analise de dados
DESCRIPTION
Apostila de Análise de Dados LaboratorialTRANSCRIPT
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s s r
rtr s
rs
r
-
s s r rtr s
-
t
s ss rst s
tr
rs ss rs
s s rs ss
rss sts
rs rrt
rs rss sts
str
t s
rts
rs
stts rrs
rrs
rt
Prs t
str str sttst
r s
r
s r
s r
rt r rt
s rs rt
rt
rs
strs sttsts
str ss
str t tt
str trr rtr
rs
rs s rs
tr
str rs
s rs
ts tr s ts a b
t r
t s s qrs
rs
s s r rtr s
-
rs s rs
s s
s rt
P
s s r s s
s s
s s r s s
rs
s s r rtr s
-
rst
st tt stt tr r trtt s ts s ts st
tsts r t sr s r stts s rss ts
rtr s r t rrr s stts r sr
t r s r stts rts rrs s s ss
rts rts tr rtrs ss rtr sts rs
rs rs trs rs rts tt trr stt rr
tr sts s rtr s s ts s rtrs
r s ts q t r r ss tr rr r
r s ts trs s s s ts s s tr
sttst srs ss q stt q sr ss tr s
ss r s r s s s q ss rtr t
rss s rs r
s ts s ss rst s sr rs r q stt
ss s rr s ts ts s ss rs ss rs
rss sts rrs rrt t r r
s sr s ts sttsts sttsts ss r rst s stts
rrs rts rss s rs tr rs t rrs rts s
rtrt sts s s s rts ts rt ss
s ts rt rt t s rs st t
t r rs sr s strs sttsts trs rqtt ts
s s r rtr s r t s s trt
t s r rs rs rs ss t s ss
r tr rtrs ss trss
s s r rtr s
-
s s r rtr s
-
t
s ss rst s
tr
s t st tr ss s s s ts tr
s sttts trs tr s tr s ts ss ts Prtrt
sts t ss sss ss rs str
s rrs tr rts rrs rs sss s rs rt ss
rt t ss st t t st
st ts sr r str rt rr t sr
sr r s rs r r rtr sr sr s
ssr trss t str rs ts
rst r srr t st ts sr s rs s
rsts r rr ts t s str q r r r
r ts stts q s s sts s s qttts s
sr rsss r s tts ss r s str s st t q
s r qtttt s rs ss rtt rr s r
tt srr q rtt ts s trs ss s rrst rs s
rt r ss rtr s s ss s s s
ts ss ts rss s r trs sts Pr
q s s s rs s r t ts rtsts
r ts s t ssr rr qt trtt srt
tr t s trs rts s q s st s
s tr t t
rs ss rs
s s rs ss sr rsss trs s s ts r
s rr qt r tr qt s
r r s Pr tr r tr rss
ss rr rs s r r rs ss trs r tr 14a
r r sr Pss s rr s st rs ss ts
strs q stt s st tr s Prtrt
st trts st s trs rrs rs ss ts r
t ss t ss sst t sst tr r
s s
s r q rt 10 m ss qr r q rt qst rrs s rt r tr s s trs
rs r r trq s rs sts trs s st
s s r rtr s
-
s ss rst s
r
rt tr rt trt rrr rt tr
t 1/299.792.458 s
t s s r 9.192.631.770 rs r rrst trs
tr s s rs st t t s
ss r ss rtt tr qr stt sttt
tr Pss s rs r
rrt
tr
r ts rrt tr stt q t s
trs rs rts rt t s rr
sr sts st tr tr s r
tr sss s trs r 2 107 t r tr
rt
qt
tr
qt tr sst q t tts ts q
ts ts stts 0, 012 qrs r
trtr r 1/273, 16 trtr tr t tr
ts
s
ts s r t q t
r rt rq 5401012 rt rt s
ts rt ss r 1/683 tts tt
s r srr
