IPo.
ISBN 978-616-237-202-5 e
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6
W.H.
2537
h u h qaudww. @ar~%uao~uddu wmu. 3nmiarslf N.& (%an&).- nl\smwv : ~enim$u'ygis&, m. 236 w&. I. ~ ~ ~ ~ ~ - - & ~ B u u A :I.Ldarjo~. cLBu. 530 '38N 978-616-237-202-5
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International Junior Science Olympiad
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International Junior Science Olympiad
60
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ona,uwuam;ngnit~na~u~~o~ii~iiu m n;ngusskqmd~~ma, h i r n uar nmuurimirn w usub3rraniu 29 forurumu 34
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1 ~~ao~~a:nis~iarnw 1
.............
n i r m V o u u a = n i ~ i i ~ ~ r n ~ ~ n ~61 n
International Junior Science Olympiad
a
mmanonaoilumidd 2 tantwoi hyu e n'onir sziiuaomitanaa~n'w~6~in
.R2 =
6asmad i ad
0
a~ni
+ B~ +
-
2AB cos 8
n"7 2 dwui~3 W G ~ UB ~ Y W I R 4 ~ i a 2 u +
fl dFiitii%m
!riniuirorrql6ii 2 + B umdC doqoinanrauuoa 2 unr yuc~ii~tamaoi&n~q$u t$u A ttoz B giyu d , sd, 96, is6 A
v Y RQU
d l
48.4' nruniuuofin"' azM 2 unz B
2 unr g i i y u ed
X unr iJ i i y u 90
~ ~ e n i2~ ai ij n n 6 ~ 0A~ B unr 2 d
A
a
n i a ~liar 7 niae ~3iu~j7ii1 da~i7u-1 1atlnirarlLnRirdi9uqud 2 unr B riiyunirdiln X + B + E =ounn4i1 X + B = -E myurmiia X unr B TnuIfi X ~inrB i i y u e oin R~ = + B~ + ZAB cos e ~ V U I F ~ 5 M U ~ U ,s
72 = 5 2 + 8 2 + 2 X 5 X 8 C 0 ~ 9 49 = 25
- -40
=
80
+ 64 + 80 COS 8
cose
cos 9 =
-2
cos 9 =
-COS
66
e i n ~ 3 3 n a 0 ~ ~ 6 cos(1so" ii - e) = -COS e cos (1s; - so") = -cos so" oin (1) ur16i-1 cos e = cos (186
.'.
9 = 126
yuaniia
A 6iar 2 iflu 1 2 6
- eo")
~aadiad 3 44
0
asmi
A v i 2 un:: B ~d1 0 i 1 y u s i iZ.u1 ~~::?6wnzauifljsiiuin~~ndu 17 niao wnzaunuoonqa flu 7 n i a a fii 2 unr B i i y u sd pionir unraauos~aninoik~o40rduipiiln
-
wnnuuoa 2 ianimai ~ r ~ ~ i u i n i q n i dd ~ ~ O i ~ A + B = 17 wnnuuoq 2 nntnoi ~ : : d s i i ~ o o d q a t dis6 o ~ fill$ A > B A-B = 7
:.
0)
:.
~ a i i a 4d
6
d
6
onaoi P tin:: i~~upionirtiinia ianiaoi E i3uianuoznwa wdifi'u d + 1: d d - ' lna R ~~ainn'ytanil~oivtfh uaruia8un$qndauoq~n~an~no5wuq P unr 6 i i y u do Zuiviiln
sina =
Q
1 = -2
Q
1
sina
=
.'. a
2
=
36
dW
d
d
a
o s z a m (s) Go ni~ninnsu16dulrsuimninaiI dniauduiuns
e n~snmi'n(ii)iio ni.m~#udqm~~nQm~u6u1du"~9mgmn'~a iflufiuiprianinoi
ri
wiauifluiums d
a
o i i i w i & ~ ~ i(v) a f l ~ ~ i f I i T l 11miaanai ~ 1 ~ illu~uiornaaii ~ ~ ~ riniau
4
U
d
nainrisanwas~"Iui6ua AB ,ir Y
sina =
Ul -
vZo sina
hodqad Q
=
vwi -
2vw:
~uroou~~urn1am~a'1dnia$n~a3"uoon6aun~iuda lo m / s nn&id~uu%nl~oi~yu so' n"u~nmr-iidssn~dniaM'n~6~a~vui~naiu8a~~u ~a~inaiu8ai(~ddou~d ~ $ o u i a n i l ~ o i i ~ n u n a ~ uvl~ unr a ~ iv2 i ~1no~ffffniafi~d u N f
E
-?;--v, = 10 m/s
m A? Tnu A?
=
= 10 m/s
i$ouianimoi&qd
a
-V, = 10 rn/s
sin~d?,
- t1 = l o m n iiyu so' ~u%n~lr%mnlJm~a%nl$
nai~G~ddiiuulJiYiin"' l o m n iiyu sd
6"$nmriumnldniailnldi~I8
V2 - vl 2
m 0 8 D
- 4 "
c
B
nisnszomnl~= AD
40 m
30 m
naludamdu
=
&cz
=
50 m
=
nlanszG nm
A
Iw"du6u~ini1irnoiaA P[d B ad c ttnzhl D szuzniadl6' = AB + BC + CD
3
d
naluP9amnu
=
~ n l l a t a d u d ~ n '3u mls naldaiadud16" 1 m/s 41yu tan-' Vl14%ff~~~~Rfl
50
-
m
50 s I m/s
$ n'ut~mi7dd
naiu<'~oan~id s iinz t flu v
0
naiu+"pleansid v unz t liflu a 6u$Kn51YJ v iinz t flu s J A44 n i s i ( ~ ~ ~ ~ w m u r ~ i ta~i~~u+n sm1 ~d ti t ~ m . ~ n a i u ~ u ~ ~ u 6 " 5 z ~ i l a 5 z u z n 1 9 i ~ n z ~
na1u+u91oanaiYJ v tin: t tflu a ~ u d I 6 n n Y Jv imz t flu s
~i~diio $8 2
A'
Y
" t
3'
~wnrliaa~amu nnA s URL t iInaiuGuu~n~u R ~ U Ui a a ~ a ~ ~ u 4a Y inqenn$ounmvu ~doaa~nna~u'nirl s unr t n'o v $8 2
slope
=
- 5) m (6 - 2)
(26
slope uo;lnsid v uar t flunaiutia
Iu4ias 0-4 7 ~ 1 3 slope
Iu4iaa 4-8
-20 - 0 = 4-0
? U I ~ slope =
hdaa 8-12 ?uii hiaa 12-20 5~1;
= -5
10 - (-20) = +7.5 8-4
m/s2
o
slope
=
slope
= O
- lo 20 - 12
= -1.25
m/s2
e ' I m ~ ~ ~ a d u w L i iio r sninndaud'lrjduraniuuonnrrn'i r ridurala~ntloa 'ban n"11iia"ngdnaiu~a g 3ffna g d i i 9.8 m/s2 w~6dr::uifU 10 m/s2 - dpnpqnuoammdoud naiuGadugud iiinaiuiia g 3 - ~aniuiuutm=raniuiaf~ azii"16uan"utiin"u - oinnmvl v unz t naiusa"uiieg
tv
U+V
s =
(T)
ms:u:
t
38 = (v-:+v)X
AB oin
v2' = U2
1
+ 2as
402 = 0 + 2 X 4s
kladmd 22 ?m9n&inioud~aunaiu~iana~a aurmadIflu5wid
m un:t:urnip d I d u 5 u i ~ d8 8 9 ~40 m ~ m ~ i ~ n a ~ u 8 ~ p i ~ ~ n : n a i u ~ i a ~ v i i I m s=u:miadIduui 5 = 1a~an14itIflu5 3uii - ~ : ~ r n i a d I d4u3uiii 28 = 5u +
11 85' - (4u + 51 a42)
5
idu
28
4t2 = 9t2 - 36t + 36
- 36t + 36 - 6)(t - 6)
5t2 (5t
hsni7tld
.
