ξ !" m=l #$%&'(& !" )*+,+-./01 !"%2+3& α45 6#$7+8+ #9+,&:*#-6;*<8+#9+&=,*>* ?6&@#ABC0DECF"?G#H#&,,GIJ 3 5+'KG?&9, + L?,#M" 'KN 2O+H#P&M*Q→#-A*O.N BG0 45?KR2 4S,*R 45?KR2 4S,*0 DT"B*U#&,>*'K#:#$%&+VIW BH#P0H'@?$%+*?&=,G??+X*? 455Y,*0?X*?0#0 @ #U K& #Z*V [5 +@+,I #< + 'O+'K:@#\&=,9 U#;I&:,0]B*?^&#UP+%2W& _+?G #UK&#<:0`GIa2$/+&;I#?60 ,`HI?b?$%*&#UN 4Ω 4YΩ*+I-#U*&;I&3I> #U#+ξ#UN+B&O+I>E,UG&W&#UN?$,I0DT" K#UN+&=,+I-0 `+$7,*&++ -*&@H2&c+6#UN L #Z: *:&+&=,+I-#UG0DE L 2.)+,GIB&O+I>E,U N*:&+??6>J &!"+7,*&+I-#UG *:&$BC0]+#3 4SYΩ 4d5Ω,*2'H&3#UN'O+#W+'Z0]B*@&\,*2'H0H +I-#U&3I>#U#+ξ4dY0 l α &?&?L8+#9+01K&K&&&?& ,#+2$/+ 8+#9+0]7+,M#QAK&,>#HAK>2>?5VIT+#$7+ M#+*&I'e?&*0f_&L8+#9+&;I $/+$6+LI@+ +@&f,#:AK&!)++@&7+,?c&MVI,AK&!)+&;I $/+0 g>"+45*X π 450 ,H2$/+B ,#+&=,M0 ]K7+,+>'ZQ?c&45#H'?^&#-&=,?L&3#?6&^& ZI0 &hW&#AVIT+#$7+M##$%&+'.+7+,5YS'ZQ7#Z* ,#bI0 >I'K_g#$%&#<++6*i+'O+'KG_& &K&=,>I'K&3#Z*W+0jZ**i+k&@#A01.+&W&+k, i?,455&*01AH>I'K_&&K+'.++k,i +$7,>"UW+G*'O+,+7I?:*#Z*0`$+'g&W& i*'.+45&*BUW+G*&3W'KE>0 ,]B*GI&^&=,>I'K0 ]>I'Kg&3 :+28+?-0]="?*>I'K&3&HI>4S&l ">&=,>I'K?5&*0]B*#$7+'KE>&=,UW+G*0 jZ##!I&=,-/:`,*#T&b**@++U*B_&3&,#- ?<LI@+#W"-0m,I'?<:>"#TK,#!I&bB*0]*:`,*#T ?*&W&Jn.K&J !" #" f*2+,+VI,?*+@&Ho+ pq2 _+#A?IM.&/o+:rs 4s mv mgh⇔ = R rM@&+,"$6&,&:* v gh⇒ = 4+?&t⇒ pM@&+,",I,&:* n t v v v= + r r r v v= n v r rIO++3&6VIu#:G'O+.$N+#H&I"Z #+#?G&=,M0 t v r rIO++3&6 !"9+6&I"Z#+,I,&:* t v v c v c α α = = pq2 _+#A?IM.&/o+:rs 4s v t mv mgh⇔ = v t v h g ⇔ = ]Q⇒ v 0 0 h l c c α α = ⇒ w 4?0&5 0& d5 45d* D BCr α w t V r V r n V r V r ? α #=&/M@& j:p&3 :+#:8+G&3 :+r24,x p 1 45?KR2 4S,*⇒S4,05x, p 1 45?KR2 4S,*⇒S4,05x ]Q,⇒,4pXR45 5 V pV V⇒ = − + & r 5 S m RT pV RT RT µ = = = ]Q& ⇒ S 5 V RT V= − + 5 V V T R R ⇒ = − + h(*]4y v 5 V T R R = − + 1] w 45⇒45?K ⇒45?KB] *,L ⇒ ,L 5 05 YzY 5055Y 55Y m T K= − + = g^&#UP+%2W& _+?G?r F F F F= + + r r r r kq F F F a = = = µ µ R d5 o F F F DF BDC= = = d5 o kq F F c a ⇒ = = F r )*G#$7+&,D µ µ F DF ADH F F F F F c α α = = = + + r 0 0 AH AD DH AD DH c α = + − ? ] w ] j p x 5 5 5 5 c α ⇒ = dkq F a ⇒ = v 0 0 0& { Y O F F F F F β β = + − ⇒ ; M"r F r &3rGI|5S p jZ*#<r:0 p ;Ir$6+,+9 U0 p $/+r%26*<28+ *+3&β4{ Y w 0 p j?6r dkq F a = DBCr#=S&/ ,2 42 R R R r R r r ξ ξ = + + ⇒ = Ω R p RI r R r R R ξ ξ = = = + + ξ'O+#P *,L '44Ω r X R R R R R R = + + ⇒ L 4Ω &*2'H&3#UN'O+#W+'ZG≡ m/#-$/+#$/+*:&+r [ ] X X X XR R ntR R Y S d5 0 5 R R R R R R R R R R R R R = = Ω + = + = Ω = = Ω + I A R r ξ = = + 0 d5 d 5Y AB AB AB U I r V U I I A R U U U U U V U I A R ξ = − = = = = = = = − = = = *2'H&\} 4}p} 4 D β α F r F r F r F r } } } } } ξ } , 5 S X T rad s T π ω π = ⇒ = = 4⇒4Y&* 5 5 5 5 5 x c t v ϕ π ϕ ϕ = = = ⇒ ⇒ = − > < Y&S x t cm π π ⇒ = − ]:AK&!)