Prs sst tr s
r s
r M L/T 2 1 kg m/s2 = Newton (N)r M L2/T 2 1 N m = Joule (J)Pt M L2/T 3 1 J/s = watt (W ) L/T m/sr L/T 2 m/s2
s M/L3 kg/m3
ss s s rs ss
sts s sts rs
st sts s rs s ts sts s s s rs
ts ts s ts 10 s rs sr s qqr ss103 s 1 milisegundo 1 ms 106 W 1 megawatt 1MW
s s rs ss
r s sr sr ss s trs
s rt s rt rt x r s X rst tr s t t s r s s tr
rt r r rrt tr rtr
ss tr t rtr
rt q rst r tt q r sr
trs rtt srs s tr v rr sr t trs st rrr x tr t t, sv = x/t
s s r rtr s
-
rss sts
t r
1018 t 1015 t 1012 109 106 r 103 102 t 101 101 102 t 103 106 109 1012 tr 1015 t P1018
Prs ts sts t 10
s rs ts s r q s r r s
rs st st qqr r s t q s r s rs
q s r sr r sttst r rrst
r rr r s s st sr rt s rr qt
r s s r rr r q sr t r
rt r rt s r tr tr rt s
s r rr r r rr r rr r s r
stt r rr rr st q r q s rt q sts
tt r rst r r rstr
ssr rr q s r q rrst r s Pr
s ss ssr ssr rr s r qqr
rss sts
r s sr r r s q s
rr r s rs q s r t st t rt r rss
q s s r rrstr s s r s ss s tr st s rss q
s t rt str rrts s rs s sss rss s s
rss sts s qt rss r s
rt r rss sts st rtt rs
r q qt s rs r r rss sts Pr
ss q s q rt s 64, 5 mm s q s rss 6 4s ts 5 rs s st rt st trst s rs s st s rss s sts sr sst
srs ts r tr rrts
s rss sts sr trs r s sts rrs
rs
rs st s rs sqr rr rs rt r ss
t qqr t s s s l = 32, 5 cm l = 0, 325 mrrst s t rss sts 5 = 0, 5 10 = 0, 05 102 =
s s r rtr s
-
s ss rst s
s r tr
0, 005 103 ss 1 rs st 26 = 2, 6 10 = 0, 26 102 = 0, 026 103 ss2 rss sts 0, 00034606 = 0, 34606 103 = 3, 4606 104 ss 5 rsssts
r rt rs st t rs st Prtt l = 32, 5 cm l = 32, 50 cm s rts s rr t 3 rss sts qtq s s rs t 4 rss sts
st r st tr rss sts Pr l = 3, 25 m t 3rss sts qt q l = 3, 025 m t 4 rss sts
s trt s tt s r r q 5 = 5, 0 = 5, 00 = 5, 000trtt q s rsts s s sr rr q 5 cm 6= 5, 0 cm 6=5, 00 cm 6= 5, 000 cm q sts s t 1 2 3 4 rss sts rstt trs rs rs s rt
rs rrt
rrt sr t rss rs r r
tr q rt sr ss
r sss rs s rrs rrt s
t rs r sr sr t s rs sr srt
s rr 423, 0012 = 423, 001
t rs r sr sr rs s rs
sr srt s srr 245, 6 = 246
s rs srt sr s s srt str qsqr
trs rss rts r t rs t sr rs
2, 0502 = 2, 1
s rs srt sr s s srt s str
rs str tr rs t rs t sr rs
st s r r s 4, 3500 = 4, 4 ; 1, 25 = 1, 2
rrt sr t st st s r rrt rr
t t r t rs r rrr t s tt
ss r t t r s qr rrt sr rs
rs rss sts
str
s s str s rs sr s rss sts
rst tr rs r r rs Pr st
r s
s s r rtr s
-
rs rss sts
12, 56 + 0, 1234 = 12, 6834 = 12, 68
r 12, 56 t qtr rss sts t rs st 6 q s s tss r 0, 1234 rst t qtr rss sts s trs st 4 s s s ss t rs st rst str s s r r rs ss 12, 56Prtt t rs st rst str s s tss