= 0 = 0
t = 6 nio
iuiii
zs h~ui.q A <u~u;luuu~~dauna~uh v0 do A 8.rgngqnfluui~qB s n u ~ ~ i u x n?iuB?v0 ~ d u imp h A unr B u r l r u ~ u d n ~ ~ ~ ~ d i ~ n ~ i n w u ~ u
MA
~uIdouii.rgng~qnI&wi.a s lunai t Wuunnd v unr t I661~d&n?R' nnd @ 4o s sinnnddi?rn t Trip A ~uId8qngaqnfluuB <uId~?un?iufi?v0 I6nnd indou A Tnu B ~ r i i ~ ~ n c j a ~ n d2ti I$& ? a i A unr B wu6'ir do B Gu11n4i~rnz naiudaum B a pnwnr6u = vo - gz naiuBauoa A a gn~nr6' = gz uinn5id SA+ S, = S
t = 3
?Âśdl4
~ u n 3i 8~'14Latii2 30114 wund 5 9~14 rani 1 SUIS ~ w ~ I = w u w ~ ~ w2 ununvia~ui~ ~~u~~~I ' u ~ U Z ~ M U R1~ rndau+Is~'rani 3 ?UI{
m s nuns 3 lfiflu S,
S = ut + p1 at2
-w
a
m s nunn 5 lfiflu s5 -+ s5
=
z1 x 9.8 x 1
= 4.9
m
27 IUUT~~~~UIU~~U'~~.I ~ R ( ~ ~ U ~ ~ ~ R ~t ~~ ~ F%I ~# ~ J~ ~~ I ( I d d
~aiaFnmnou$~ iRgssiimiad~dih
~ n d a 3 ~ ; 1 ~ ~ u ! f l K 8 ~ ~ n ~s4 ~ ~ ' 1 ~ ~ 6 w i . ~ v2 = u2 + 2gS o~IKii 0 =
u2 - 2gS
S'1"
ut~~dT~;1~piiuiiundd nunaiuda v Qlfl
v2 v2
u2 + 2gS = U2 - 2 g - S =
2
2v2 = 2u2 2v2 = -{2
winaiuda6u (u) oin
=
- 2gS
up u2 -
v =
2 -u
v =
u + gt
6
0 = u-gt
gt = u
l6~tdh.d(4)
) ~ I u ~ I u ~ ~ P ~
F sin 8
C N sin 0
u?a M Koadnaiumia g tan e
F
had104 32
P unr 6 8
6
u u d n i ? iiuuin 40 N i i i n ~ ~ i i ai i y u is6 Cu P armii s waiduwd~oud~~dn~ri19ia3'm~diiii~i1lGu~aR"~~dupd0rii~i~viila a a ?ia~dunaamru?nP, Q nn$uwi s d ~ a u d ~ f ( n " i l G i ~ n ~ m 0 5 ' ~ ~ i d u ~ d d
44
0
asn7
I
oinhndGirmalfi~A u i a 40 N unr iiritiidila d f i n u
'
uAaa:14iPma'*lbdugul
6'1
6 IdulJsnu~PI1) srI6 s & ~ d
d
l S -e
tan 36
=
S
S 40
= 40 tan 36
= 23.1
Oi a
wa
6 du!dmiapI
-
N
e ) 936 3 iiuuiauinniipl 1) umiqnddiarmr
s s&odqaiio s ~ 1 4 7S
6 i i y u lad n'u P I~uIri'I$iRimrarii6
It:
aaainn'u S sin 36 = -
A.4"
s nuoudtp
6 & ~ d3)
40
s
= 40 sin 36 = 20 N
ni99.1
-'A
s n G o o ~ q ~ d i ~ I G ~ a n i m o r ~ ~no~ N idu~dd~i d"
k a n i ~ a d33 +x
F cos 0 +x F cos 8
(GI
riiwuaI~iinux ua:: y liluundbainuuriu iilira F n r r i i i o l q b u F uuiun'ui!u fiisiotmrlGTmp ~~~~ +x orgaasenura8n ~~IP 1 ura I W otiiatiiouniila
0
asw7
~d~iR8u a, uan m, oz~nnu6iauorrgnRadu~Pi1~a d umrmuaa m, unr m2 g n $ i I ~ ~ a ~ a o o n o iuradnrrciiio nu m, iiuuiniriii~u d uramnrriiildo m2 a n d u Action-Reaction
find ml o r l M i d Ram m, s r l 6 i i
mlal uan m, 3na1arii.1 -
m2
T
T
=
mg-ma
-
mg(m + M) - mg(m + M sin 8) m+M m2g + mMg - m2g - mMg sin 8
=
wlairhr8ondin'u
mMg(1 - sin 8) m+M mMg(1 - sin 8) +
6aaiwd 38 uan m Bn$uk$~nklnffnn"oaw~ur~n~#~a~ndoun" A ran A e n l n n ' u ~ o n f ( ~ a n M ~ m ~ 5 d d m d o nw%pl~a#a&on l~d T, 12lutiiIn
naiuii.rqaqmdk+on B nu!n~mu&on B lzjvim = 3.2 m/s2 d 5 u naiuri.rq.rqnnnai%onA unr B nu!; I m ~ ~ G ~ n I i=v 2i nm/s2
.'.
A' N L i n t p a n 3, 5 unr 2 kg I$undoudlduu~unu$udse3n~naiu ~ 8 u m - 0t.2~ R j ~ dn unr u &nriaurrwiiaw5a1~ond~nsrwiiauan 3 unr 5 kg IMJ~ n Piio~du LifjuuiiIw
kled14 39 o o n w
1111
30
o i n ~ du I$~csaWa~3onsrwiia3 tun: 5 kg ~?lu T, MI T, oinuaa s urn: 2 kg sin
- fl - f2 - f3 30 - 6 - 10 - 4
30
= 1oa =
ioa
a:
m,, m, Wn .u?nunr%~nanoa a: R ?to ~=u=~iaainpu'n~iaunau~nnanoa
m& n ~~onuiiuuuni& m i ~ a ~ i ~ 6 i i ~ i 1 ~ 1 ~ u "~~imi$ad-tu~mdnu nuo~nu n m i & (x) &diutii~~n!itiin"u~i~~nunanu~!& ~uo~n"unmwmnnbsudv8anu miiuoaw inunmmi& (x) !~~in~t~admi&~unu (N)~ W S I ~ ~ ~ Q ~ LAction-Reaction L Z J ~ L ~ ~
Iana"aclw (mg)
ri?ani7aA 42 iidsirn~otnd~ii&rn~~udna'I~udi~a~~do~ Laiumtod~inw~nda nuuan m 4 auoduu~1i&luukdsiridsn&d~udi$u 0.9 mg, mg, 1.1 mg I~adiur9uonuiu dQ1 4 %.dl$ 8 %.dli UP: 4 3 Âś d l ~ ~ l ~ Evli~noanuddoa~doawoW ~l&J J~OJ~M~BJ~S n~iubnrviiI~ ai&tiiuuradmunmi da1viin'~rrrandai$a~unw (N) mrd N Ia.j~vi-16'~ mg huia3~araniunmiitvlsiu'naia~iia mnaiu6ia~in ZF = ma lu3aairrn N = 0.9 mg mg - 0.9mg = ma a = o.lg = 0.1 0.98xm/s2 9.8 qnna Y
.'.
CF CF
=
o
=
l.lmg - mg
=
ma ma
a
=
o.lg
.*.
.*.
a
=
o
Lf
= 0.1 X 9.8
= 0.98
Y
4
v nan
m/s2 i~191u
v =
/d+ at
= 0.98 x 4 = 3.92
oin
t = 4
s
m/s
s 5dsiidn71~8an.~d = 16 s ?idsiiu'nai~8?
044 t = 12
unroin t = 12 s 44 t nnnmunrl~&~liiuunnr(lCiR4zd w7~zuzn1416~in$u~6n~iYI vxt S
rng'
=
mg' =
GrnM -
240
N
=
51 x (16 + 8 ) x 3.92
= 47.04
m
44
6u11rillm sam8outaa1uuu~uuiuAui~ua Ielaijnaiuria
*
fi~tkrzuuszl6iiN = mg cos 36 I& ZF 10 mg sin 36 mg sin so' = ma a = g sin 3;
.'.
num~oudaluiin21uiaay %in ZF = ma mg - N = ma Y N = mg - ma
Y
WI
a ~m~nl5iiRn vector a &pl Y
ud
. a =a
Y
sin 8
a Y a a Y
= = =
a sin 36 g sin 36 g.sin 36 sin 36
= 9.8 x
N
= 420
-1 x -21
.2
- 420
9.8
= 2.45
m/s2
~LYIU~U (11
X 2.45
rlu
rlo
~snirud46 i i w ~ u o a n u qw$auuwi~dijuaniflw4 ivii%aau?dnnu s m ~ l ~2 uivi1~8aT~1U%nn %zdÂśdivil%m ~Y$IWUV~V~JLVI~G~ 700 I ~N ~~U Y ~~~Gnuoa?"Bl~r~~oinusa~a~msrni~au~n
mg,,,
= 700
N
..
.
N F sin 8
N = mg cos 9
c
N=mg-Fsin9
6aarhd 47 n o n m F~ un: F2 $ilfiimgu,n m iuabnuduu6u~ ~C(d~ud~z~~naiui~ummiu F1 Idu p Tma F, un: F, Giyu e 6"uuanu &pl &nhuuoq ttludh
Fz
-
F. sin 8
F2 cos 8
I
wid1 F, 1641
F, cos
=
f
Smax
mgv r \F2 F2 sin 8
-
pNl (N1 + F, sin 8 = mg N, = mg - F , sine) = p(mg - b, sin 0) F, cos 8 + pFl sin 0 = p g =
Fl
-
Cung cos (3 + p sin 8
F, cos 8
=
f
=
m2a(N,
Smax =
mg + F, sin 0)
= p(mg + F, sin 8)
F, cos 0 - p2 sin 0
= W g
Fl - COS 8 - p sin 0 cos 0 + p sin 8 F,
10 x 9.8 = 98 N
g=5
x 9.8
= 49 N
1 U 1 d ~ i s L:t u i n a z~~~~~~n ~ ~ 6 d n ~ ~ i i d o s : : u u tflugdd IWSI:LLS;I~J?PI 10 kg &flu98 sin 30" ddi~YiinVY49 N un:uTa#auaa 5 kg filiflu 49 N zzuus:ny~&iia!iriusa~%amiu
a
t
~q~zhmdoddo F cos 8 = f F cos 8 = pN 8m ZF k.d61u?&d~!i~flupd iwn:iinaiub 97n ZF = ma ma N = ma + mg - F sin 8 umuIu 43) Fcos8 = p m a + p g - p F s i n 8
6634
F l*iln'u
N+Fsin8-mg
=
F cos 8 + pF sin 8
=
pn (a + g)
F
=
Pm (a + g) cos 8 + p sin 8
w (a cos
+
+
g)
sin
iheimd s i uan m huoduuuaa M iiura F Eiarruulrinioutf ( i i ~ u ~ s ~ n d m i u i ~ u m n i u a~~un~rhnlrr~du~;r~~umniu~m n t dHa": sM ~ ~di iu; rps ~ aunr q ~ 1 ~ 6 1 ~ naiu~i;rq;rqntfuaa m &nvfouoduu M Wuiriiln ~siranduaam uan~urqdnrrriiiauanm QWIfs il]uii~qdi-ii~'uan m iniaudld wina~uti;ilhin
~ 3 ~9z
-
n1~~~1a~un
Y a -
20 sin
1 36 - x 20 cos 3 6
=
20
2 6
v = 7
mgh - fs = 20 X 10 sin 36
-
1 X 20 cos 36 2 6
X
m/s
1 ; mv2
1 10 = 2
100 - 50 =
a
20 2
- x - v9.8 10 v2 9.8
A,.
