → →

=

> N > 9 9 N:> N

> > > > > >

G Me : : : : : :r r r r r r To'$- Work Do!e→

= + ÷ ÷ ÷

> N > 9

> > G Me :

r r To'$- Work Do!e

→

=9

>

r

+ ÷ ÷

>:

r N:>

> : : :

r

÷ ÷ N

>:

r

÷ ÷

> N > N

> > G Me : : : :

r r To'$- Work Do!e

→

= ÷ ÷

> N >

> > G Me : : : :

r To'$- Work Do!e

→

= ÷ ÷∞

The N'h )'e+ (! 'he 0r$3('$'(o!$- *(e- () $' (!*(!('# .So 'h$'4 N

> >;

r = =

∞

There*ore4 > N >

> G Me

r To'$- Work Do!e→

=

÷ Th,)4 'o'$- work o!e (! o3(!0 'he "o# (! 'he 0r$3('$'(o!$- *(e- () &$--e8 A")o-,'e +o'e!'($- e!er0#8.

To'$- work o!e / : =A")o-,'e +o'e!'($- e!er0#?

He!&e4e

e

GMA.P.E./ :

R 4 () 'he +o'e!'($- e!er0# o! 'o e$r'h ),r*$&e.

Be&$,)e4 r > R e4 () 'he r$(,) o* 'he e$r'h.

C"!$)!"t#on o3 Aso!)te otent#"! ener*2 "t 0R e?5:I*4 $ "o# o* $)) 68 () 'o "e o3e $' $ he(0h' =R eh?4 *ro 'he &e!'er o* e$r'h4

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ee

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R hR

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R hR

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h> R

R

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G M hA.P.E./ : >

R R

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G M hA.P.E./ : > : : :R R

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B# "(!o($- )er(e)

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A' $!# he(0h' 6h8 $"o3e 'he e$r'h ),r*$&e.

: Inter9 $on+ers#on o3 otent#"! "n/ k#net#$ ener*#es:

Ex!"n"t#on:

S,++o)e $ "o# o* $)) 68 -(*'e 3er'(&$--# ,+w$r4 'he work o!e o! 'o $ "o# 'h$' )'ore (! 'he *or o*0r$3('$'(o!$- +o'e!'($- e!er0#. A "o# (! 'he )'$'e o* re)' $' he(0h' 6h8 $"o3e 'he ),r*$&e o* 0ro,! )$#4 +o)('(o! P w(--

+o))e))e)4

Po'e!'($- e!er0# / 0h4 A! k(!e'(& e!er0# / ;

Wh(-e *$--(!0 $ "o#4 $' +o)('(o! O4 -o)) o* +o'e!'($- e!er0# $! 'here () e5,$- $o,!' o* 0$(! o* k(!e'(& e!er0#4 ,e

'o (!&re$)e (! (') o'(o! ,e 'o 0r$3('#.

P.E. Lo)) / K.E. G$(! $' 'he +o)('(o! O4 $) he(0h' = h : ?.

>W = h : ? / 3

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>W h : W / 3

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Lo)) o* P.E. / G$(! o* K.E. Work o!e $0$(!)' *or&e o* *r(&'(o!

Th() e5,$'(o! () &$--e 6Work e!er0# e5,$'(o!8.

I*4 * / ; 'he!4>

0 h / 39

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> 0 h / 3

9P.E. Lo)) / K.E. G$(! 'h() () -$w o* &o!)er3$'(o! o* e!er0#.

Whe! *or&e o* *r(&'(o! () $")e!'4 'he o'(o! o* "o# () (!e+e!e!' o* (') $)).

<"- o3 $onser+"t#on o3 ener*2:The +r(!&(+-e o* &o!)er3$'(o! o* e!er0# )'$'e 'h$' 6'he 'o'$- e!er0# o* $ )#)'e re$(!) &o!)'$!'. E!er0# &$!!o' "e

&re$'e or e)'ro#e ",' $# "e &o!3er'e *ro o!e *or 'o $!o'her8. To'$- Work o!e =or To'$- E!er0#? / P.E. K.E.

Ex!"n"t#on:

S, o* k(!e'(& $! +o'e!'($- e!er0(e) o* $ *ree *$--(!0 "o# re$(!)&o!)'$!'. I' e$!) 'h$' k(!e'(& e!er0# () &o!)er3e %,)' "e*ore h(''(!0 'he 0ro,!