t s
t sr s rss sts rst tr s
r rss sts r r qt rss
sts Pr st r t
3, 1415 180 = 5, 65 102
r 180 rst trs rss sts s r 3, 1415 rst rsssts rst tr s trs rss sts
rts
r ss s rst rt r rss sts
s rt Pr r ln(5, 0 103) = 8, 52 st 2 rss sts rt rtt ss s rt s r ln(45, 0) = 3, 807st 3 rss sts rt rtt ss s rt
Pr ts s ss rtt q s rs s ts s ts s rss sts
q rrt s t st rst
rs
ts rss sts st s rs rs
12, 5 cm
0, 00020 kg
3 108 m/s 6, 02 1023 1, 03 106 s 30008, 00 cm/s
rrt s rs r s rss sts
25, 38 cm
2, 361 m/s
9, 563 103 s 3, 45 g
7, 96 106 m 0, 0335 J
3857 N
s rs tts sr s rss sts
s s r rtr s
-
s ss rst s
235 m+ 32, 2 m 2, 052 m
2, 02 105 g2, 1 cm3
ln(351, 0)
s s r rtr s
-
t
stts rrs
rrs
r t rs q r rr rst rt rr rst s r rr r s sr q r rr sr tr rt ts r r
rr r rr rr sr st rt rr st abs t r r tr r xmed r rr xverd st
abs = xmed xverd Pr tr rr rt rel t r tr rr st abs r rr xverdst
rel =absxverd
rr rt t sr rst trs rts t q r 100% str r rr rr rt st rr
s tr s ts rrs sr sss trs sts trs
rrs rssrs rr t rt r str rr
s s tr s rr ss rrs t sr ts
rt s s s
rrs stts s rrs sstts s ss r ts ts r
sr s ss sts q s s ts st sst
tt r r r t s ts rrs
sstts s
r t trs t s r q trs t sr t r stt t rr r r tr ss
ts ts rt rr t q r trtr t
s tr t r t rsst r r r s t q t
rtr tr
rrs trs s ss rss rts ss trs q
r rt srs ssss q s s s rss
P tr rs rs tr s s strts qs rs s
s s r rtr s
-
stts rrs
s ts rss trtr ts rs t trs rs
rr srr q st sts ts rtr s
rt
rt u rtr ss srs rs q sr rttrs sr rt r rst
rt t t t r rr r s r r
r t t rss rtt srt
s ts rt sr rs s trs t
rts rts s rts uA s qs stsr ts sttsts trs r rr rrstr rts q
rtrs sttsts trs t s r t
sr sr strrt s rts uB s s r t ts ts s rs ss sr s rs sr q s ts
r rtrs sttsts trs s rs r s rs r
t rtt r s rrs trs rs ss
rt s rs r rts r ts s rr trs
s r rss rr s s ssrs r
t rs ss r rt s rt
sr srs rr tr r ss s s
s s r rt ts trs
r t rr q s r sss ts sr Prtt rt
rst sr rr s rst
tr rtt r r rtr
r st r sq tr r tr rt ssttr s
t rt st tt rss rt tr
rt tr rt tt t t tr
sr ss q t rt rst r rst
t st rs s rt tr qs
q trr r trr r s
Prs t
rs st ss strt r r
r r srs sttst r r rss sts rs
sr rt rst st r rs rs r rs s
rs sr srt r rs trs ts s r r
Pr tr t t r q r
t s rr ss r rr t r s r r
r r rr s tr r rs r s r r
s ssrt r t r strt str sr
r r rs r rr t sr srt trs rr
st rr rt
r tr r tr rs t r srs
rts sr t tr tr qt trr r rr
t sr tr s r ss tr Pr tr rs sr tr
s r ss rt t str s rts sss srs
s s r rtr s
-
str str sttst
rts sr
Psss ts ts str r tr rs t
t rs t tr r tr rr rt u q rr st r r rr t Pr tr