1
I;"
--
A*.
?
V
~
U
I
W
I
W
~
S
~
~
6aeliiad ss van m unr M Qnyn~nnilmurimliakuofda~ann~a donkbonlflvim nfiaariin uaa&nos~fl~fldoud~duu~udd~ud~r~ndfla~v~aumniu~r~iiaw'a~flu p $I~I?'m m8oun?llljurrur s 4snya van M snadoufi6miadilm4any a 8 mn?iu~auoauannanoauf~r~n~aoon~inKu 114' m Jnaiuza v, uaa M ri ~ a i u f i av2
P
S
4
-L
zptioum
=
0 =
zP,fim mv, + Mv,
n'mduaa M nfiQnRmsr!6nia s' k n y a $iuear3uan"u
(gf
uan M l f l 6 n i a - s 4swym
M
2
u5u%anmiutriin'u rng cot e
=
(F sin 8 ) l
NIL sin 8
=
C cos 8 mg 5
N,
=
1 mg cot 8 2
.'. f
=
-21 mg cot 8
~aeniqrri58
wB ,' --------
mu AB aiaofintananaumtua inu n~un'iyu$ n"YriuasrKu o ljugn C.G %a4 1 mu 1nuoddiaein A ljuaur ;ua.mmiu uianlu c ~irujnquinn~a~loansannu qu ACB l j w 20 eawiiiyxl @
s 3'
B
N~
66nnau~a~nsrn'iioniu AB lnul~?.r'usa ilfj~nn'A uar B d u N, unr NB RIU 616" 'uinrmuuia L urnnus N,, N, unz mg
ZFy = O .*.
~niu~uudsou~n o N A c o s e x 4-3 = N B c 0 ~ 8 x23 L
NA cos 0 + NB cos 0
=
mg cos $
(NA+NB)cos 9
=
mgcos$
NAsin8
=
mgsin@+NBsin8
(NA - NB) sin 8
=
mg sin @
, [tr]
NA = 2NB 6t11ub.d(I)
ZFx = 0
s,
N~ (N,
W6fl
- N~
(st)
--
tane = tan0
+ NB)
(5 m e)
,tan
kroriiad 59 a~n~ilfmqogiulurmqn haulat#wt%n
T, = 30 ~ T riiusa7a~#ut+on N T, unr
w $fia98i1~viila a:
5nnasr~u ZFx
.'. 30
~ C O 6S6
=
u
=
T~cos 36
T2 = 30 N ZF
Y
.'. 3 0 6 s i n sa" + T, sin 3 6
= O =
40 + W
W = 20N T, tvilcu 30 N, W = 20 N
=
tan$
tan$
=
-1x t a n e 3
4
=
mtan
(itan e)
N+Tcose N
.'.
T cos 8
= =
W W - T cos 9 ~ n ~ (13 f y
T sin 9 = p(W - T cos 9) T sin 9 + pT cos 9 T
= pW =
.. m =
a d
FW sin 9 + p cos 9 PW g(sin 9 + p COS 9)
tdodufi~uoaWl un:: W2 uutrouq Aon B sru~nrioutnnrtdon B gnssna Aourau~nnii~ A U ~ ~ : : TB ~ ~= ~500 I RN
.'. N 3 -W- W
=
R sin 6;
=
Rcos 6 6
=
2
Cq=o
0 (1)
= R sin 6 6 + W
-cosso" sin 6 6
~sin6o" W
2 F
- -F x 2
w
-f 0
h i4 p4 ~ m d h u n h h a w d w a ~h ~
~
pLw - niu (T) l o naifhii'lunistn8oud 1 sou dn$?tl?uii
4 d
- n?iui (f) Aa o"iu?u~auntnnaudu I wd~tlt-aai GnPi?tlSOU/?UI~~ n3oi2~094
uan IM'aiamhuduan m lnnduan M
iiua&Iiiwo~$uiio don~~duvdou T~ = o mvk rnnaiuhuoaimgd B sin F~ = -
R
mg
=
mv; -
R
h a h d 66 'innnyu~ou~1ojkludo'wri8a13~plu~mi~m~uw~iauo~~11~o?ui~ PP
0
~WII
Tannyurou~atoq1 rou Ig~aai24 ta'iua = 24 x 3600 juiii 8 d o 0 iio ~~51li?r'ayu u1n 0 = t T $0 raninzursu Ifii 0 = lunriaw1Rou/3uiQ 366 M%
366
0 = 7iT l ~ m i ? ~ o q f f 1 / ? ~ 1 3
~uu"nnio oin Fc = mv2 R
..
0 =
24 X 3600 = 0.0042
oom/?uiW"
6aadl.d
68
go A ALP:: B ~~0u~uiuCuim::nkb~~(u'i6aun"u6a~~1u~1u daub B ill:: c o i uurwaii8uan"td t#uw'iuquu"naiauoado A, B un= C flu 20, 5 un:: 10 cm ~ i u h (iinyuKo h A 6 a u n a i u h so rou/ui?i Ob c sm4uhunaivdi*ii1m B unr c ilnaiudlriih p l ? ~A unr B Ulnaiu8a (v) IY;inVW
t' =
u sin 4; g
... ~an1$a~unaflun1~indoud8u sing 46" 2U
S
=
ucosaS x
S
=
u'cos
MV~U'IU (1)
2u sin 4d g
' 66 66 x 2 ~ sin
g
u sin 8
-SYSx
o~nlonu"
- - sin e 4 COS e
â&#x201A;ŹI = arctan 4
tan 8 = 4
W l Sx o1n
Sx = vxt =
(u cos 0)zt
66n~b.d(3)
3t!giu u.
(land)
HI t Qlfl
S
=
u t + -1g t 2 1
h = zgt
WI AB ain
AB = ut
2 2
29.46 cos 3;
--
-14.7
=
UBt
(u,sin 3 6 ) t - -21 x 9.8t2
4.9t2 = 58.8
sin 3 d + 14.7
m m u (Wort, W) d u ~ u i t u ~ d ~ ~ i n ~ n ~ ~ v ~ ~~rlu ~ ~ z ~ n "
w F
2IJ
1)
c
~ . r d m u i ~ o n l ~ d o u u~ iJ~I R D
Idpl 2)
-
W = FxCD
-.F= 8 N
sin AAOB
sin
(13
A O ~= A B ~ +B O ~ 1 3 ~ = 52 + B
.'.
