to 2010 hsc... · "# $%&$'()$#* (+ -.(/, (0 (*+ /$+(1# -..23+ (* *2 +45$++04..6 *$+*...

13
m S v 2 o r = GM E m S r 2 v o = GM E r T = 2πr v o r 3 T 2 = GM E 4π 2 t v = t 0 1 - ( v c ) 2 t 0 = ( 1.0 × 10 -6 s ) 1 - 0.9999 2 = 1.4 × 10 -8 s(2s.f.)

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Page 1: to 2010 HSC... · "# $%&$'()$#* (+ -.(/, (0 (*+ /$+(1# -..23+ (* *2 +45$++04..6 *$+* - /$+('$/ 76&2*7$+(+! 8# *7(+ 5-+$9 :(57$.+2# -#/ :2'$.6 -()$/ *2 )$-+4'$ *7$ ,$.25(*6 20 *7$

!"! #$% &'()*+) ,-./

!"#$%!&' () *+,,) -#,./01) 2 !"#$%&'()*')!'+"!#,3

!"#$%&' (

45

60(%$+" '.117 %' 8%91& ()

mSv2

o

r=

GMEmS

r2

vo =

GME

r

'! + ',+""10 0+7%#' !: !0(%$ ,1+&' + "+0810 !0(%$+" '.1175 */1 .10%!7 !: !0(%$

%' 8%91& ()

T =2πr

vo

;/%</ ;/1& '#('$%$#$17 %&$! $/1 1=#+$%!& :!0 !0(%$+" 91"!<%$) )1%"7' >1."10?'

@07 "+;

r3

T 2=

GME

4π2

:0!, ;/%</ ;1 '11 $/+$ + "+0810 0+7%#' ,1+&' + "!&810 .10%!7 !: !0(%$5

!"#$%&' )

A5

!"#$%&' *

B5

tv =t0

1−(

vc

)2

t0 =(

1.0× 10−6 s)√1− 0.99992

= 1.4× 10−8 s(2s.f.)

C

Page 2: to 2010 HSC... · "# $%&$'()$#* (+ -.(/, (0 (*+ /$+(1# -..23+ (* *2 +45$++04..6 *$+* - /$+('$/ 76&2*7$+(+! 8# *7(+ 5-+$9 :(57$.+2# -#/ :2'$.6 -()$/ *2 )$-+4'$ *7$ ,$.25(*6 20 *7$

!"#$%&' (

!

"#$ %&'()*#&+,'-('. -(/ &, ., &#)% 01$%&),2 )% &, 2,&$ &#(& &#$ 34 51%&

)2)&)(66/ 7$ ( 6,8(6 5(9 :)& *$&% %6,-$' (% )& 5,;$% 1<-('.= (2. &#(&> (% &#$

#,')?,2&(6 8,5<,2$2& ,+ &#$ ;$6,8)&/ )% 8,2%&(2& -)&# &)5$> &#$ 34 8(2 2$;$'

<(%% &#',1*# ?$',! @26/ %(&)%A$% &#$%$ 8,2.)&),2%!

B2 5,'$ .$&()6> &#$ '$6(&),2%#)< 7$&-$$2 ;$6,8)&/ (2. &)5$ +,' <',C$8&)6$%

)% 6)2$(' +,' &#$ ;$'&)8(6 8,5<,2$2&

vy = uy − gt

(2. 8,2%&(2& +,' &#$ #,')?,2&(6 8,5<,2$2&! D,' (2 (2*6$ ,+ 45o uy = ux =u/√2! "#$ '$6(&),2%#)< 7$&-$$2 E)2$&)8 $2$'*/ (2. &#$ #,')?&,2&(6 (2. ;$'F

&)8(6 8,5<,2$2&% ,+ &#$ ;$6,8)&/ )%

KE =m

2

(

v2x + v2y)

=m

2

(

u2

2+

(

u√2− gt

)2)

=m

2

(

u2 − gtu√2+ g2t2

)

-#)8# )% ( 8,28(;$ 1< <('(7,6( -)&# ( /F)2&$'8$<& ,+ mu2/2!

!"#$%&' )

G!

v =d

t

=5× 2π × 1m

3 s

=10π

3ms−1

(2.