q rt st r s r ssrt r rr
rs
str str sttst
str sttst t s rtrs
rr rs sr r str s q r rr
stt rt s t r ts st t st trs
r sttst rtt r sttst q t r t r rs
rtr str rrstt
s sr rs rs r r rrs rqs
tr r t rts trs rs tr ss
str rqs trs ss sr rst r r
str r str t t s rrsts s
ts s rs s 32 s tr tr rs r r rs r rst str srs q s s t
s t q rtt ss strr str rqs srs st
rts trs ss s rqs s tr ss sr strs
str t str rqs sr t s r
s t tr r tr str rrstt t
s ss strs str
srs q r trs ss str rs q r
s str t rrt ss rss s ts rr srr s
s sr trs stt s trs ss s strtr rrss
t t r q r s t t sss s str
trsrs r s str tr str t sq
q t t r sr trt tt ss str rq
t q r sr str r r s sss
s rts tr r s tr t ts
s s r rtr s
-
stts rrs
s ts s s str rqs s ts st trs
sss str rstt ss str
s s sss s s rs rrs rtr t ss rrs
ts rs sr t rss r s
tr t ss tr r st r s r s rrs
str rrst st ts s tts q s rt
rt str str t sq tr
s s s srs s str s sts strs
t t r s str r str rrst
str t sts q s s st ts rs Pr
tr r s q r r q s s s s
r rt r s
str Pss t sts q s ts s ts q
s s trs Pr tr r ts q ss r
tr t r t rts ts
str ss r t r strs rs r r s
n > 30 Pr s ss rtrst rtr str sttst ss tr s t st s rsss s rrs sss
tr rt r s rs ss
str t tt st str ss r q s s ss strs rs qqr r s
s s r rtr s
-
r s
r s
r s s r rtt rs s rts ts
s r s q r trt r r stt r sr ss
r n r tt s trs ts xi s r X t r sr r
x =ni=1
xin
s s st s rtt s ts s s
s tr r t tr trs ts r
r st stt r srs s s s tr r
n r tt s trs ts xi s r X t s sr r
dm =
ni=1
|xi x|n
s t rqtt r rr rs s rs rs
r rs r rs s s
r
sttst t r s rqtt r srr t srs
t str r r
rr s r str s s r xit r n trs ts s r X r
2 =1
n
ni=1
(xi x)2
x r t s n trs ts q s rs s t trr r t r sss ss
ss str ts t r str r
S2 =1
n 1ni=1
(xi x)2
x r str q t sr q s q r ns r tt trs ts str q q
ts
S2 =n
n 12
ttt 2 s r n n 1 sstt r s n 1 n S2 rq str stt q s rt r r rs rs n st st ss
s r
s r s r rt s qrt rtr srs
s s s tr r t tr n trs ts
s s r rtr s
-
stts rrs
s r stt rt r t r s
r r r t Pr s r r qr
st r ss r q s r s r
=2 =
ni=1
(xi x)2
n
s r str
S =S2 =
ni=1
(xi x)2
n 1
q sr tt srt st r
=
1n
ni=1
(x2 2 xxi + x2i
)=
1n
ni=1
x2 2 x 1n
ni=1
xi +1
n
ni=1
x2i
=
n x2n
2 x x+ x2 =x2 2 x2 + x2
=x2 x2 q stt t sr t q q sq t
x2 =(1
n
ni=1
xi
)2
x2=
1
n
ni=1
x2i st
ni=1
(xi x)2 = n(x2 x2) = n
i=1
x2i 1
n
(ni=1
xi
)2
s r
s r s r rt s r tr
s r str S q r qr r tt n s trsts st
m =Sn=
ni=1
(xi x)2
n (n 1)
st rss stt r r rt x r s r q sr rss s trr s r str S qrtt t r tt n trs ts rs s r m trs r r tr 1/
n Pr sr s t rss srs r s trs rtrs s r sr t