+r*+4'∆? 5 55 o g l m cm ω ⇒ ∆ = = = [∆? ⇒?^&#-&^&ZI:AKL4p&* ]7+,+>Q'45#H'?^&#-&^&ZI?r z 5 T T t s∆ = + = & 5YS Y T t s T∆ = = + Y d d{dd s A A cm⇒ = + = + = ]Q,*+W&#-+ :+⇒ v v v v v v r d b b a d a d r d d d d d − − = = − = − = − + ~ r a d r f d f d r a d a r d f f ⇒ = − − + − ⇒ = + − E>' a d d f + E>0q2 _+>#8+9&,&3 E>'r ,y a d d a b d f = ⇒ = = − d a b f cm a − ⇒ = = n f R = − ⇒4Spd4Y&* h(∆}D,&3rD} 4} pD ⇒ 4 ppD ⇒4Y&* ]Q~⇒+WAE>&=, ≈&* M"#$7+'KE>&=,UW+?r&* p•2@++U*8+#9+,I#3?<LI@+-#H/&b## !I€+k+I"G$H@++U*0 D } pjW >I*^&$6& !+?G+@++U* pq2 _+#A?IMOp?/p,pp@&'@'K+@++U*0 &U#'O+#P 2 42↔2 m? 42m? r242 xρ+ ⇒2 ? 42 xρ+? o o p l l h gl ρ − ⇒ = r#!I/&b#0 2 r?W2I>'KVI"Z0 ? r# @++U*0 ?r# &=,'@'K+@++U*?c&N#W"-0 ρr'@?$%+G+&=,$6&0 +r+,@&f+$7+0 f&2.GI#=G&W&#:?$%++&O+9&G !Ir ]G*<&3*M'@?$%+* 4'+#$%& @6M'@?$%+* 4S55+)+*% !" 'O+ TVI,*&W+f&&3'@?$%+'O+ #W+'Z0DU@*,W+k,M*<? 5 µ = 0E VI,*,WN+f&0g>"+45*X 0 ,0 IO+&U&I"Z#+0]B*+,@&&=,M ?^&&o+ !"J 0 &I"Z#+8+#9+$6+LI@+6+,@&, 5 0hW&#A, 5 #Zr pM&I"Z#+6+,@&)+X+,@&?c	+"G0 pjZM'O+$%0 !Ir ,BO+,I&3ZK&?b?$% ? 4 4 0,#bI&9,* ?$%+'KNU#] 45512 5 45S,*0 m,I#3+k+I"GU#B*I+ B,?G#H551B,?G#Hd551 +k,&W&B&3W&&W&U0]B*W2I>+B,I'I+J !Ir ,#UK&#Z*+@+,IV4d05 pY #<+'O+ 'K:,#\&=,*,*+W&#;I0hW&#AAK >I# ?6&=,#UK&V 5 #Z&U&!)+J !Ir #:*:&6 4 4 4 4 S 4 Ω d ?* HN+I-#U&3I>#U#+ SV ξ = _&345 F µ O'H&3#UN>?60 ,0 d 4 Ω BO'H&\d0]K#UK& r ξ S d &=,_J 0 hW&#A d #Z&O+I>G d &^&#:K&O+I>#3J !ISr •++f&&3W'K 4 #Z'(*M <+'@?$%+*4S5'+Q*<#>?G&,5*, b #;I+EVI,*f*,W0+f&?*#‚,&3 '@?$%+4'+0g>"+45*X 0DT"LW&#A#?6?^&ƒJ !Idr j<*MW+IO++3&6_&&K&=,>I'K &. &•+&;IE/M0`HIAHM f&_&&K*#:5&*B .AH&*0H)+.+$7+%2#bI)+?b.,I' A& &I"Z0 ,0 j!"?>I'K+BJ]KGI&^&=,>I'KJ 0 `HI#<G**>I'K9,&3y 4d5&*W6>I'KG#-+ _&B>".&W&U>I'K5&*0hW&#AAKMJ !Izr `GI&W&#U@*,W$%+k,M*< 28++G+*&\ •+?^&'H0H)+*<28+ +G+'O+?*M^$%0 jqq` * F r J „… `†}…`n f&;I $/+?&;I&I"Z#+0 HI?G&;I $/+,#$%&r ,Mr m g T m a− = Mr T N m a µ − = ( ) X N m g m g m g m m a m g m g a m s m m T m g a N µ µ = ⇒ − = + − ⇒ = = + ⇒ = − = n,@&r Xa a a m s= = = Mr 5 m g T m a a− = + Mr 5 5 ms T F m a N m g a T m g a m a µ − = = − ⇒ − − = ]QI",r 5 5 5 m g m g a m a a m a m m a g a m m µ µ − − = + + + ⇒ = − − 5 X S X a a m s a m s = = ⇒ = jZM'O+$%,450 5 5 Xa g m s⇒ = = nf*?'@?$%+ZK&'K+B0 gc&#bIr 5 5 mRTm PV RT P V µ µ = ⇒ = gc&,Ir m RT m RT m RT P V V V µ µ µ = = = d m m m m V V V V V = + + = + + = 6* * * ?'@?$%+ZK&'K+*lB,I' I+0 5 d d d m mP m m P m m m m m m = = = + + + + ]r 5 05S S m T m T m T m T P P atm P = = = = ⇒ = ⇒ = = N r T r P r ms F r P r T r $ $$ V V V F r F r F r * F r P r T r 5 F r