BO CD
~ n w h(2)
= 12 m
i m
= 13 =
w
O~
12
rtnulu(~>
= 8 x 1
= 8J
=
mgh
= 10 X 9.8 X 0.2 = 19.6 J =
mgh
= 10 X 9.8 X 0.5 = 49
W & 4 l ¶ d ~ d d M= 49
J
- 19.6
J 29.4 J
= 29.4
=
ad
nardii liflusruzmia s '6~uimi1qu 6"iiuazi~~iuv~~~za~%am~iuLBuiYi~lm IGoonw F k%g'6~uiiqu8 n'uuuanu iikmaiulhnaii'a1631 a = o .*. ZF = o tu#o F cos 8 ivi~n"yusai%umn~u ~a$uaiuvf~aurai~~m~~u~: iviin"Yaiuvaausa3rri3ua1uau
0
34117
F sin 8 F
4
f
F cos 8 F cos 8 Fcos8+pFsin8
=
pN
=
y(mg
=
ymg
- F sin 8)
Cung cos 8 + y sin 8 W = FS cos 8 - pmgs cos 8 cos 8 + y sin 8 -ymgs cos 8 aiuveai~~ai%emwiu = cos 8 + p sin 8 F =
&$u
-ymgs cos 8 a~uvs~iir~i~u~miuivi~n"~ cos 8 + y sin 8 76
Ipuan 5 kg mnneinilp 20 m o~nlniiiiza~ilu daiina~u$uw?rbn"ur:uzw~aKanr~d i d o ~ p ~4.0n nsui~6s:u:mia l o m ~:d5mriBa3u~viiIm Y d wunlhs~rlusaua:s:u:m~atdua~u ~ d sF sa: s ayluuua8uanir kua~uuoaurahuitlu aiunu
,
S(m)
,
5
10
4 1 ~ ~ 8 4 i i T 4 n "=~ i w&41~~~6d6d&lÂśd!d
mgh - Fs h=10m
5
X
=
1 1 mv2 - mu2 2 2
1 1 9.8 X 10 - - X 10 X 40 = - X 2 2
5v2
v = 10.77 m/s
mn-aiuS?dB a~nnpnnrajnuM B duiinu61a5a (mgh
t
3:~)~ nyfiO+ zmvB
mgR sin 3 6
mg sin
1
=
1
=
2 mvB
= g~
:V
.'. N - m g x -21
=
2
umulu(1)
mgR R
siu~loaiisasiird= w~aaiwandn"id8uuid 1 2
0
mgh - fs = - mv2 - $&up 1 mgh - ; mv2 = fs 10 X 9.8 X 2.5
1 -X 2
10 X 2 5 =
fs
d a liir:u:~~aa~nr~~~tiuani~naud!&i~u c dd
d
a i u ~ a a i ~ a=ww&a~u~aunidnuurzl mgh - ( p g cos 8) L - p g S = o h mgh - p g cos 8 sm 8 = p g S
5:u:
h (1 S iilfi P
h - J.l.h cot e C1
=
S
S
=
h -(I-pcot0) C1
- p cot 0)
F
=
mg sin 8
aiu$n'i
=
419ddl6
Fxs
=
mgh
~"sldiii M.A
=
sin 8
mg cos 8 1
d d u t:
iiaahad 81 oonura 3750 N ~a.rdondlmn'uaonidu~indou~nuui~ld"n 5000 N ynlmod
k o
~ia~imin~u~u~~srurnia lo m nudggi#u'lddutiilm nL(
0
alp11
~ I W Y U S O ~ ~ ~ U ~ ~ ~ ~ F B U 8ar8n$~1~~r0ni~d8~fiki5r11::n1~ ~ K I ~ ~ ~ L L ~ Q s~r
go~ 1a~aondu8ur:orma 2s mauuiuo?mclrnbod$uui'1~nialo m ~ons:mdouM ut5
rl
WIQ 20 m
& ¶ h
4 l ~ d n ' l = 3750 X 20 = 75000 J 41pld?if = 5000 X 10 = 50000 J 4
~l¶dVlgtgi%~ = 75000 - 50000 = 25000 5
nudtjtgiituiriiCu 25000 J w
d u t:
klad7dCl82 iums~unanuui~fi 520 N Ul'1dm8uuuln~ji8~~0.1 da~n71ug.a5 m b u o o n
usa6i.d 250 N rnui~drr~%mw~~a~u~o"uaddu 80% ~ ~ P i o a ~ ~ f i w i m ~ m u ~ ~ ~ f i n ' i y u ~vilmn"nr;u*lU ~~"Iflfiui? L unr M A nqud = L
,
oin
drrh%niwi~dsoana =
sin 8
=
M.A hdniadfjui ,x 100% M.A fuviianqug
5 13
8 = sin-1 5 13
h.himhyu sin-'
5~8uriu
o a~iu(naiu%au(C) ~ ~ u n a i u ( b d i i ~ f i a ~ r ~ ~ n ' a u u ' ~ ~ w ~ 1' uJnriau 'tdbuu~d J/K w?a call 'C naiufu$uhaa c uas C n'a
a niammia~i~lloan~iau i ~ o i ~ ~ I 6 ~ u n a i u i o u o z u ' n iizi i~cunii ~u ~a iaa n i o f i u i ~ z u o p i a ~ i d i u~um u ~ z u ~ 1 u ~ a ~ i l l ~ i n w ~ o u ' o o ~ ~ 1 r o l 1 ~ i n m ' 1 ~ u d z z 1 n ~ ~ o ~ n 1 z u ~ i u naiuiou tiiaooni?lu - #udrriln~~o~n1suui~811'atd~~0innaiuiouiii~i~ (a)
-
80 'C
*50 cm
)
-
oinqoln~riz o O c 33 eoOc rzfi ao iosnlnn 4 4 naiuuiauoagi~zon~ u i a ~ i f 50 i ~ -u 10 cm ininv~ 40 cm Q Z ~ ~ ~ uI n a i u ~ i a u o ~ 6 i d40 z mcrn ~ z f 60 i $84 ntnn i#otiidronuia 30 an ~ z g a n i i20 oc olj 20 cm $atdsn?iuuia(ua;sn'idzon8~20 cm ~ z d30 i n 4 ninn t lfuiio r o l z u u g m q r i g ~ n i i20 *C olj 30 io4ninn
fi%V D I ~ $ ~ ~ ~ ~ U N 20~'CP+B30 U
OC
= 50
OC
O'C
lflo"~9r1ni~l$n~iuioun~~~vi1n'~ Q isuin' luri-raiam o-t u13 imp$du21uamlltrr i i f ~ l ~ ~ n ~ i u l u p o m Q ilo~ g 'C~ ~ u ~ i n flu 30 'C I u i a 4 i a a i t-2t 2 l u a o 4 i i V d ~ ~ a ~ u ~ ~ a - r ~ f lua::lu'li-r~~aai u ~ o . ~ ~ a - r 2t-5t u o ~ m n a i p t u n p ~ p ~ C u s30 l n *C au 80 *C I$ cS iI1unaiu~naiu~~u~1~w1zuo~ vo4ii4.1 cL ~ ~ u n a i u g n a i u ? o u ~ ~ i w ~ ~ ~ o . j ~ o ~ i ~ n - r 3miasian-1 o-t ~ u i t u n - r i u i o u= mcsAt
~ q a i m d88 wtiouZiuqauan
o oc n ~ f l u ~ .loo h g
B r ~ ~ I u m r u50 : g gom~i~ w~uartautriil~ ~~wu~liinaiu~naixl~ouo"i~wirv~awiunrn~ruri~u 1 cd/g unr 0.4 cal/g0c ~9iuiiK11 n a i u 5 ~ u i i d a ~ 1 t ~ i r v ~ ~ n i ~ ~ n o80~ tcd/g wna3u Ifiqomw~riarmlut 'C $3 t arsioasg'~rwiia0-20 ETsuifunaiu5ouam = fiuifunaiu5~ur$u 100 g
20 oc
Y
OC
OC
(mcAt>nlmrur (mcAt)&
=
- t) + 100 X 1 X
= 100 X 80 + 100 X 1 X (t
+
50 X 0.4 X (20
8
(20
- 0.4t + 40
- t) - 2t
(~L),Y,,& (mcAt)$l,,P, +
-
0)
= 160 + 2t
-112 = 4.4t t = -25.45
p o m p S R m n u d u unmdi$itiqannoumna!liwua 0
~j~up~~n~~amiriin'u'
"c 6 l o r w i ~ i ~ ~ d i l ~ l u d a t d ~ u u(naoumna) Hni~r AIR wiI~~infiuiarnaiu5~u d i l 20 'C fllU00flUl ~ ~ ~ f i ~ l f u ~ 3 1 ~ ~ ~ ~ ~~I ¶~J ? ~t:I M1¶ ~( M fQ ~lN ~~~ Q%u - ~ maaZitfla ~i~uifunaius"oudni~oonuioin~i 20 'c unr~innirur = 50 X 0.4 X 20 + 100 X 1 X 20 = 2400
fmi~naiu5oudarwnouZi~i4a m n?' aln
Q = mL 2400 =
mx
80
l U
nin
R Q
B
P
A
htrrm.tw& OR fiur8uuuaain A
POR
~ =B4; (LPI AQOB d Q ~ =B 36 luaauu.rn OQ 8ui#uituanin P ~ =QQ ~ =A60" IU AQOA tan 66 = QA QO
=R
C n1 sin 9%
n, sin 0,
6aah a d 94 i ~ o i i n a n n r ~ n r z ntnudvu y unzmudia"~l ~ ~ u a % n n r z n i ? l u G 61dF dugmldnirua~nasnyuinuhu imzmudi51 niwCliii~~sinu"o1~1flniws3a
~r~dmudfi uaad~norrnuilluuaa~i~i imzuua%~~(1'ido~ps"msz~mn"ufiou~~1dn"a slaainudiJi iaudiai~zfii~iiaalmunrzsiu MH-JQQn n"11~'66~7?a~!dg~n"~~?a'ssw<ain~dd gm 0' n"i%w'i6mniwo~a~~d A& qdnroiCl~ilrifimniw~~~ iio nasnyuannnudi51 nrzsnyuunzinudi?~
9i0!d$~tn'nfllYi6&1~
%udAB unz AD du%%mnnsznu BC un:: DE du%~nz<ou ioldtlua%#n::<au BC unz DE u i ~ n h d 0' in'nfiu mwdnid ofl n u m w d n i ~ ~ o ~ ~ ~ ~ ~DO' n~aJ~du~z~ ain ABCF un:: D D O ' o::!&ii tan$=
.'. DO'
10
30
cm ozidudmodhnii2adi lo cm = lo
uaaoin 0 idaPiiuraudiin~?'n"n~w~rlmnn~z~~nszonia"i lw~~~n4pil'o~mnn~znu v Y w ~~~j,in&ns::snia'7$~o::Eounn"nr~iar5u 61'7~iouua~~%w"ntw~in~audraiu~.~%oz$nn'uM" gn c lnu c du~wpu"nnianaiu16~v~~n~zon1fi lii;ln~::onifi2f iviit% 20 cm tin:: PR
c $ ~ l ~ ~ ~ u d5 icm a"l
e Ilnqldh (Q) S 2 ~iindodrr~uanunzdrrgnerdnriaufiu paaufl"(c) - 3dn~rsu1 oyninddsrg 1.6 x lo-lg c a us~ssni~~dszpld(h u ' ~ a u r a ~ ~ ~ ~w n' unndrqaii~~Raanirar r~ra w n'nn"u drrp r G ~ ~ r a n " u i u r a ~ni1mrr~iiadrrqIdfli1iain ~n"u
ZF = o Y
F B : : : ~ ~ ~ ! ~
F~
D Pg
COS
45 C
+?
~I)=[S>
.*.
F~ sin 4 d
=
F*
F~ cos 4 d
=
F~
.*.
