rn enfu rn M L[L'ck f*

?o^l A,-

EnuXy L I;|,^'lse' Mo

R.rgrl bac)L'a) '

-t;n,',ilt Yl e)hd

Ktwelrc EneeflW "{ a &3'd b,efr-

Ktnth' c Enu' gV 4 an aflfr ae|ale 4

rr0lo.hva +o ond -$eremc€- is the- surn

.Jluc-l,_ D a bst a-fl a)'n- cta :

I, turehc rnwfl1 Xo hilbo+eh&L

hoo a. nrno is e4'aal h tlts +n t'il mass

0^d a rvnotiare co'6r€sP *eh| +o +hot

Poo+{ dU

4 *ao P&"'

P&e H""}

4 'il* sffu/ln

"t +lt. rno53

urtet tt lhe s Tttun ) Ptqs

A Tfi,a- l<tnqhc wentt 4 +t\e- p^"*icb-s ve)oh'e- lo

W mass C-n*tr' - nLn2'WE LM lY" l" L'1''il fil

h)hcve, ?i r.s rare- pos, hcn txph'r fron +4^r- ."rna'ss

cwfuY h +ta it\" Pu*td-' - -*n ,

Rrg,ct bo "16 + & fl1"'8 qte 4 y'"")-cL""'

Foa thrs casa ! ve]o * * qnl p*2)as1o rd'hue

+a ++,L rnqss cenler ?, = cD X gi

l-fr"UYfi

C,cher.a us z ang*Iar ue]o q d tl*- t""tf rre-l'ah'ne"

1" +t4 *l eren; YYk /"- cJ1"*d"

u*o a)* Ul{,Ye^ff fl"l kir'I'}tc **ru

For a R, g,rl bo d y9_

40

I Y"l =

K.f 2 Lf,-l Vr+/?

Lv"

t iI ruxrt'*th

L'.lhere f rrefreor^k tlu Po.rho.n Wchnr f*'*., H* ce^rrler,r

4 rnasd rc un6 dlrY'nQrn) + rrlr% drn '

J,iJ )* rf fu, = f$ fcoxr)'t'nYD

rYn

M

>ff! U'"? twti +-w,i)x(* +v? +=i)J t:.;i;i;;'i ,,I

r/*

,.,,d

fll(,1"'9- btz

-U6qw's|%z^ t"?

r[$J,ftt$'*,[..n't

/ )b" A 2t'''+llJJ

Arr"] "tr -Urrydr*l-L ? ..^ uS+v

{U tr^\u**r.I1I "Gqq,2tu :: 42r"3

-tp{^,}Lo,Lor uJ

{adf"*

L r r.\.r.. - T-^ t,:r"wza l,rr d * I*r Q't - L''tz- *'f).--

- I,6rtn*rb t Ilu *i - I3z-*A "-0-- v rr ^L

-Drule\,c),.. - f=6 (&*J + Y*"

2^

[ox ll d*JIJ

F{

-+Ll')./:-

No,r LLFv"zr-l/-,E ,

q Prrnu'|a'[ o1@D '

tA'tI =

No\e i

oJv- crh o sezn

LLMV. * L &o*i-rr=-G)L

L Ir.tuOx +

//

hctve. SoYngf"t- a'D

It Ane'h' e;nl,n1q te'n

hoi r's d4^e'1a {-rons)rt'an1'

ioth W -o**'t 't vu'hq

I

Rrgrd bod6 U nd .rE o\hft Pure xoto,\ic A

q \^4

t_

7- 0 >c'rn ia co l\ t rr 9q Y oo l rrh V}'"-

XYZ.

L'o'

rrderunc,

tJ !he-;hc^r o"^ol

wtz- et centerq

+ Ccutcdc.Fe, k-.rnghe E'nqntt r '

l'1-. o,t.), + ?- Foh c/Y\" f;4

"d rnoss is chosell' borql\e,l +o

Loz = tc6 =o ) @z-3

K'E = +*u3+ +Y"'*

\c,=urol'Dhur'te)l's{'l^r-dtatancAbdute-e/Y?# ) ;li-{"1^r, c,rrl*err { *a

.\,lv axrh 'h ^'otoJn crn 7' o-"*gl 8- a*

v.v ) J- nn lobz ) t *L*oLz-,.,% --\ 1-ILcL

= J- L'Y"**1 )cD "-/ ?,

vlYoment 6 lnenhc" + uFH*- bod'6

d"oui +kc- a):- "6 'to*a-h 'm 7'

Non t rrotahou.