Fc =mv2

r

=(0.2 kg)×

(

10π3

ms−1)2

1m= 22N

H

Page 3: to 2010 HSC... · "# $%&$'()$#* (+ -.(/, (0 (*+ /$+(1# -..23+ (* *2 +45$++04..6 *$+* - /$+('$/ 76&2*7$+(+! 8# *7(+ 5-+$9 :(57$.+2# -#/ :2'$.6 -()$/ *2 )$-+4'$ *7$ ,$.25(*6 20 *7$

!"#$%&' (

!

"# $%&$'()$#* (+ ,-.(/ (0 (*+ /$+(1# -..23+ (* *2 +45$++04..6 *$+* - /$+('$/

76&2*7$+(+! 8# *7(+ 5-+$9 :(57$.+2# -#/ :2'$.6 -()$/ *2 )$-+4'$ *7$ ,$.25(*6

20 *7$ $-'*7 '$.-*(,$ *2 *7$ -$*7$'9 -#/ *7$(' $%&$'()$#* 3-+ ,-.(/ (# *7-* (*

52''$5*.6 4*(.(+$/ (#*$'0$'$#5$ $;$5*+ *2 &'2/45$ -# $%&$'()$#*-. /$+(1# *7-*

3-+ 5$'*-(#.6 -554'-*$ $#2417 *2 )$-+4'$ *7$ /('$5*(2#-. /$&$#/$#5$ 20 *7$

,$.25(*6 20 .(17* *7-* 3-+ -#*(5(&-*$/ 1(,$# *7$ $%&$5*$/ ,-.4$ 20 *7$ ,$.25(*6

20 *7$ $-'*7 '$.-*(,$ *2 *7$ -$*7$'!

!"#$%&' )

<!

WE = 9.8ms−2 × 2 kg

= 19.6N

-#/

WE = 3.6ms−2 × 2 kg

= 7.2N

!"#$%&' *

=!

-5> $)0 (+ &'2&2'*(2#-. *2 *7$ +&$$/ 20 '2*-*(2# 20 *7$ )2*2'9 -#/ 2&?

&2+$+ +4&&.6 $)0! @7$ 54''$#* *7-* A23+ (+ 1(,$# B6

I =εsupply − εback

Rcoils

+2 37$# *7$ )2*2' +.23+ /23#9 B-5> $)0 /$5'$-+$+9 *7$ 54''$#* (#5'$-+$+ -+

/2$+ *7$ &23$' C-#/ +2 7$-*D /(++(&-*$/ (# *7$ 52(.+!

!"#$%&' +

=!

E2' - &-'*(54.-' -)24#* 20 &23$' *7-* (+ *2 B$ *'-#+)(**$/9 P = V I 3$5-# 5722+$ *2 *'-#+)(* $(*7$' -* 7(17 ,2.*-1$ -#/ .23 54''$#* 2' ,(5$?,$'+-!

@7$ &23$' /(++(&-*$/ (# *7$ *'-#+)(++(2# .(#$+ (+ 1(,$# B6 P = I2R +2 (+

)(#()(+$/ B6 )(#()(+(#1 *7$ 54''$#*!

F

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!"#$%&' ()

!

"#$ %$&'()*+, -% &'(($&.$) .' .#$ /'*)0 .#$ 1+-2*+, .' .#$ 34 5'/.*6$

%'7+&$0 *() .#$+$ *+$ 2'+$ .7+(% -( .#$ %$&'()*+, &'-/ .#*( -( .#$ 1+-2*+,0

%' -. -% * %.$1 71 .+*(%8'+2$+!

!"#$%&' ((

"#$+$ -% ('. $('76# -(8'+2*.-'( .' &#''%$ 9$.:$$( ; *() ! <$. 2$ 1+'5-)$

*( $=1/*(*.-'( .#*. :-// 9$ *&&$%-9/$ .' *(,'($ :#' -% 8*2-/-*+ :-.# &*/&7/7%!

"#$ $28 -()7&$) -( .#$ -(($+ +-(6 -% 6-5$( 9,

ε = −dΦB

dt

>+'2 .#$ -(8'+2*.-'( -( .#$ ?7$%.-'( :$ &*( .*@$

dΦB

dt> 0 %' ε < 00 -!$! .#*.