FA = FE
11lb1olZilu~
fi
Aaohad so nrgnnuuan m dihnoapn e n ~ ~ d ~ m o 8 0 n u ~1anannuudnrpnridrrg u~n Q
1mu~unrnaln15Cu iilili~oomaeiniiuada8uyu ~ e TRU or8wdjjninn"Y~aimlm X -
oin~d
I I
'
I I
:.
-
L------
T sin 8
m
X 0
mg
uanaiisan"nsrn"idons4nnulil F 8uusasrwiiadsr9 T~un~annuviian"td 8usru:: x oind T sin 8 = F
=
2
X
sin e
=
i
x
=
csine
tan8
=
KQ~ mg12 sin28
tanesin2e
=
KQ2 mg12
KQ2
Tsin8
=
-7
T cos 8
=
mg
KQ2 tan 0 = 7 x mg
-<*?
-
w l" P tflug~uut8uoc ~UIUI~AIP ~
sin8
2
T cos 8 F
e u'riitiooq ya e
(33
WI
fipd"~ +IC
P ijiaaain A uar B nsrw"1do+IC iilu E, un:: E, m u h h TRU EA = EB
c
"Ex
=
2
:.
2KQ sin 8 d2 4 c0s2e 8KQ sin 8 cos28 d2
sin8 cos 8 = 2 sin 28
Z S =
4KQ sin 28 cos 8 d2
v fio
n~iuiiaPm61dAir:~iia 2 qn
d fio
rroriiarmi1a~n&naa9urrua~u10dn'~au1u~d~i E
d RIUA째'I&J
aiPdlunlsPl째l +1C ningm B IJgn A o9i~rhniafi~J~u~Viilm siu'rnnii +ICsin B 1J A = V, - V, szuz 2d
660:
w=
q<V, - VB)
2.4 x lo-' = 2 x
~ o - ~ ( ~ o o- ov,)
1200 = 2000
v,
= 800
- VB
v
~nfldflid B fiu soo land 6aad1d
104
lunuiu~d*rinditnuo1.8 x lo5 N/C aiulumdidszp
3
JnBpnouu' sin A
nin?iut%# B oin v2 = u2 + 2as
= mv" -
2eE
CFs = E
s - %A
.
nuu&rHh (I) 8unaunrmul nmah ~ ~ u a u t l a ~ ~ a n d ~ i i u ~ u d ~ ~ ~ ~ w
I2
I,,
=
Il
vs?u R,,
=
v1+ v2+ v3
=
Rl
=
=
I3
+ R2 + R3
Kaeni~ad107 44
0
2bPI7
nan~a~i~#uwdadn~:~td~d~iejiu I 114t ?uii ~:i5tbnnsoueiiu8udwid"i~~ku down fiiIw3ibnnlou 1 oymn ids:? e d Ifitam t uomnn~ouejiun oymn k1fudx~driiul2lune p l r
91n
.*.
I = Q t It = ne n = -It e It
huau5tbnmaudi<'
,
-
-R2=
L2441
Rl
A241
oynin
... (s)
slope
=
0.05 - 1 1 v
3s"n'~
n'iwun~nvsdda1o~3giuniu
A
I
I
4 51
A
C
D
B
B
l u u f i w o . r l ~ ' ~ i i o &Tno A un:: D baiiiBugnri3uan"od c unz B ~ugn~Rua<u =1
-
R~~
12
- 1-
-
R
~
+ -1+ - 1 4
6
1+3+2 12
B l2 = -
2 n
0 tili4iIdi51
Tbd (w) wiRi&IK~in
(P) Wo
'BC
Hl
E Volt -- 3
RBCQ l f l
nin
v,
V =
IR
=3
v, RAB =
:.
3 =
1
Wl
E 91n
10"
I x 10
= 0.3 A
uristndou1dAi 12 land
6aoni.leff 115
6n%as~fld~l~uy"7ud5:fls'u6au6m1% iooo W 220 V ~nsmld40 W 5 mas wnsmld eo w 220 v 1 mas wGoys+ia 1100 w 220 v tf8u
220 V 500
w
220 V ~ I ~ ~ " ~ ~ ~ o ~ I ~ ~9=~fl3~66â&#x201A;Źl~ddl~Vil~~ ~ I ~ Q M U ~ ~ W ~ ' O U ~ " ~
&adled
ii7
wnj.nu~AidnzrmluR, luddmluilunai 1 u14 i~onaiuiis$nCiouR, Qu 4
had
6qeni1ud
1 18
r:
d
%d
Y Y ~ M H ~ ~ w ~ ~ ~ 400 ~ uU~l nI ~~l ~ 6L ~Q~ ~l 5D~ Uf i ~R ~~ L ~ 5 6 ~ d s1000 " ~ ~ l R l f f ~ ~ l f i
1aa6 1fi~#~sni5tij~fiiIfirj~iiu~;~uaz 1000 u i n ~ r ~ ~ s ~ % L n ~ a s d ~~ oV lUnRl P ~ I Mt~ud$3lus ~ ~ I H u R ~ S ~ I4Imn Y ~~~~ ZI~Q AQ ~U~$ R U ~R U LIR Q U ~ ' U U I U U 220
dui%adibltAounz roo mn d o i g ~ ~ d o d ~ o i r n u ~ % u d1000 ~ " Iuin d &$ ~%udi~*ldossinm~osd5"u~ini~1 eoo u i n $u5o sioal+'ldGiounr = 150 yira ~ ~ u ~ ~ t n ~ ~ a d ~ u 6 1nn&lnra iff?"u~z
7
s naf mu l ~ n ~ z u n ~ w4 n i urflu I
(mud 1) RRA3 islidana 16 I.
nmqimu 2549
oymnndamdou~~uuua~~aa~n~'1mda8aunaiut~auuin a tllunoi t, udim6oudio~io
miub2nthdunm t2 nfioin&iimbauifiw$i~un~iu~~aana~a daiiuuinii16"n~anda uoauuinnaiutia~ouurnou~~mda nalu8akaduuoaoymn~u~rni1ani~~nd6und$anuniiuuln iviiln atl(3tl + 2t2) 1. a(3t1 + t,)
5.
2.
2.
(3tl
+
3.
t2)
atl(3tl (35
+
+
t2)
2t2)
at1(3t1 + t2) 2(3tl + 2t2) "
I a d
B
r
Y
~8nnuifiauaoml ttordnntjaFiuao m, iiunirnlji~Gi~iniruuniuui~~vanu njnoauuuouuui rr~nnirrii~~ucu:diiouoa~~n$ano~u'an"uw"~~n"~ofl t8naioiriamdoudoon~fln'a~naiu~iauui~ a, oirio&w"nn"uiu t riouda:npmsinnir dnn~a0ienndadiiaunaiuda1iilm~njsindiio
unarn&no~n~noonainn"u~~da 1. alt
5.
3.
2.
(
''( rn, + m2)alt
m2
ml
rn, + m2)alt
ai):(
oyrnnndamdaudk~ua~~a~un'ffnia~dat~u~~u~nia~uim~da ludaanninh bodludaaurn
oymmndoudbi?onaiu~ana~a vo dutaain~andauoa~anihwun Iuninnboudi~uio~mn i
J U
tnnounnaunaiudanafi
d
V,
.I
4 .
a,
~ilurrurnianranuauoasru~miad~~~o unrinnoum~aunaiull2
n4.i v2 Iuri~ufim~o~n~iuuoa~rurnia aamnaiuli?t~ifuuoam~mdouil&mn v0(v1 + v2) + 2v,v2 1.
2(v,
+
v2)
vo + v1 + v2 2. 3
VOVl + V1V2 + V2 + VO
3.
5.
v0 + v l + v 2 vo + 2(v1 3
+
vz)
4.
2v0 + v1 + v2 3
4.
mnimqam 5.0 kg 1duu$u~::ur:~'huur4vuim 40 N hfiniiyu 37 mmfYuuu3l1R'u & d a h % x u . nnul~tlmrnusarhmiia?"~qun:wuuni 0.4 ~ ~ ~ ~ ~ o u d ~ t l n ~ i u ~ $ ~humiin3iurh vuim~rii'Im rl 3 4 tuo~sinmriuTGuriainGvuimg = 9.8 m/s2 URI sin 3 i = cos 3 i = 3
1.
a sin 29 sin (912)
2.
a sin 9 sin (8/2)
3.
2a sin 29 sin 8
4.
a sin (8/2) sin 9
5.
2a sin 28 sin (9/2)
1.
tan 9, = 2 tan 9,
2. tan 8, = tan 8, 3. sin 9, = 2 sin 8,
sin 9, = sin 9, 5. cos 9, = sin e2
4. 2
i.~u3~ ~ W ~ ~ ~ ~ I & L ~ ~ ~ ~ ~ ~ ~ ~ U ~ ~ ~ R N I U ~ I g~MW ~ -: : W ~ I I ~ d~~oifinaiidoia~~~A1~~u'~uimu1nniid~n~~~el~ri11m 1. 6 mg 2. 5 mg 3. 4 mg 4. 3 mg 5. 2 mg P. mu T a m m z u n ~ ~ o a u ~ i ( m ~ n P g u ~ f i i ~ ~ u r ~ ~ e l ~ ~ ~ ~ z aL f Yuoa~ntfu ~~z~n~aoavoai d'uh T = k c Imu k flu~iinaes'? ~ i ( ~ l ~ ~ ~ ~ 8 4 ~ ~ ~ to~I ~~a i i~n i~u d~i LTo i ~f d .f i ~l Q~ ~~~ ~ ~ l ~d i5 f ~ ~I Id mumrunias~~J~uu1d mnrn~1arn~~n~dduu~~~doa~inn1suu1~lps'3~~~n~ius' h I I d A A ~ m n h u m i u u i ~ u ~ u ~ ~ n ~ n ~ d n u ~dogornt~un~dnuu'hl I J d ~ ~ ~ i u ~ i ~1 ~oam R'u (~a~nf i T I % ~ f J I f I a ' ? l ~ a l fdfildlril i) a ~~unif.adQmQii t (t, qanii to) 8.