r rr s rts trs s rts rs s rtrs s
r rt s r m sr t q s q q st
s s r rtr s
-
s r
r m
i xi x2i
ts
xi =
x2i =
r s r
r m
i mi (g) m2i (g
2)
3, 002 9, 012
3, 015 9, 090
2, 915 8, 497
2, 998 8, 988
ts
mi = 11, 930
m2i = 35, 587
s r r ss t
m =1n
1n 1
[ni=1
x2i 1
n
(ni=1
xi
)2 ]
Pr ts rts s rrrr t n = 5 rr r s r m rtr q s s strs s t sr sstts rtt q r r r s
tr m
trs s r r qtr s ss t s
rsts trs r 3, 002 g 3, 015 g 2, 915 g 2, 998 g r m rt u(m) ss s s trs ss m t r q rt u(m) s s r m s rssrrtt r ss t
r m ss m
m =4
i=1
mi4
=3, 002 g + 3, 015 g + 2, 915 g + 2, 998 g
4= 2, 982 g
rt u(m) sr s r m s strs ss rt s strs ssrs r s r mss r q r rt u(m) sr
s s r rtr s
-
stts rrs
u(m) = m =14
1(4 1)
[4
i=1
m2i 1
4
(4
i=1
mi
)2 ]=
1
2
1
3
(35, 587 g2 1
411, 9302 g2
)
=1
2
1
3(35, 587 g2 35, 581 g2) = 0, 022 g
q sr rtt t rssr rt s 1 rsst Prtt s rrr rt r 0, 02 g s t t r m = 2, 982 g rt u(m) = 0, 02 g r r ss t t st rsst s srr q rt tr st s s
q rt trs ss s rt ss s ss s
r ss rst trs ss s ss s q r ss
sr rr t r s ss s rs
m = 2, 982 g u(m) = 0, 022 g rst m = m u(m) = (2, 98 0, 02) g
rt r rt
t t rt sr rss
rtt r stt r q rr ts s ts rt
sr ss stt s rr rt uc s rrst rr tr s ts s rt sr sss ts rt s
rrs s s ts sttstt ts s trr s s ts
sttstt ts rt srs q r s srs ss ts
rts sttstt ts r s ss st ss s sr trt q
t rt sr s s ss r
s trss t r rt ss r t rtr
s rs ss rts sss ss s rts s rs
s rt t s rs ss tr s r r rt
r s rt t s rs ss s s rrr
ss rss r rt q ss rr
s t q s ss s ss s s
rs s tr qt s r s s t s
q stt f r s s F st stt x r s tr X st
f = f(x)
str rtt r stt f stt x rtx = u(x) r s X s r r rt f = uc(f) r s F
q x s t r r n s r s X s tr q r x s r stt r r rr X ss s s rs sf x sr rs t P r f = f(x) x = u(x) r sttq s s x s rr f(x) r rt tt f(x) t x = x r uc(f)/u(x) sr rt tt r ss t r f(x) ss t st
uc(f) df(x)dx
x=x
u(x)
s s r rtr s
-
rt r rt
rtt r r rt f r rt x
q rt r rt r s s F q st st r s tr X trtt rqt s rst r s s s ts r s
q stt f r s s F s s stts x y s rstsrs ss tr X Y
f(x, y) = x y q ss q q s s X Y s sttstt ts st X t Y ss s trs r rt uc(f) F rst s s trs rt u(x) u(y) s s X Y rstt tts trs u(x) u(y) r uc(f) sr ts ts strr s trs rr s s rs rts s r rr r st
s s rt Pr tr ts sr sst s s trs
t q s ss s rt r r trr s ts
tr s r Pr srr r rrt
sr s s trs rts u(x) u(y) r rt uc(f) s rtr q s rrrr t s r q st
=
1n
ni=1
(xi x)2 =
(xi x)2
s r rss srs s s tr r sr
rr stt r r rt ss s r s qs
rss r uc(f) = f
u2c(f) =
(fi f
)2=
[(xi yi
) (x y )]2 = [(xi x) (yi y)]2
=(xi x
)2+(yi y
)2 2 (xi x)(yi y)