.#$ &7++$(. A':% -( .#$ '11'%-.$ )-+$&.-'( -( .#$ -(($+ +-(6 .' .#$ '7.$+ +-(6!

B#*. .#$ ?7$%.-'( )'$% !" .$// 7% #':$5$+0 -% #':

dΦB

dt-% &#*(6-(6 :-.#

.-2$0 -!$! -. )'$% ('. .$// 7% .#$ %-6( '8 .#$ %$&'() )$+-5*.-5$ '8 .#$ &7++$(.

-( .#$ '7.$+ +-(6! "#$+$ *+$ C 1'%%-9-/-.-$%D

E! "#$ &7++$(. -( .#$ '7.$+ +-(6 -% -(&+$*%-(6 *. #! $"% " +*.$0 -( :#-&#

&*%$ ε < 0 *() -% &'(%.*(.0 %' .#$ &7++$(. -( .#$ -(($+ +-(6 -% */%'&'(%.*(.!

F! "#$ &7++$(. -( .#$ '7.$+ +-(6 -% -(&+$*%-(6 *. *( & #'(%$& ) +*.$ -(

:#-&# &*%$ ε < 0 *() -% 6$..-(6 2'+$ ($6*.-5$ :-.# .-2$0 -( :#-&# &*%$.#$ &7++$(. -( .#$ -(($+ +-(6 -% -(&+$*%-(6 -( 2*6(-.7)$ :-.# .-2$0 '+

C! "#$ &7++$(. -( .#$ '7.$+ +-(6 -% -(&+$*%-(6 *. * *(#'(%$& ) +*.$0 -( :#-&#

&*%$ ε < 0 *() -% 6$..-(6 2'+$ 1'%-.-5$ :-.# .-2$0 -( :#-&# &*%$ .#$&7++$(. -( .#$ -(($+ +-(6 -% )$&+$*%-(6 -( 2*6(-.7)$ :-.# .-2$!

!"#$%&' ()

;!

v ∝√r

v2 ∝ r

"#7% v2 5$+%7% r :-// 9$ * %.+*-6#. /-($ 6+*1#!

G

Page 5: to 2010 HSC... · "# $%&$'()$#* (+ -.(/, (0 (*+ /$+(1# -..23+ (* *2 +45$++04..6 *$+* - /$+('$/ 76&2*7$+(+! 8# *7(+ 5-+$9 :(57$.+2# -#/ :2'$.6 -()$/ *2 )$-+4'$ *7$ ,$.25(*6 20 *7$

!"#$%&' ()

!

!"#$%&' (*

"!

!"#$%&' (+

#!

mv2

r= qvB

r =mv

qB

$% Bnew = 2B &'()

rnew =mv

qBnew

=mv

q2B

=r

2

!"#$%&' (,

*! #+ &'( ,-.'& '/)0 ,12(!

!"#$%&' (-

! 3'( (2(4&,-4 /)0 5/.)(&-4 6(207 517& 8( 9(,9()0-412/, &: 9,:;-0( (<1/2

/)0 :99:7-&( %:,4(7 :) &'( (2(4&,:) 8(/5!

!"#$%&' (.

"!

!"#$%&' (/

#!

=

Page 6: to 2010 HSC... · "# $%&$'()$#* (+ -.(/, (0 (*+ /$+(1# -..23+ (* *2 +45$++04..6 *$+* - /$+('$/ 76&2*7$+(+! 8# *7(+ 5-+$9 :(57$.+2# -#/ :2'$.6 -()$/ *2 )$-+4'$ *7$ ,$.25(*6 20 *7$

!"#$%&' ()

! "#$ %&'&() &( *'+,-.$/ 0 (+'1# *+2$ ($0' 1#$ .+&2/ +( 1#$ '&)#1 0(,

0 /+-1# ($0' 1#$ .+&2/ +( 1#$ 2$314 %&1# .-''$(1 1'05$22&() 3'+6 1#$ *+/&1&5$

1$'6&(02 1+ 1#$ ($)01&5$ 1$'6&(02 1#'+-)# 1#$ .+&24 /+ 78 1#$ '&)#1 #0(, '-2$

1#&/ .+67&(01&+( %&22 '$/-21 &( 0 .2+.9%&/$ '+101&+(!