Fu/ a

t? \{",

dA rnuo,6

bo dX

XY

0,1^A d

t+rnd er 6.0

r h A g.ero errol

p\one ) t,.ch e,yg ru-cme/n feil b qr'. sjtu-, +a

plo n e. rnofi orn tPo "a

tteJ

a -L t<r"lre4 o-* cen*vY

XYX, & %'e

')_I \.'6-K'Li : L(1

L

zhoVc +

llxennple \-{,'l

C ,s ,* VLr-I-€- l-+tz !z- ur e- k c- e n erL2i

s ho6n ; S"o '

Prston A = t t4& L

Rod AB: 6,oern, Z\

FJU ohee,l D = 5o ttg

Rort,us { gt6rohon: hBcno

Itra ra&S Y = 30 C-lrrt

At thA tr,s\e nf "{- t r"tre-.a+ / p tv: lrrn

-\D +hr- rtgr,f cr* a sPu"l @ V a

+ \+.,a- c'rtr YJG- a/)

A la rnot/1

3"o crn/Sea .

lngI

?iston A =- J?qnslqftEt

Rod AB

Fly t^chrJ D

ptone, rnohon

pure Rolq+lcrrt'

A)t--l-.7

G) Krnofic

f'r )n =

0,rw5X SI ptvl7

p rst-an9-

L txE) +./-

qs W*I*CI)

LB) Kn e,h'c

I

=

Enwg1 {* R"o"J Umqss cenler 4 Rud I

\leJo u{z4 o6 rnq s4 cen*e tr -eng u!-oy ue-lu-t "t fu'€l

trons /q h*,cln s

vc

Z

6oSrn B

2--

Yt'

= . {gkoV

P, sry,-t (.(ctro,{) : q3^\60

7o ,

Stnzo

\eJo u\ * R is at "rrgv*

{=Qo-fi=

Vs = vA t @as L)x f ae

on6le *o o B

Qo-t45'l{ =q 6.8so

arn& .

+fifli)= =t +QgourXa\V6 (c*au

tfu'[ rCIrct4-srh'zJ2

IF

\g

= 3t +.6CIR|Qt)zoi

- r6 LCng Slhzo ?

,1gq3vg = .56z8ae4

@t)b = '113uCAB

3

(e)

U E)rs'-r- L

2

r-lt-L uasYc7

tl Q,s a

*@.'d8qtX.Y13ca6g +,zost cfraB =

, 733qm4g = 3

'er I4 AB'Velo{ } rnoss CQtnt'

\te@ r, ,-A r- 4,og7?Ve a. lo t + \'09tr,\

Vc 2 lot + l'152 1

Vc a 1'sgi +l'tsLl2^

To^ 6 Rg

0oog =

ug =

=j --_@

4.oe ? wdlseu

6"tE -l@.

t P-v,(L ) q,o81LL*-/

l?- v/

Qz.to f +-*o'sott ) J?'6a,W

X ('5 XCccoeo?| srvlroi)

.qlq I

n\aCotdtVr-

,

---

@',.

14, vrek c- EnenSg

Cr; = @sox u'f) xt-o '?

558 .rr-r Ll )' Tote1 i('g

r t' L"u)pKE 3 3.u.)n+ u-E)no+

= 4 S + q3.6, + SsZ.tV

= 6se zs (t)

O W rrd o*/ lho aryu-lax sPwd

2-3

l

/

lf e-

+l'y_ ,

h,o

o

\d

dJ

T

=,L

+ C,C

r-= Lrh'(? + jfvi"r*m

^cat e- * cae-t!"

l<,rnehc " *uVV

e x-frres s e.d oa

: 2 Fi'qL

eY*qna'l

Y,tr rl bo d't"4 +',.'.4-

*"

'f<reea

cpt n

e^rkd

J

f e 1l'1 CVe + 6 xIi.)

= C Ei). v-.

(L -)*...-Y-4.x1t )

= L, Gr"Vo + L J Op.. og.d*4m.t:,) m ,

,d*njq..ir"r$= J- rnvg. $" * I mv.,'v. + I L lo"

Vt'v

/?

.l} l;a",1o + Jdrr'vP.olrr' J,'l-rn

-\ F"!. + J*0"'C6xfP')d*1/ rn

=- F. v" + ;J " JW, Y'Qtc)"lnn

,(?

o

T

T"H

fr, iLtp,"Wi 4ru+6'n't

-t

-r-_= i tr.\,tc_l- 6.tu\c I

/ ( , '(- t ft: I

\F.V" + Mc'd

th{=

|--

fr ence-

unengt

futto mt)A t.:orkLc s obtala W

'ratq.fi o ns ,oo &a\e fo"^ amd 9,^ , rute?rcJ^ "l f'tb

0oT = ^16 Tr-T,: N,_z

h\ereI, T- wr.- lh e va-l,.'tql * tr'rr'ohc' ***Y

L* Cernfi5ura-|rcrn6 t L Z'

Vrl":Ncrr1/-d.rru-bbfuconseruahrna{"rcaa

h)n. : hJo/p d'om'a- h'6- thr- nc'n- cr'nseYveh€-

$rrcel..0

= -VtNnco'

f{ = N"+ \Nnc

1.,I r*';-6'4t

&rofifrarl'nl I Lo

l-ha Wn.

l,rlhe.ra ! r r Vz Ctrs l\ s V a,hrteo

Lo

:o

ry pftenfr ".!