'h$' () $! e5,$- $o,!' o* 0r$3('$'(o!$- +o'e!'($- e!er0# $&5,(re "# $ "o# $' 'he

h(0he)' +o)('(o!. Le' ,) &o!)(er $ "o# o* $)) 68 ke+' re)' $"o3e 'he 0ro,! -e3e- $'

he(0h' 6h8. The "o# +o))e))e) +o'e!'($- e!er0# $' h(0he)' +o)('(o! P.

P.E.P / 0 h $! K.E.P / ; To'$- e!er0# P /P.E P K.E P




Th,)4 To'$- e!er0# P / 0 h ;

T.EP/ 0 h

A*'er ro++(!0 $ "o#4 $' +o()o! O4 $! "o# &o3er) ()+-$&ee!' 68.

Th,)4 P.E O / 0 =h ?

We k!ow 'h$'49 9

* (9 0 h / 3 : 3

9 0 h / 3 : ;

9 0 h / 3I*4 h / 4 'he!4 9 0 / 3

A)4>

K.E. / 39

There*ore R

> K.E / = 9 0 ?

9

R K.E / = 0 ?

K.E.O / 0 4 k(!e'(& e!er0# (! 'er) o* he(0h' .

T.E.o / K.E.O P.E.O

T.E.o/ 0 0 =h : ?

T.E.o/ 0 0 h : 0

T.Eo / 0 hF(!$--#4 $' +o)('(o! R4 %,)' "e*ore h(''(!0 'he 0ro,! ),r*$&e4 K.E.R / 0 h4 () 'he k(!e'(& e!er0# (! 'er) o* he(0h' h.

P.E.R / ;

A)49 9

* (9 0 h / 3 : 3

99 0 h / 3 : ;

9 0 h / 3

Where ( )R

> >T.E. / 3 / 9 0 h

9 9 T.E. R / K.E.R P.E.R T.E. R / 0 h ;

T.ER / 0 h

Th,)4 'o'$- e!er0# o* $ "o# () &o!)er3e ,r(!0 *ree *$--(!0 $' e3er# +o)('(o!. Th() () 6L$w o* &o!)er3$'(o! o*e!er0#.8 There $re !,"er o* e$+-e) o* -$w o* &o!)er3$'(o! o* e!er0# (! o,r $(-# -(*e.

E@ATIONS

1% Work / F Co)θ % Work / F . '% Power/ F . 3 B%Power/ F 3 &o)θ %Power/work

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=% Work/Power ='(e? 7%E!er0# / Work >% K.E/9>

39

% P.E/ 0h 1% Work / K.E P.E.

11% K.E. -o)) / P.E.0$(! 1% Lo)) o* P.E. / G$(! o* K.E. Work o!e $0$(!)' *or&e o* *r(&'(o!

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GMA.P.E./ :

R

DI;ENSIONS

PHYSICA< @ANTITY & SY;O< DI;ENSION NIT

Work / F M L9 T:9X 7o,-e

Power / F 3 M L9 T:X W$''K.E./P.E./ Work / 39 / 0 h M L9 T:9X 7o,-e

SHORT @ESTIONS

Prof: Najeeb Mughal, Composed by Tarvesh Kumar Page @



@% F 1: Co!3er' o!e k(-ow$'' ho,r (! 'o %o,-e)Z

We k!ow 'h$'4 Work / +ower ='(e?

Work / K(-ow$'' =ho,r?Work / >;;; w$'' =;;)e&?

Work / . >;7)e&:> Se&

Th,)4 >K(-ow$''.ho,r / .>;7o,-e)

@% F : De*(!e w$''.

Whe! o!e %o,-e work () 'o "e o!e (! o!e )e&o!4 'he! +ower () &$--e o!e w$''.

>7o,-e

Power / >)e&

>w$'' / >%o,-e.)e&:>

@% F ': De*(!e %o,-eZ

Whe! o!e New'o! *or&e $++-(e o! $ "o# $! (' &o3er) o!e e'er ()+-$&ee!' (! 'he (re&'(o! o* $++-(e *or&e'he! work () &$--e 6O!e 7o,-e8.