u2c(f) = u2(x) + u2(y) 2 (xi x)(yi y) u(x) = x =
(xi x
)2 u(y) = y =
(yi y
)2s s ss rs x y
rstt trr tr rt q tr r
s qst s s x y s ts ss strr q tr r str ss rst sr st q r r s ts s
rss rtr s ss r q sr
s s r rtr s
-
stts rrs
r rt
f(x) = ax a = stt f = a x uc(f) = au(x)f(x) = xa a = stt f = xa uc(f) = a xa1 u(x)f(x) = ex f = ex uc(f) = exu(x)f(x) = ln x f = ln x uc(f) = 1xu(x)f(x) = sen x f = sen x uc(f) = cos xu(x)f(x, y) = ax by a, b = stt f = a x b y uc(f) =
a2u2(x) + b2u2(y)
f(x, y) = xy f = x y uc(f) =y2 u2(x) + x2 u2(y)
f(x, y) =x
yf = xy uc(f) =
1
y2y2 u2(x) + x2 u2(y)
rsss r s s s rs s rts s s rs
ss s f q ss s rs ss tr ts
u2c(f) = u2(x) + u2(y)
ts q r rs ss s F q ss s rsss tr ts X Y q rr q rtr q
u2c(f) =
(f
x
x=x
)2u2(x) +
(f
y
y=y
)2u2(y)
st q ssr trr t r r sr s r d r rsstr t q s rs f(x, y) r s rs sr ts ss stt tr r ss s ss rq s rs ss X Y sr s tt tr s s rts sts ss
rr s rts s r ts s rs ss s F q ss srs ss tr ts strs
ss t t s r stt f = f(x1, x2, ..., xN ) r s s F s s stts x1, x2, ..., xN s N rs ss tr X1 X2XNsttstt ts ss s rt s sr trs
ts q r
u2c(f) =
Ni=1
(f
xi
xi=xi
)2u2(xi)
xi s rr stt is r s tr Xi q s rs rsf
xi
xi=xis s ts ss r s rs ts xi
r q rss r r stt rt ss s rs
ss tr sttstt ts st s ss rtrs rqtt rs
ts rt s qs s stt ss rr s s rr s
str N rs ss tr sttstt ts q r ss srt rtt q r q st
u2c(x1 x2 x3 ..... xN ) =Ni=1
u2(xi)
s s r rtr s
-
s rs rt
s s s rr t s N rs ss tr sttsttts q t sr t rtt q rtr r s
rst rss rt rt srt trs s rts rts s
ts s
u2c(f)
f2=
Ni=1
u2(xi)
x2i
s rs rt
ts ss rts s rts sss s rtrsts trss
s rs rt ssr r s rt
rss rs sr rs r s s sss rtrsts
q sr ss Pr ss st srr rt q
stt x s t rtt n trs s r s tr Xs s r r stt ss r r
x ss rt rt uc(f) r st rt u(x) ss r trss rt uap(x) ss s rtrsts trs r ss s stt f r s s F sr
f = f(x, xap) = x+ xap
xap stt rr s rtrsts trss r r f = x + xap r s s F rrst r stt ssr q q ts
u2c(x+ xap) = u2(x) + u2ap(x)
uap(x) rt ss s rtrsts trss r s stt x r s tr X st s tr ss rt tr rss ss s u(x) = 0 q rt r s uc(x+ xap) sr rt rt trs ruap(x) st uc(x + xap) uap(x) Pr tr q r s tr X s rrr ts s t rs q rs
r s r sss ss u(x) >> uap(x) q sr strstr rt uc(x+xap) st trs rt tr u(x) st uc(x+xap) u(x)
s r stt f r s s F s stts xi srs ss tr Xi i = 1, 2, ..., N q s q rss rrs s rts u2c(xi + xap) = u
2(xi) + u2ap(xi) q ssttr rt
u2(xi) q st
u2c(f) =Ni=1
(f
xi
xi=xi
)2[u2(xi) + u
2ap(xi)
]
rt
r rt uc s rst t r rssr rt rst r s ss s strs s rs rs s
sr ts s ssr r rt q r tr s rt
rt ue ss s tr r
s s r rtr s
-
stts rrs
tr str sttst rs q sr rt tr sr
rt