0ll lL. l,rceAi1(O

e/.en$ ? t^,'

fuJw cgn}eYrryhve-

-1 +V = O ) T2tYz:\t tVt

( T, +\z ) - Lr, +V') = Wn. r- Z\__:

A {-,vce F is ca tted c,,nserrra}.re- rf +r*- ,oovl,t

6jone Ld Lt l**4t+o *al du'tn1 |-l\L rnohcr4

o{ i}s ,rna*zvra!' polnb t& '+y'cshan f^* (oaA"'

2,lrlrli'mdefenc)en*4t+'ePa)-hctcsn aeuh n6 #-otte !':"nt

' !, _ ,1 \.-{ (., a

t L fortnlConS € YYo-'nv

lxl>z = .f f.r.tl= lr,''ctz ;v, ,It €."t2 v ctzt-

L, \-.l i1 \/

Lr

I ence

potni

CphseYvahve tt"t* adl o n +'}"- scr m g rno'*enc..l

of +t^L br% orrr-d i* tn&!-unolmf * *tfr'h

ar^d hrrnr- ? = rCr)

@ trnP].ro-l +ha| #'p ,,n'tor,rc'nc) ts a hn"tt"f

4 & Fo' "h'm d'+wct*'* ScaLqr fun ch'' VU))

p ot-anhcJ ny*tu -

^ucl h/ =?'d'a '

V( Y')

N,-z =- j i' = 4eYti-v&Dt'b

vcr, )

otn

bff

polenhd e*ut8V lrunfrnserva'hr'e {<rce \n

,r.e}"dH

E quoh"t'

drtt'*nhcUil@al {+..r,-

i, g lnloxk

o{ he c}'a nge

H.n.u 6Yr{< done

39rYo '

dorts- tt*) t', '\P f- aq uo'ts ro ePai ve

E+.%o n8 t)o sed pa+ a

p, tenl-ia,t Enerqr es o{ som€ Conse vvahve. {orcel

2.

L Pi c e h, tse bn-onY ctu.ve- Cr

vV51:-V@).*Jf-ai

Ct

%

= fr'-JD

)dJ

For a unslsnt $xa E, r't"Fh

-V(Y)= F.Y = -Fx-x- trUl

TL potenhq0 smer'3.d d - 3d*t'v 2 f3.a*= m6zc

3' For a- Vata o! ,rnuh.d fur,u F, amd E'

colr H"r, E : -?u = l() €Y

dv = 6 F,a?, aE,aL )

=-F,.dCY,-.n)= F_

-FCro ts.dv = -F(r)

* ctat r"n : "ir= Yo 7 V

da-fun 0

* F.z

ia gd'n a^d Gt*.O

2_r-) f= L' ,y, z)dzb

Iu ,o,o 1dx

2

J B (Y'e, o

o

."1t'

;1fl,7)zYL

rJrd

T*@.'l,L;./it+rn

a) (z

>

Inv

tO\*Y

,?- F (v) d-!:)--F$dv^

\Y

trr

p6r)d y

0

@) Foa n,rhuJ Grqvrfufionatr fuouFb): -911gl

-7)-

)r arob V :

cDt$r dalrum \ a 6

./L( v- - [ E(-> otv| --,1v?fD

- e-Y$a*

tb) For o

it" sprrng

l.$ lv^/ L, =Hernce F ( a_)

lsarrr "d sPrrnX f<trces, Lt, + s p,rtJ o^rr

h,r- f ,"> lrr- "" ex,Le.n6rczn, €- = .1r- LO

Lrnsx,efd,*A ).eryth

= - f C.> = de- = dY a""ol H..td4 ,

8._fV= IJD

fc")ol e *49

Nrftr, d,afum 0j unstreclucJ il*fc.lO*fiE.rrch.m ?io= Io,

**r€

fC*, = Ke or^*rl q ,CB) to r\t .eurcl

l.l"lt 6C=e,) *t 1+* O<leryq\c/n,

Lc) Foy torsrona.l spnrn6 .o"rn exro-[ cs*b,\r- M(rl . *ts)Sv r.lahve aruar h,,ow* -{ & hdr,oeezr 11.-- etnda ,

\r. - O

[ = I +[B) de. fta q bnqsv *.rta,.^*!. '&prrngd.

t {orar,r..^,[ Sfif4 he&s k+ = Mt = t/+ 0 '

V = [+ 0] ocJh unt r^lts]ed C;:ln&l5uroh.^./y.

qa +r-{ dafu"n.