Work />N. >

O!e %o,-e / >N.>

@% F B: De*(!e +owerZ

Whe! work () 'o "e o!e (! o!e )e&o! 'he! (' () &$--e +ower.

Power / work '(e

@% F : De*(!e &o!)er3$'(3e *(e-.

To'$- work o!e (! $ &-o)e +$'h (! 'he 0r$3('$'(o!$- *(e- () e5,$- 'o Jero $! work o!e () (!e+e!e!' "e'wee! 'wo

+o(!') (! 'he 0r$3('$'(o!$- *(e-. S,&h 0r$3('$'(o!$- *(e- () &$--e &o!)er3$'(3e *(e-.

@% F =: A "-o&k o* woo () 'o "e '$ke! 'o 'he "o''o o* -$ke. Doe) 'he "-o&k +o))e)) +o'e!'($- e!er0#Z

The "-o&k o* woo +o))e))e) +o'e!'($- e!er0#4 whe! (' () '$ke! 'o 'he "o''o o* -$ke.

@% F 7: Doe) h#ro0e! *(--e "$--oo! +o))e)) $!# +o'e!'($- e!er0#Z

Ye)4 h#ro0e! *(--e "$--oo! +o))e) +o'e!'($- e!er0#4 "e&$,)e (' +o))e))e) work ,e 'o he(0h'.

@% F >: De*(!e e!er0#. I) (' $ )&$-$r 5,$!'('#Z

The $"(-('# o* $ "o# 'o o work () &$--e 6e!er0#8. I' () )&$-$r 5,$!'('#.

@% F : Wr('e ow! 'he e5,$'(o! o* +o'e!'($- e!er0# *or $)) 68 -#(!0 o! 'he ),r*$&e o* e$r'hZ

A")o-,'e +o'e!'($- e!er0# / :e

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G M

R

@% F 1: Wh$' w(-- "e +ower4 (* 9;;;7 o* work $re o!e (! > )e&o!)ZWork

Power /'(e

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Power / . w$''

@% F 11: E)'$"-()h $ re-$'(o! "e'wee! *or&e $! 3e-o&('#.

Ans-er:Work

Power /'(e

F. Power /

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Power / F . 3 4 () 'he re-$'(o! "e'wee! *or&e $! 3e-o&('#4 (! 'er) o* +ower.

@% F 1: Wh$' o #o, k!ow $"o,' (? +o)('(3e work ((? Jero work (((? !e0$'(3e workZ

# Work w(-- "e +o)('(3e4 whe! 'he *or&e $! ()+-$&ee!' $re (! 'he )$e (re&'(o!Work / F &o) 1

Work / F Co) ;o

Work / F

## Work w(-- "e Jero4 whe! 'he *or&e $! ()+-$&ee!' $re +er+e!(&,-$r o! e$&h o'her.

Prof: Najeeb Mughal, Composed by Tarvesh Kumar Page >;



Work / F &o) 1

Work / F Co) @;o

Work / F =;?Work / ;

### Work w(-- "e Ne0$'(3e4 whe! 'he *or&e $! ()+-$&ee!' $re (! 'he o++o)('e (re&'(o!.

Work / F &o) 1Work / F Co) >;o

Work / F = : >?

Work / : F

@% F 1': Wh$' h$++e!) 'o 'he k(!e'(& e!er0# o* $ ",--e'4 whe! (' +e!e'r$'e) (! 'o '$r0e'Z

Whe! $ ",--e' +e!e'r$'e) (! 'o '$r0e' 'he! k(!e'(& e!er0# +er*or) work w(-e +e!e'r$'(!0 $0$(!)' o++o)(!0 *or&e).

Th,)4 K.E / Work

@% F 1B: Wh$' *or o* e!er0# () +ro,&e4 whe! work () 'o "e o!e $0$(!)' *r(&'(o!Z

Whe! work () 'o "e o!e $0$(!)' *r(&'(o! He$' e!er0# +ro,&e. Th,)4 Work / He$' e!er0#

@% F 1: Wh$' '#+e o* e!er0# () 'o "e )'ore (! 'he )+r(!0 o* w$'&hZ

The e!er0# )'ore (! 'he )'re'&he )+r(!0 o* w$'&h () +o'e!'($- e!er0#.