!"#$%&' (*

:()2$ : &/ 1++ /#022+% 0(, 1#$ /*0.$.'031 608 /9&* +; 1#$ 016+/*#$'$! :()2$

< 1+ 1++ /1$$* 0(, 1#$ ) 3+'.$/ '$/-21&() 3'+6 1#$ #&)#$' ,$.$2$'01&+( 608

7$ 1++ )'$01 3+' 1#$ /*0.$.'031 0(, &1/ =*+//&72$> +..-*0(1/ 1+ /-'5&5$!

!"#$%&' ((

!"

vx =∆x

t

=300m

21 s= 14.3ms−1

#"

∆y = uyt+at2

2

uy =∆y

t−

at

2

=−150m

21 s+

(1.6ms−2)× (21 s)

2= 9.66ms−1

?

Page 7: to 2010 HSC... · "# $%&$'()$#* (+ -.(/, (0 (*+ /$+(1# -..23+ (* *2 +45$++04..6 *$+* - /$+('$/ 76&2*7$+(+! 8# *7(+ 5-+$9 :(57$.+2# -#/ :2'$.6 -()$/ *2 )$-+4'$ *7$ ,$.25(*6 20 *7$

!"

!"#$%&' ()

#"

!" #$%&' &( %))"*"$%#&'+ #, #!" *"-#.

/,#"0 1' %))"$%#&,' #, #!" *"-# &( ,))2$&'+ $"+%$3*"(( ,- 4!"#!"$ #!" #$%&' &(

5,6&'+ #, #!" $&+!# %'3 (*,4&'+ 3,4' ,$ 5,6&'+ #, #!" *"-# %'3 (7""3&'+ 27.

$"

, %' ,8("$6"$ &' #!" %))"*"$%#&'+ $"-"$"')" -$%5" ,- #!" #$%&' #!" 5%((

4&** %77"%$ #, "97"$&"')" % !,$&:,'#%* %))"*"$%#&,' ";2%* #, #!" %))"$%#&,' ,-

#!" #$%&' <82# &' #!" ,77,(&#" 3&$")#&,'= %'3 % 3,4'4%$3 6"$#&)%* %))"*"$%#&,'

,- 9.8ms−2 32" #, +$%6&#>. !" $%#&, ,- #!"(" #4, %))"*"$%#&,'( &( #!" (%5"%( #!" $%#&, ,- #!" !,$&:,'#%* %'3 6"$#&)%* ),57,'"'#( ,- #!" #"'(&,' &' #!"

?

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!"#$%& ' !() *+!( ,#-- .) *+"+--)- !' !() /#")0!#'$ '1 !() !"#$% .)1'") #! ,+

02!3

!"#$%&' ()

4)*-)"5 -+, '1 *)"#'/ #

r3

T 2=

GM

4π2

6! 0+$ .) *"'7)/ 1'" 0#"02-+" '".#! #$ !() 0+ ) ,()") '$) .'/8 9,#!( :+

M; # :20( :'") :+ #7) !(+$ !() '!()" .'/8 9,#!( :+ m; .8 )!!#$%

!() 0)$!"#*)!+- 1'"0) ")<2#")/ !' =))* !() :+--)" .'/8 #$ :'!#'$ )<2+- !'

%"+7#!+!#'$+- 1'"0) .)!,))$ !() :+ )

mv2

r=

GMm

r2

+$/ $'!#$% !(+!

v =2πr

T

6$ !() 0+ ) '1 !() !)-) 0'*)& !() ")<2#")/ 0)$!"#*)!+- 1'"0) # *"'7#/)/ .8

!() %"+7#!+!#'$+- +!!"+0!#'$ '1 .'!( !() )+"!( !" !() 2$& :)+$#$% !(+! !()

)<2+!#'$ ,#-- $))/ !' #$0-2/) !,' %"+7#!+!#'$+- 1'"0) !)": & ") 2-!#$% #$ +

:'") 0':*-#0+!)/ )>*") #'$ !(+$ 4)*-)"5 -+, '1 *)"#'/ 1'" !(# 0+ )3

!"#$%&' ()

*+,

?() !'!+- :':)$!2: '1 !() 8 !): 0'$ # !#$% '1 !() "'0=)! +$/ !() )>(+2 !