,
lo.
dr-g q unndr:g 4q rfinttiuanir aiaojliianirtgurru- L ereiaaaiadnp dim d o ' 1 ~ ' u r a ~ ~ i ~ m l d hs, ~ aflu d ryrb~
11.
g d ~ r d d f l i f i a i ~ d i u m50.0 u n tdoanda !+r~uu~tiaiiul*l220 v uiu 1.00 $aiua I# w <a;ll~!d6V'!lbl 1. 3.48 MJ 2. 3.30 MJ 3. 2.80 MJ 4. 2.20 hf.J 5. 1.10 MJ
is. k~ttnaiindaann~~munrran~a~r~uiu iiyumnns~mu30'
qo dnaindrrp q
~Kan-Ouoonltl j i m ~ ~ n ~ i ~ n ~ i oinuuatWuld id ~lKa5Y9#n=n"oues~uulrJein~~uanrn'ouliiutduy ulriiln I. lo"
2. 2 6
(mud 1) R%C/ 3 islidand
niniznzz<m~in$u~6nzidna~u8auaznni 3. i~uunzidnaiu8ai~nzia~i0inna1u~u1~~o~naiuii~ d9~8naiufiadidd~u M u 1 wriaunai qiaauzn oymnindoudsinq~iil~~aunaiuii~ a nuiunaiuii ynq i u i * naiuli?ozdutu a l u t, iui8naiullaazdu at, qiad 2 naiudan.rA12hriani t2 qia4d 3 d n a i u ~ r i a ~ d u F P 5 ~ ~ i f . ~ ' ~ o ~ ~ u i m ~~~unaiufia~:am naiu~i~~~uizn a4PunqR 449:hni d u 2t1 r%a~naifl$1"Bi"a1J 2.
...
-
1 x [(3tl 2
+ t2) + t2] x at,
~ ~ o ~ o l ~ u a o u ~ b!.
.*.N + 40 sin 37째
ZFY = o
= mg
3
N + 4 0 X g = 5X9.8
ing~ndoufi~urin-nuti 4.4 mnri?uifi2 5. L Q S I P I ~ ~1
uuah
1. 2.
?4"41'7
sind b = ZF' + PQ + QR + RX Koaumn vector a ~iqul~ulsd"~ruin~~ sinzd &S = 30 (&dogain; iiqun'uuu?~briounG~ I.f~Lflu8 fll~t~~$~tdf!d 4 %?a @h%fu rnmr:;~ o'R; n&ntYaqalarfi4u 30 6" nu3 ; usn) A
XYT = 38 6 2 ~('.' MS//YT) sin A XYZ s:I6ii 2+ = 38 z
a
N
Y
-- T
.*.+
=
38 2
oin A MNO ozl6j-1
A
8
(MOu
= 2a
= 2a)
a = 82
01nqfl b
=
ZP+PQ+QR+RX
=
a cos $ + a cos a + a cos a + acos $ 2a cos @ + 2a cos a
=
2
=
-
2a
sin 8
e 2a sin 28 cos 2 2
z -
1
8 cos 8 sin 2 2
a sin 28 9 sin 2
nisnrzTnn'w6 b dsluin6viifk
a sin 28
e sin 2
6. I Q B P I ~3
ainqo
~waiia
5
7. ~~apl$ia I
t:
1. 6Guu Free body diagram i d ~ n v ~ a l i o a s i n 3~ lura u uu~6tranaaiaaz
uwaiia
wunidqcl q nda 2. 4 p d m q a d o m m y u ~ ~ZM= ~6 o uuaura&niluazwvlun"uM"qn9 nda t o qn o IvYitriai~guia L RR Moment rouqn 0 (IriRnTu~uukinN, uaz W)
5Si7 B
0
M,,u
("
(N, cos 8,) 2sin 8,
= MR7U =
(N, sin B,)(L cos 8,)
sin 8, 2 sin 8, --cos e, cos 0, tan 8, = 2 tan 8,
yv
el uaz e, iinaiuld'uiranuno tan el = 2 tan ep dW
4
W NA un: NB fluurad~firn#n~nr:n"ii~I (2) - (1)
1. riin"sld*ri(P) n'o ~iuC(pdnrm11u 1 iuifi wil6~in P = jl~dau R 2a /?uiG 2. n&,iuldfli (w) $8 c i u b ~ u ~ $ p d n r m dwfilb~h i f l w = Pt T R ~ t I ~ i a ~ f l u 3 utin:i i w d~1i~ufiu2n ~iRi&l4fliain
p = v2 -
R
Qlfl
1 -
R
=
1 +-1 -
RIR,
=
L + 11 0 4 0
is. baa~lia2 uuGa
ninr#u%3s;lnnszwu r#urruanin unz%%azn'ouoinngn~s~zfiau %z!Kii yunnnsznu = yunzfiau 2. mrwyunnenld id n'11M'~ul~nnrrnud~uu'Id id yanz*iouiiazdduud id 1.
fa%s;lnnsznuunz?a#nzn'ou iiyuszwiiaCu ~iih eo'
uuaiia
myuGnrvvnnnpuaaatund n f l h =
sin 0 (LOJ~lnlff sin e lufi3a.1
"IrsaJ=
91n
1.414 = -*.
sin
sin e Diniff sine f i % J sin e sio a,a = 36
= 1.414
x sin 36
1.
arctan (l/4)
3. arctan (2)
8.
2. arctan (1)
4. arctan (4)
x B n ~ o n Q n n d ~ Q n ~ d o u s i n0.40 d q ~ m IGannauulru kuluudn:n~~dns:nu#un"ilG~d~aiu-
is.
~~iM~liIfinaiu~ou~unis~duw~~~~cU"auan 0.5 k g I u h n 200 CI
w nuiinn*lszwii~~omt1J
4 .
uaznml9ukyJlriadv naiufou~i~tnzuo~nsww~~duvoa~~w~uni~rii'Lm
t pmwcii
(smb%sdmi)
loo kgJ K
1.
is. tiiu"ni"suu%46~i~insz~n~41szu1u~auo"flsida 2.0 m/s
CI
rlu
4
Q . J M I ~ ~ S I L ~ ~ ~ ~ R L ~ ~ ~ ~ ~ ~ ~ Q L
wo~nifunszan
17.
1. 1.0
m/s
2. 2.0
m/s
3. 4.0
m/s
4. 8.0 m/s
~ ~ i s w i < a n n i a n o ~ ~ i i m d s z n o woamna1n4u'n'imss%d~n~w u~au 1.45 ~r1~9l04~cU"4ld-i4'Ldn"d m s s r i i f i i ~2.90 ~~du~6~anisn"i~fi~~~n1snzn"~unn"u~umniu~u iYar5onl~~nKos I. unaKoa~5uniaoins1a~~~4~ldu"s~a~1~na lmuilyumnnszmd6;\nii 3 6 ~ ~ a ~ d ~ v ~ ~ ~ ~3 6u " a 2. u m K o ~ ~ ~ u m i ~ ~ i n u a a ~lmudqumnna=mul~nii lmudyuolnns=muT~snii u"991~)96H~ 66 3. ~ l ~ 4 6 0 4 L ~ ~ ~ 1 4 0 1 ~ ~ ~ 1 9 6 I u " 9 ~ d
4. L L ~ 1 ~ 6 ~ 4 l ~ ~ ~ 1 4 8 7 ~ 9 1 ~ 9 1 ~ ~ ~ ~kltldy~Fln~3tWlibRfI?l du"s9189l6u"4 6o' 4 4 - ei 18. nszon~6~yuo"uww.jus~unaid6a~w'i~u 80 cm n"7a1a?~qM'i;loinnsz~nuu~#u~~nu~wdi~~ s z ~ z m i a60 c m
~z~Amni~iiaoinns~~ntmiIm
1. 24 Cm
2. 34 c m
3. 120 c m
4. 240 c m
is. u ' n d ~ ~ d i ~ ~ l 4 % Q ~ 3 " ~ 1 4.uiiIfiilftmnia~niiouddwuim 4 ~ i ~ ~ ~ ~ d ~ ~ L ~ l ~ 3~ diuoai~~dwu'i~oud
RiwunIfi'naiuuialdn"nwo~~nud~u f 1. f/4 3. f/3
I. - 2 o l a n d 2. 20
land
3. - 1 o o h n d
4.
l o o hnd
CQ iiohdldflid~mP unr Q a 1 ~ 6 1 $ u nSruH uouiidi i'JClnnupnnz 1inrRi61uniuudnrmaunir = 4.0 Iodu aam VQ - Vp
24. 101~aridau~da%o~~a0~!~~371u~d 61 Vp unr
bldi I = 0.2
W
2. 4.80
d
t
uin
Li'jo~elsrul~aLiion 4' C i pn naiuiia&uimlnndqm 1uuiuunoui.c)nqmria ~rmzuraKiuoirnn F ii8sraMsr~iiuariumg uar F iidiuindqm anmaiulhuoaQguaz~~mu'a iiiiuini(tp ii.nvtiMiiun~~.Ir F ~riiuindqa 612 3m uiaa F dw'nnubiu mg n"1'1w'~~san'W$Corn naiurianmaa ba 3 9a dQmPqmii~naii1 w Ro mg ii1iiiinaiuB g C 4 8m n a i u ~ i a ~ ~ ~ q a ~ m ~ o ~ n a ' i ~ ~ ~ mnziiuraCwb ~~~a~qaeinrio~ Coun41 3.