ue = kuc
uc rt k tr r ss str sttst rr tr rt r r q r k s s 2 r rt r r s t s str sttst st r rrs r
95% r str ss r q st r strt tt r r r s s tr r k rr tr srs 2 3 rqr r tr rt sr
rs
ssq s rrs ts r s tr s r st s
rssr sstt tr
t rr tr s ts r q st t
r s r s r ttrs
rr qt rt
rt r 1 m r
rrt tr trtr t 350 C rtrr trtr 200 C
tr s ss rt 2000 stts Pr trr tr s stts rtr s trt n = 100 trts t s tr rst tr str
tr trs
r stts
tr s stts s
stt tr s stts s
s r str trs s
t r r q r stt 35 s s trs t q q sr t sr s tr
h0 = 2, 0 m s trs t r s rtr rs 0, 01 s Pr str r str rqs stt tr strstr
tr ss s r trr str
t s trs t q s r rrst r r srs s s
rq str rt r s q s tr tr
t t+
s s r rtr s
-
rt
str rstt s 35 s trs t q sr t
s s r rtr s
-
stts rrs
s s r rtr s
-
t
strs sttsts
str ss
s s rsts sttsts s rrs sts trrt s ts tr
str ss s q str rtr t r r s
n > 30 ss ts s rrs str ttrs s r Pr r ss tr stt rr t rtr
str s rts stt x r s tr X ss ts q q r s rs t str rqs s s
sts st rss r
y = ymaxez2/2
ymax =1
u2 r str z =
x r sttst r x
s s s ts r s r tr str str str s rts xi r s X ssrr q x s r s ts rstt rtr t ymax rr 2 tr 1/2ymax str t q st r tr rr tr t s r sr stt srs tr r
s s s str rtt r str
ss s s s rsts rtrs sttsts trs r str
q t q r n s t t s rss srts r s r t s ss rsts rss ts
tt s r s rs s rtrs r q s stt s ts sss rtrs rtr str s tr
tr str ss str q rt s r ss tst st r 68, 27% t q 68, 27% srt tt q s t t t s ss t s r
s r rt uc rts 68, 27% t r r tr tr z = 1 z = +1 str q s q s t r r s str
qt s s tr rt st str ss sr
s t sttst r r rt ue qt tr r k r sttst z r rt ue sr t rt uc r r rr z s r s st
ue = zuc
s s r rtr s
-
strs sttsts
str s rts xi r s X rststr tr ss
Pr q s t rt uc r z = 2 ts rt ue = 2uc r 95, 45% s rsss s sss rt rts sss s tr
rt s st rt tr t s r
uc m t q ue zm r r z ssr r rs trss str s rs ts ss r tt s rsts s
0, 67 50%
1, 00 68%
1, 28 80%
1, 64 90%
1, 96 95%
2, 00 95, 4%
2, 58 99%
3, 00 99, 7%
3, 29 99, 9%
rs ts z tt s rsts s q srss tr r k s ss strs r r s
rtt rsstr q t rt r str ss
st s rtr r r r s str t r
r qqr r s str t tt st s
str t tt
s s str q r sn < 30 str ss sr t sr r stt rt rst
r qs strs trt s XX r q rs qss tt s sst q sr s
rr r r rts ts qt trss r rr ss
s s r rtr s
-
str t tt
r tt str sttst q r rr s rsts sss rss
r
f(t) = y0
(1 +
t2
n 1)n/2
= y0
(1 +
t2
)(+1)/2
y0 stt q t r s n rss q r r f(t) t s tr t r sttst
= n 1 rtr sttst r rs r r s
q rss t st t rt
str t tt str st r str ss r s s rs t q rr rs t s trs r rt rss str q r str t tt rtr st r rs r t r r st rtr sttsts r str ss str