%+ ) "):+#$ 0'$ !+$!& ' !(+! !() 0(+$%) #$ :':)$!2: '1 !() "'0=)! 9,(#0(

# #$0")+ #$% #$ !() 7)"!#0+- /#")0!#'$; # )<2+- +$/ '**' #!) !' !() 0(+$%) #$

:':)$!2: '1 !() )>(+2 ! %+ ) 3

*-,

?() %@1'"0) 9!() +00)-)"+!#'$ +0!#$%; '$ !() + !"'$+2! #$0")+ ) .)!,))$

!#:) t1 +$/ t2 + !() 1'"0) # 0'$ !+$! .2! !() :+ '1 !() "'0=)! # /)0")+ #$%

+$/

a =F

m

A

Page 9: to 2010 HSC... · "# $%&$'()$#* (+ -.(/, (0 (*+ /$+(1# -..23+ (* *2 +45$++04..6 *$+* - /$+('$/ 76&2*7$+(+! 8# *7(+ 5-+$9 :(57$.+2# -#/ :2'$.6 -()$/ *2 )$-+4'$ *7$ ,$.25(*6 20 *7$

!"#$%&' ()

!"

ε = −dΦB

dt

! "#$ %$&'()"* '+ "#$ ,-./$" )! #).#$0 -" 1 "#-/ -" 2 "#$ 0-"$ '+ (#-/.$ '+

"#$ ,-./$")( 345 )! #).#$0 -/6 !' "#$ $,+ )! &-0.$0 )/ ,-./)"46$7

#"

8'"$9 :'0 "#0$$ ,-0;!< "#$ .0-=# /$$6! "' #-%$ - ,)/ "#$/ - ,-5 >-! "#$

,-./$" )! 60'==$6 !'4"# ='&$ 6'?/?-06!@< "#$ )/)")-& ,)/ /$$6! "' '((40 -"

- &-"$0 "),$ >-! 60'==$6 +0', - .0$-"$0 #$).#"@ -/6 "#$ "),$ A$"?$$/ "#$

"?' $5"0$,- /$$6! "' A$ &$!! >-! "#$ ,-./$" )! "0-%$&&)/. +-!"$0@7

B

Page 10: to 2010 HSC... · "# $%&$'()$#* (+ -.(/, (0 (*+ /$+(1# -..23+ (* *2 +45$++04..6 *$+* - /$+('$/ 76&2*7$+(+! 8# *7(+ 5-+$9 :(57$.+2# -#/ :2'$.6 -()$/ *2 )$-+4'$ *7$ ,$.25(*6 20 *7$

!"#$%&' ()

!!"#$%&#'( )%*&#$"+ %$$+"+*%&'*, -%."+/ &*%#(,

0,+ '1

,2!+*$'(32$&'*,

0,+3 #( ,2!+*$'(32$&#(.

4%.(+&, &' .2#3+ $5%*.+3

!%*&#$"+,

0,+3 #( ,2!+*$'(32$&#(.

4%.(+&, #( &5+ &*%#( 6#(

789 ,:,&+4; &' #(32$+

+33: $2**+(&, #( $'#", #( &5+

&*%$< &' !*'32$+ "+/#&%&#'(=

>4!%$& '(

9'$#+&:

)*'/#3+, <('?"+3.+ '1 &5+

,4%""+,& %(3 4',& +@'&#$

!%*&#$"+, #( &5+ 2(#/+*,+

12"A""#(. % 524%( (++3 &'

2(3+*,&%(3

B%, &5+ !'&+(&#%" &'

!*'/#3+ /+*: 1%,& &*%(,!'*&

C D+&&+* &*%(,!'*& %,,#,&,

&5+ +$'('4: %(3 &52, "#1&,

&5+ ,&%(3%*3 '1 "#/#(.