~ Q B P I2G ~ uuaiin
1.
$ua6nzidnaiu8a~~nz~anifiunisn.izqm
2.
~ ~ l ~ ~ ~ ~ ~ ~ ~ ~ l d ~ l ~ d ~ L L ~
3. WI
s 1n~(LWog"1ud t A
4
i Y
4
iaprinai.udadir v0 ~uomnounuunaiulhsza~naeudagmgaqm~uo~aai t, W15ZU~VlI.Jg38m ein sm
=
~ u f i K n n d b l d n a o-t, i
+ mrh
naiu~aluuu?sz~~~~~' n?iuBaluuu?fa'Iinq& uiGn?iuli.rn~Gag %nili?"Blgaon!d6au~aiu6au w'iyu e nVYuuasitl
0zlK ~1?luP53fiu1uuu35luLvilfY' u cos e FI?I~~?$~U~UUU?~;~ miln'tl u sin 8
.)u sin 0 Sx = S
Y
=
u sin 8 t 2
v2
Sx = u cos e x 2t
oin'lonu"
1
S = -S Y 4 x u sin 8 t -- 1
u cos 8 x 4
2
.'.
2t
tan 8 = 1 bnan1mP;Fndiiiyuarctan 1 n"lJiiua3r6"
8. 1 ~ ~ f l &3 l
uuah
I. uPrn'RgmnGtfrr n~aaius~o$d~a~a~sridduuduw&aiu~nld"d~u X
+
+
d
aY
n"11N' umroon~in~ulilu 0.8 uoa E~ n ibinrznu& &iio E u ~ r n r $ u ~ f l ~ ~ ~ 0.8qurn ~ ~Es riRu6au i~u 2. U B ~ Z ~ ~ L ~ U Y Isand U 20%
P
P
lo + lo sin
3d - m g
=
ma
lo + lo sin 36 - ma = mg d
Q Z ~ Ymg uinwqaiuo a = o
... mg
= (10) + (10 x
i)
= 15
N
i~n~nui~d~Bun 15Imgu ~~rii~i~
.'. F
=
mg sin 8 + f
Ir
84
~1114410 g O'C
Q een = mcAt i l10 g
o'c
Qdl = mcAt
Q", = Q,iiu mcAt = mL + mcAt 20XlX(18-t) 36
-
= lOX80+10XlXt
2t = 80 + t
-44 = 3t t
~ 6 0 d Q ~ 4alfluIfldI~ @ ~ R ~a n~~ Q t u n p r i ~ r m ~ o ~ Ioa'Ci ~un:: ~nii
Isjqanji 18 * c
.'. ~cun~u'od~ o 'C u ~ ~ a i i Z i u ~ . m n o u i ~ n ~ I i ~ u ~
12.
r~armi'ia3
uuah
1. ~ g ij$a~upsrCwfiaiu$nu"idufiaa o E, = mgh 2.
n ~ n i ~ o y ~ n d w n " a iwnsauwfi~iuanwi~n=w&~iu$nu"ijdinaKa ~nn~~~i
I.
d i f i iie w f i a i u h 1 ~1.iau~ani f l ? l ¶ J % ~ ~ 3l1L0 ~~l ~ i l ~ % ¶ d d ( i 1l ~¶hll ~~H ~ ~l lf ~ )l~ M ~~ ~ l d d l l ~ l d n a i u 5 o ~ $ i i l f l ~ m g ~ dm d ~l K~~~i ~nQ~ =~ mcAt 4i
is. r~apriiai uuata
2. 3.
<
I
,n a i (5uiii)
I
10
20
40
30
R
=
50
mcAt
n, sin 8, = n2 sin 8, oinnguo;lntund n Bo din5r~iiCnm el iio 4 ~ ~ ~ ~ l ~ ~ U $ 4 d ~ ~ ~ ~ ~ % ~ ~ ~ 5 ~ ~ e, iio 4u~'n~~$afiu~ud?ah~n~~n'in"~~~du~~ua~in
~ n ' 1 n " U
oinlonu"uuaYa8w"nm~iyuso" n"Ytjasouis 4lm'nlH e2 = 3 6 n, sin 8, = n2 sin 8,
&a (I)
sin el
=
sine,
= fix
6 -sin 3 6
f
8, = 6d yumnnsmuiviih so" 15. I Q W B ~ B4
uuaar 9a
0
asni
rinnpuarniund n, sin el = n, sin e, edfii.inmdiidi~ss'~~iiGntnuin 4u e oziidirfou unrlunianbnir si?nai.rdiidi~naiir"ninu'ou yu e eziidiuin ~.ssdM'ninsloaoini~ < ~s9.lriiir"nrnuoaufia
&Uu
e1uo1n1ff >
e IutinY?
niw
t=l
d
u ~ ot = 1 u"n~uu$aw'au8~sida 2 rn/s ozkszuznia 2 m ziianszon d - 2 ~ I W ozziianszan d - 2 Kau v ll: m4uu v , , = v #.
=m(L
lumm'nn fi4un'nt~l~nii4u~nn~zn~n"~zu"lon~d4utniwdu so0 nisnzw'ounn"Ynun1n' sinnpuo~snn'n, sin el = n, sin e, d
sz~uifinmrnzn"ounn"~~wum~u~~utni~ e, = sd hv e, > el fizu n, > n, $u;o un~dioadun~~sinuo~iid~~di~'Ln!du~~iwn?~n m el %~c~nnrsnu
oln n, sin 8, 2.9
sin 0,
= n,
sin 8,
= 1.45 1.45
, seavia I
1 I
is. ~aarmtYaI uuak
,PrC'H
VBJ~H~?
=
sin 9 6
-
1
2.9 - 2
8, = 3d
is. raaerGa 4
uuatn
mw~in~nudi~m~in~~~n~wgtimn"~ ~mfYu~?aiiianiw~3a ioldgtimiiinniwiAau
94
ainIonfl6niwdum
0
2lipl1
3
s' iYii'~oafmq m = s s' = 3s mrzuzQq n n T1
:.
r ~ a a i a4 uuatn
=
1
1 -S + s'
~ ~ ~ ' l d ~ 1 5 ~ ~ ~ 1F ~= d KQ1Q2 1 ~ ~unzdazgrQmi6uan"uu"~sawn"n ~1!6~1~ R~
&~VULLQ=&
91
-
:-r-w
I. miu!dAi
F2 Q A
-
7
-
-
-
q2
F1
L
2r
y
F E Fio uradnr~iisioda~ +I gnouu'Inu E =
n--~iuoiia8nfldfliFio c-ndnrzillumrii + I ~nouu'nnrpnndald&8n Qnwi&bullii~n~iuha~nflv~fl~Iuau~u!d~ia~~iauo v = ~d 4-4w 3. Iumiulvlhmfiiuo m1uldfliszrin'nsin11?iaanunnu"ldfli~a~du"9~"si~a ndi3%nu"Zdfliiini7 2.
1.0 cm'
vx =
100
v
c~nfldlrl*h8~~1 x iiin'u loo had 22. I Q S I P I2~
uuaim
~ ~ 3 ~ ~ t l ~ d ~ l " I k i 0 l ~ ~ 1 ~ 3 ~1 nliaubam d 3 ~ ~ ~ ~ 1 ~ ~ ~ ~ W ~ i ~ R
&!.I~HI
Q 1= T t:
~w'd~iuau8t8n~soun~wu~1 n oynin udazsylinddszg e tS ~ X ~ M ~ W UQG =I ne Mtliu!daia 16tar81~n~rou n a y m n ~ ~ i u m s l ~ d ut ~ a n i
.'.
:.
I
=
nev -
L
a A ' (wand)
~ m l w s t o n ~ d ~ u l u u u a ~6ao a~in~~ naiuhiu vv,sam~andataduuoa hs~onInn7udaaOA 9upl (psoulupl uoa v,)
3.
d o
w a
u?n m, n'u m, ~oaAm6"6aat#~natui~ nmnatlm~aunzoduu& rniu&~(iuduyd&i iou~ddoo~~~a~~noianin~ Ri~um1~~i~ol;d~un'u~unaiuda~uw'n8"iz~~ia s~"i~un'u m, n'u w a d m, (rn1uSauo.r m, Loms&~nmsinm,) iuuiatiin'u v samnaiuhoa m, iiiounuwun &nazdwn"'$u (aoululJuoa m,, m,, v)
4
1~1ajdG~:Omilm A ifluf~~~un:~d~~iumdUU BCD iflu
B
~ i Âś d h I au'6iu1au 6 61u ~ d ~ : $ i 7 ~ t f l ~ ~ ? R R~ 3 l ~ ~ l ~ n uni?uirAiuiR'uaR'oh u BC ~au'naiudiiuniutflut~d sa~i naiu~iuniu.s~us:~iiadni~ A n"y D
R
D
AV Tmui 7 = ailuiinadun:8uaruu~
VAT E: uoauoa~aaiiiuumauur:Kuuoauoa maa1u*iot~u$u6n'i~m~doqmw~fiiw"u d'u I oam (moulupluoa y, V, A) W E :
mg cos 8 am
mg sin 0
s
=
maAB
=
g cos 8 ut + at2
=
2R =
ain mg sin f3
, 1
2
(g cos 8 ) ( t h )
tAB =
/x.....