V= Kt . KEza'/) ')

I @)

V\ov{rles s }6rces

Ne- tisf Some {rxce* ,-o}u"}.t

* frrrcea o\'uc"h to gr}"e-r qYe

e.Q c}.l ^*b Perfrrn^ tzo o\-K'

! l'1 q 6n#e f..* F = q\'

2' Reo.cl-?on Er qt conta-r--* P t

il, p .rrn c-o* ,U = 3,, u-pr

anL un*c\-c*l qrnd Scrcn-o- heinr

(,Oolr\(dg5 *+rou6-1"r, rn &vr&^rtly

X E Srnca \,11

t^rr*lr, A +lxed7

= Kr'O =O

=F.V = gVlG!=o

brd 6 LcJ{ hs -

!_

z Rsqclion o.t Srnoot\ conra.-l- nrth q {.r*"} boc}b o,.rJ" crco,lhou! *bp I grn@ fi: NE.V = Nvn:o qsa*hev N = o fo x rvn pen& n6 se_Joqr.e-h.nn, 0/r V;=rfo Ip 8eh"oh_,qqa

Reo-cl-iorr.trcr}AaI

hnxl- $orni o#t a,

Srnooth ba-[f

il,rr") f, b,qonJ Socl*qt 0u- ErnootL

,4 rn ci- 1rJ = R,. % =T-.6o

t$ Parr of {eac}ion R o.nd -T, a* A o* srnoot}r, bd) and

|>er.lltel 6T srnoot{, fun6x- 3ornf, srnce tJ= Rvn+gR)70=6

L,e) ?a;u of *-eqefi on q.f s nnso\ln. Contd r.o dtl^" crt Ls tlhouf

S[+ ,arhcs- W = N, F" ,%, I GN,m),Sp.= Nr tfr..ra- n.vf, )+-Vpr =\'pr:

t Palrr of 4_eaclton P, qnol -F, u* cpnfacl' F, a'^d P^ L!tt-{F

ho sl+ g 1v1&- vi =_ R1,vp1 * (-(,) ,vfz &)vp,t vlL

['f)

CB ) Pai'' of tens\o rB tn l€,\* ,ri.** srble-

CaUr- 8rn u* t'l = T6. 61 + C-Te ) .Dr, z fteq r - g. o;) -aD e#^/^r = f= o {.trr \hnherndrnc, .{ladvcnom cly

L,\l 1 = €'Yu +rr( h"or.| rh e>cl-enst h-b- k r/*

-+g

tl Pa;x "t teacliohs ot$r- to

ux'vt rtStd rod otlh srnoor-h bqtt ohc.r soc.t*s[ d*r]Or(smooth hrt?- {ornh, q^d cololehey QoqJ can*)stncr '".: FE-Unt C-trA)ua = Fa.(Vn-%)

+ FA"Cixr{B =. Fe-.6YtA6)e :3

Fe*

h

d"*e- x-_-z

L

\nlovK Enengj Re-La,t-ions &-Interc.,nrrec-[e-d Sryste-rn "& RrXro\ Eu&eo,

&.*-

t=w-ff-,. n

)

v,) -

T2-- Tl = Nr- z-

('1T+v,1 : W''nc-lL

-[h ese. 'eguolionA qYe- +Flr."l +-

cr-r\ a&ded + {t '-d^*f d te-Lqhons +"t

Sgr,tezm u)|u ",r t nrral v e- vgorl,< ol o h e- q +{'q tn}e tn oI

e/^ol {0\r- ex}..a-rrJ F^r-ceA dn +4^L Sc6ate'n 'Etnc-e- Sc/r^-a'

o-d H,\,a- 'frrrcca u,rl'trclt **- gxler r\q'' q/'td rnfern-cl-a bU

+t* suJ" s cr",[rrl trrt + er^t +^a tn'Jo'r\r- Oh qr{:f freJot}rcra'

+o rre.otucr- to {1^L {ott"*'nk fir"- t<c-a.( g5 l

-L = frr"r++ur* T" - I = NJr ',+

tex* l- z

r n o! \ r ct r't o..t b""l r ea

+t^* tAho\a-

Czncr^enPort& n6-

\Ae(n €,r)

-r * t,r.r+evl = vtl."rnr *er#, Qjv,n++*vrn-)

- tTr t \ryt{*e*,) = Wn: lh++.

+ Vrr,t+qx\ =.o -I2-f V,nt+er.+!= Tr +Vn*+tv*,

iS olJ r nlerrno.l- f<"rcel t t rutevocfrcrn

fi.(,^n Vf..{ q uo.}t",n @ (,cLl} +eclrc*-$u

o-nL fu7}t_cn- us ""k.!*+l

i

").@)