>4!%$& '(

7(/#*'(4+(&

92!+*$'(32$&#(. 4%.(+&,

2,+ % "'& '1 +"+$&*#$%" !'?+*

%(3 &5+*+ #, "'$%"

3#,&2*D%($+ &' &5+

+(/#*'(4+(& 32+ &' &5+#*

"%*.+ ,#E+

F'$%" 3#,&2*D%($+ &' &5+

!5:,#$%" +(/#*'(4+(& 1'*

(+? &*%$<,G "+,, ('#,+G 2,+

'1 "#H2#3 B+ 6%

('(C*+(+?%D"+ *+,'2*$+; #(

789 ,:,&+4

I23.+4+(& '1

#4!%$&

9#.(#A$%(& #4!%$& ?#&5#(

&5+ !5:,#$, $'442(#&:G D2&

#(,#.(#A$%(& #4!%$& '(

,'$#+&: %, % ?5'"+G %(3 '(

&5+ +(/#*'4+(& %, % ?5'"+

>(,#.(#A$%(& #4!%$& '(

,'$#+&: %(3 &5+

+(/#*'(4+(& &' 3%&+ %, #&

5%, ('& D++( ?#3+":

%3'!&+3=

!"#$%&' (*

J5+ 1'*$+ #,

F = ∆mg

=(

7.5× 10−4 kg)

×(

9.8ms−2)

= 7.35× 10−3 N

J5+ 4%.(#&23+ '1 &5+ 4%.(+&#$ A+"3 #,

B =F

IL

=7.35× 10−3 N

(0.3A)× (0.2m)

= 0.12T

0,#(. &5+ *#.5& 5%(3 *2"+G &5+ 3#*+$&#'( #, #(&' &5+ !%.+=

KL

Page 11: to 2010 HSC... · "# $%&$'()$#* (+ -.(/, (0 (*+ /$+(1# -..23+ (* *2 +45$++04..6 *$+* - /$+('$/ 76&2*7$+(+! 8# *7(+ 5-+$9 :(57$.+2# -#/ :2'$.6 -()$/ *2 )$-+4'$ *7$ ,$.25(*6 20 *7$

!"#$%&' ()

!" #$%# "& '$($)%*"+ ,-.%$# ./$ 0#$'1 2+$ *# 0#$' %" #).+ %3$ 4$.5 3"/*6

7"+%.--8 .)/"## %3$ #)/$$+ .% . /.%$ #$% 48 %3$ %*5$ )"+#%.+%1 3$ "%3$/ #$%

'$($)%# %3$ $-$)%/"+ 4$.5 9$/%*).--8 *+ ,/","/%*"+ %" %3$ 9"-%.:$ ;%3$ #*:+.-<

.,,-*$' %" %3$ ,-.%$#1 =+ %3$ ).#$ "& %3$ ,.%%$/+ '*#,-.8$' "+ %3$ #)/$$+

*+ %3$ >0$#%*"+? %3$ 9"-%.:$ .,,-*$' %" %3$ 9$/%*).- '$($)%*"+ ,-.%$# 9./*$#

#*+0#"*'.--8 !*%3 %*5$1

!"#$%&' *+

!"

3$ :$/5.+*05 *# ,6%8,$ .# 4"/"+ *# . :/"0, === $-$5$+% !*%3 "+$ -$## 9.-.+)$

$-$)%/"+ %3.+ :$/5.+*051

#"

3$ .''*%*"+ "& 4"/"+ *+)/$.#$# %3$ )"+'0)%*9*%8 48 #*:+*@).+%-8 *+)/$.#*+:

%3$ +054$/ "& 3"-$# *+ %3$ 9.-.+)$ 4.+'1 30# *+ ,6%8,$ :$/5.+*05 %3$

5.A"/*%8 )3./:$ ).//*$/# ./$ 3"-$# !3$/.# *+ *+%/*+#*) ;0+'",$'< :$/5.+*05

)0//$+% *# ).//*$' 48 $>0.- +054$/# "& $-$)%/"+# *+ %3$ )"+'0)%*"+ 4.+' .+'

3"-$# *+ %3$ 9.-.+)$ 4.+'1

BB

Page 12: to 2010 HSC... · "# $%&$'()$#* (+ -.(/, (0 (*+ /$+(1# -..23+ (* *2 +45$++04..6 *$+* - /$+('$/ 76&2*7$+(+! 8# *7(+ 5-+$9 :(57$.+2# -#/ :2'$.6 -()$/ *2 )$-+4'$ *7$ ,$.25(*6 20 *7$

!"#$%&' ()

!"

E = hf

=hc

λ

=(6.63× 10−34 Js)× (3× 108 ms−1)

1000× 10−9 m

= 1.99× 10−19 J

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