ZF
=
ma
mg cos p
=
maAc
aAc
=
g cos p
aAc
=
8 g cos -
g cos 8
2
(1)
7.
LQaa tan 28 A
AOC + 9 = 90" A
A
AOC+AOD
=
96
.'. AOD
=
9
A
7 ""aJ
nin%t~as
w g
A
A9UM
DOB
.'. AOB
= 9
A
28 X
A0 x = A 0 tan 29 x lmnii AO ~vi16i.1 tan 29 6 v i l tan 29
TZUZll19
= =
~ ~ i % t u i d ~Ai u t' m ur~anrri~nnda~ B, dC
unr D In' AB = BC = CD = d
=
AL, LAT
e = -18Od an.
y = -
VAT
Yv
ai 4 2 A' 'A' L U B Q ~ H Q U L 1Wa~n1r:6'uva~~naaa:~%uvu ~~~ -
A
14. LQIB R(8
uuaga
- sin 8) ~ds&andqIflmuIiYnar:s:w1~ti;l1u~tuaasnau~i1~:~:~11~1u~~uas1u ~ i ufi16a nyunru 1 rau s:M~qn7 nd~uuasnnulfiwimqZZR ua:r:s:m.rluuuar~u~?iu 2nR
R"1da!i%nndau1n"s A'B a=6i1<us:s: AB
n
sin%
A'B
=
Re
x
= =
AB-OB AB - A'C' sin 8
=
R(8 - sin 8)
3.
(W,
- W1)/2
4.
(W, + W,)/2
is. 1~1~d~li~finnu%un"unisA8uvoau4aua~ 0.5 kg ~ u o i 9 n200 W n u i i n n d r m i i ~ g o l v q f i 6~~::6anlflu~~'UY'iadia na1u5ou~idaIuni~~noumn~~1~w1ruoam~idii~1lm
14.
~ i n n 1 s ~ n ~ 1 i n u u ~ v ~ ~ i ~ n ~ w u i i u n ~ n " ~ u n i ~ 0 1 n o i n i n I ~ ~ " ~ u eImud i~~~fia~~m~ (i7yus;lnnsrnu~viin"u45'
yutY1n~~rU4ditviin"y 30'
61iim~5~d~n~voaoinin 1.0 f l au 5 5 4
~"n~vvoauejuun"?~idi~viilm 1. 1.4
2. 1.5
15. ~ i n a n a i u u ~ a n i692 u
3. 1.6
4. 1.7
"
du
nm Iu~in1nt~~niaei1~~'UY7~u~~eiu~~n~num~~~ii~n~viv 1.52 Q ~ W I
~~I~uI~FI~MuQE~~Iu~'u~~L~~~IMMG~u~~~Y~
I. 692 nm
~ n 4.34 r x lo14 HZ
3. 455 nm ~ t i g4.71 x 1014 HZ
16.
2. 692 nrn
ttnr
4.71 x
lo1* ~z 1014 Hz
nm LLQZ4.34 x uianaouinaau doagnlh&6oa~inna~n~~i~ru1udauuauo~w'iu~nu~z~n$1"~~~a~a~ oonoinoohoo'smlfa 20 m/s uiuouing Q~uou~ninuiarnaoainnauIun5~~n~ai unr%ld ~ius~ussyn6aud6;15183 8.0 m/s ~ r ~ ~ u n i w ~ o ~ u i ~ n i a o u i n n a u ~ ~ o ~ n ~ d ~ i n ~ v i K a u 4. 455
rviilm m/s 2. 32 m/s 3. 20 m / ~ 4. 12 m/s 17. lil~una~uniann~annla~ila~~u"j81n1~1 wuiiqus;lnnr::nuTai;unii 60' ~rIitiun~ciiuuinsi?nnia & u v ~ w ~ d ~ a s i n i n$asiPSauoa~t~1~9uRanai;ruuuni~viiI~ mu 1. 1.50 x 10' m/s 2. 2.00 x lo8 m/s 3. 2.60 x 10' m/s 4. 3.00 x 10' m/s d d is. s.mmvuinvoai~naiuICiavoan~~~n~ai~~~nnuqu~u~ua .aai1Mliimn1w~u1~~ifaIu~nvoa~~9~ d nodi~a12 cm ~ i n n ~ r ~ n 1. 3.4 cm 2. 4.8 cm 3. 8.0 ~m 4. 20.6 cm 18. ~ ~ 6 ~ ~ 3 l ~ ~ ~ ~ ~30 ~cm ~i f lI ~~ ~ ~O ~~l~ ~d~~l blL l~ Af l ~~ ~~ f ~l l ~~ ~~ ? l ~ 1. 40
6$lu 3 1~19104a"s;lq cm 3. 30 cm 4. 40 cm d eo. ~iaayninnuoymnioWu?n~nuuunux oynin 1 drrp ql d x = -a o y n n 2 dr:p q2 x = +a unroynn 3 Jap +Q d x = +l.5a oavi$mnhudrrp ql/% iiisio~rn=ilfiiicrI4AinK6;1 1. 10 Cm
2. 20
vu
tp5~n'idooyrnn3 8 u y d 1. +25
2. -25
4. -5.0
23.
a a a r ~ ~ ~ u ~ d ~ i a d i ~ u u m ~ m a ~ d i u ~ i~irmm~~~m.rer'L#uua~aa~u~im~~iin"uwum n"a~inn"~m uae m"aKiuwiwuin:81"adnaiuKiumiu r
1.
naiuZuw"td~oaKiu~oaniu~w~uu Z'w'uS"n"'1udivoa tan e
2. 8 = 36.8.
.d JTLUIQJ 3 i %atan 36.d
=
3
117A du~nusnvosKu19m o fiuF;1째i~~iavoaai A
Hl%:tlZ
AB
Qlfl
tan 36.G 3 -
4
.'. AB
=
AB OB
= -AB 20 = 15 m =
AB+BC
= 15 + 1.6 = 16.6
m
3. LOap14'a 4
uuaGa
%'w'?
t v 0 0
Ralakia
~ u ~ ~ f l . b i d n a i u ~ a ~ n :dunisnr:o'm 6aai oinnsidsddiii dud M = A
dD=
AC = dud D
i~g$ulJ&~nga~mdiaai t, i ~ ~ r u r m i q = idanal w barn
+ AgvulJIAi:u:nia t
A'
t, ... wnni ?&~:u:mia 2 d
n't A + B + c + D
=
a d wun A +B +c
=
-3 ~oa~zu:rniagaqn 4
Sx = u cos 6 6 x 2t
1 mv2 2 v2
mgh 2gh
= =
v =
4 2 ~ 9 . 8 X 2
= 6.26 m/s
u~nawdnrrriiio4~ d d u~adRai~t-jln'mnounna~o 20 sin e = 20 x,
8
= 16
= 0.4 X 20 X
iisai&nniddiCounii 4-
&'
20
sin
N 6 10
= 4.8
N
" E W
e ~auuam~srmdoudna f sr d. d
¶JMff%¶d i ~ 9 1 ~ <f 1~ ~ ~ B I F ; I T ~ ' U Y ~ U ~ Iii~;lnv~lf~n~:n"li€l ~~CI~~QMM
?"mq8u~d iwsirim~inaiuPsana~'a F + f = 20sin8 8 F = 20 X - 4.8 = 11.2 N 10
6m
6Y~aa~n~i~~~an~i~aluiiuavuiun"u~uiii~ad~ruim 11 N
E p + q=
mgh+o
= 0.5 X 9.8 X 0.1 I
+
.'. E,,,
= 0.49 J
Ep + Ek = o + 0.20 J
.. E,,
= 0.20
J
= 0.49
- 0.20
= 0.29
~ ~ u a i u u a a u ~ a t ~ u ~ n i u0.29 i v iJ i ~ ~
B
is. maclga 3 uvriin
I. 2.
nd
J
ha~~iinmsiddaunoiuz gpm~~ozrn& rnn~iu5oui$3oin Q = mL R i f i = aiulu 1 wi3uimi ~ a ~ u a z ~ i w & ~ i uw~=~~to i n
0
asw~
n e i fiociw')
uwaisi
4
tuounaiiu 2 finaia I ~ L J ~ ~ I ~nl~sin ~ el H =I n2 R sin u e2
-
nuK? -
is. r ~ e m r ~a
nomi, sin 4 d
sin 30'
sin 8, -sin 8, sin 60' sin 9 6
v1 - -
v2
-
v1
3
x
lo8
vuimniw - r z u z n i ~ r t ~ i i f, a s iinz sr ain -1= -1 + 1 un: RitY-a(uuiu = f s s wuima"6;1~ . j z ~ ~ % i g
-1
f
= 1- + - 1
sr
S
-1 -- -1 - - 1 f 12 2 1 1 -6 - -- -
19.
tsaaia 4 uuaiin
f .'. f
12
wi?fiOjnaiulfia R
= 2f = 2 X 2.4 = 4.8
cm
5"fi~n2idn'Jiriin"Yu 4.8 cm
= -2.4 cm
1 1 imhudu~nudr2uuar n n ~ i a l w i r b w i i af, s unr s' l h i n T1 = 5 + 7
uar6i&%uiu= sr
M = s'S-
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5
iiilioasin q, unr q, lilwIrrprirnmaG~anauu 91 iiflld -25 F%l411i?~d3~~ q2
q1 q2
- = -25
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6iGiuan
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r
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