@% F 1=: De*(!e +o'e!'($- e!er0#4 k(!e'(& e!er0#Z

The e!er0# +o))e))e) "# $ "o# ,e 'o +o)('(o! () &$--e 6Po'e!'($- e!er0#8. A! e!er0# +o))e))e) "# $ "o# ,e 'oo'(o! () &$--e 6K(!e'(& e!er0#8.

@% F 17: Yo, $re )(''(!0 (! $ o3(!0 &$r .Do #o, +o))e)) $!# +o'e!'($- or k(!e'(& e!er0# w('h re*ere!&e 'o

(? 'he &$r ((? 'he e$r'hZ

A) I $ )(''(!0 (! $ o3(!0 &$r4 I +o))e)) +o'e!'($- e!er0# w('h re)+e&' 'o +o)('(o! o* e$r'h $!4 w('h re)+e&' 'o),rro,!(!0 o* o3(!0 &$r k(!e'(& e!er0#.

@% F 1>: A) $ +e!,-, "o" )w(!0)4 $' wh$' +o(!' () (') k(!e'(& e!er0# $(,Z A' wh$' +o(!' () (') +o'e!'($-e!er0# $(,Z

A) $ +e!,-, "o" )w(!0)4 (' +o))e))e) k(!e'(& e!er0# $(,4 $' 'he e$! +o)('(o!. A! +o'e!'($- e!er0#

$(, +o))e))e)4 $' 'he e'ree +o'(o! e('her $' r(0h' or -e*' o* e$! +o)('(o!.

@% F 1: Wh# o 'he "o" o* )w(!0(!0 +e!,-, &oe 'o re)' $*'er )oe '(eZ Wh$' oe) h$++e! 'o (') e!er0#Z

The "o" o* )w(!0(!0 +e!,-, &oe 'o re)' $*'er )oe '(e ,e 'o (**ere!' *r(&'(o!). I') e!er0# () &o!3er'e 'o

+er*or work $0$(!)' (**ere!' *r(&'(o!) $! he$' e!er0#.

@% F : Doe) 'he 'e!)(o! (! 'he )'r(!0 o* )w(!0(!0 +e!,-, o $!# workZ

No4 'he 'e!)(o! (! 'he )'r(!0 o* )w(!0(!0 +e!,-, oe)!' o $!# work.

@% F 1: I) k(!e'(& e!er0# 3e&'or 5,$!'('#Z

No4 k(!e'(& e!er0# () !o' 3e&'or 5,$!'('#.

@% F: A 9.; k0 "-o&k () 'hrow! ,+w$r *ro $ +o(!' 9; $"o3e E$r'h) ),r*$&e. A' wh$' he(0h' $"o3e E$r'h)),r*$&e w(-- 'he 0r$3('$'(o!$- +o'e!'($- e!er0# o* 'he E$r'h "-o&k )#)'e h$3e (!&re$)e "# ;;7Z

M$)) o* 'he "-o&k / 9.; k0P.E. o* 'he "-o&k $' $ he(0h' o* 9; () / 0h / 9 @4 9; / @9 7I!&re$)e (! P.E. / ;; 7

Le' 'he !ew he(0h' "e h

New P.E. / 0h

0h :@9 / ;;0h / ;; @9 / @9 7

'here*ore h / @99@. / .>

@% F ': wh$' +o(!' 'he +o'e!'($- e!er0# o* $ "o# () '$ke! 'o "e JeroZ

The +o'e!'($- e!er0# o* 'he "o# $' 'he ),r*$&e o* 'he e$r'h () '$ke! 'o "e Jero =Po'e!'($- e!er0# / 0h4 where h () 'he

he(0h' o* 'he "o# *ro 'he ),r*$&e.?.

@% F B: Doe) 'he work o!e o! $ "o# "# $ *or&e e+e! ,+o! 'he +$'h *o--owe "# ('Z

M$# or $# !o' "e. I* 'he *or&e () &o!)er3$'(3e 'he! (' oe) !o' e+e! ",' (* (' () !o!:&o!)er3$'(3e =*r(&'(o!? 'he! ('

e+e!).

Prof: Najeeb Mughal, Composed by Tarvesh Kumar Page >>



Prof: Najeeb Mughal, Composed by Tarvesh Kumar

chapter 7 torque, equillibrium, angular momentum

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