rs str t tt r rts rs r
str t q rtt str ss r tr r
k s rt ue t r r sttst t r rs r tr rss s q r str ss rt ue sr t rt uc r r r sttst t s r s st
ue = tuc
s s rsss s s ss rt
rts sss s tr rt s st rt
tr t s r uc m t q ue tm
s rss s t rt
r rs r t eff s r r s q ttrt r
eff =u4c
Ni=1
u4ii
s s r rtr s
-
strs sttsts
N r tt ts rts ss ui rt ss is t i r rs r ss is t rt uc rt Pr rt r rs r
q st Ai = ni 1 r rt r rs r t st Bi r eff r tr s tr r tr tt rr rt r r q t
rt str ss sr t s trr str
t tt sr s rr
r sttst t ssr r rs trss r rs r eff str s rs ts t tt s rstss r rts rs r rs r srs q
r t s s s rs t r str t tt q s rs z r str ss q r rs rt t
r rs
r eff
t68,27% t90% t95% t95,4% t99% t99,7%
1 1, 837 6, 314 12, 71 13, 97 63, 66 235, 8
2 1, 321 2, 920 4, 303 4, 527 9, 925 19, 21
3 1, 197 2, 353 3, 181 3, 307 5, 841 9, 219
4 1, 142 2, 132 2, 776 2, 869 4, 604 6, 620
5 1, 111 2, 015 2, 571 2, 649 4, 032 5, 507
6 1, 091 1, 943 2, 447 2, 517 3, 707 4, 904
7 1, 077 1, 895 2, 365 2, 429 3, 499 4, 530
8 1, 067 1, 860 2, 306 2, 366 3, 355 4, 277
9 1, 059 1, 833 2, 262 2, 320 3, 250 4, 094
10 1, 053 1, 812 2, 228 2, 284 3, 169 3, 957
11 1, 048 1, 796 2, 201 2, 255 3, 106 3, 850
12 1, 043 1, 782 2, 179 2, 231 3, 055 3, 764
13 1, 040 1, 771 2, 160 2, 212 3, 012 3, 694
14 1, 037 1, 761 2, 145 2, 195 2, 977 3, 636
15 1, 034 1, 753 2, 131 2, 181 2, 947 3, 586
16 1, 032 1, 746 2, 120 2, 169 2, 921 3, 544
17 1, 030 1, 740 2, 110 2, 158 2, 898 3, 507
18 1, 029 1, 734 2, 101 2, 149 2, 878 3, 475
19 1, 027 1, 729 2, 093 2, 140 2, 861 3, 447
20 1, 026 1, 725 2, 086 2, 133 2, 845 3, 422
25 1, 020 1, 708 2, 060 2, 105 2, 787 3, 330
30 1, 017 1, 697 2, 042 2, 087 2, 750 3, 270
35 1, 015 1, 690 2, 030 2, 074 2, 724 3, 229
40 1, 013 1, 684 2, 021 2, 064 2, 704 3, 199
45 1, 011 1, 679 2, 014 2, 057 2, 690 3, 176
50 1, 010 1, 676 2, 009 2, 051 2, 678 3, 157
100 1, 005 1, 660 1, 984 2, 025 2, 626 3, 077
1, 000 1, 645 1, 960 2, 000 2, 576 3, 000
rs ts t tt s rsts s r rtsrs rs r eff q sr ss tr r k sss strs qqr r s
s s r rtr s
-
str trr rtr
str trr rtr
s strs trr rtr r s trs strs sttsts ts ts
t tt r s trsr sss str
s s ts r s rts q r s s
ts s trs s rss s rt rtt s Pr
str sss s rts r rs r r rss
q s str trr rtr sr t ts ss
s t r sr sr s ss ssrr q t r
str qqr t tr rs rtrs tr a a+ s s tr t rrt s t rs qtr
rtr t rs rs s sss ss rt ss
rss s str rtr str s srr q
r ymax =1
a+ a q r r y(x)x sr
tr r =a + a+
2 r stt tr r sr r
tr sttst rt r tr ss str rtr
=a3
a =a+ a
2
rtr q t tr tr a a+ trs a r
y(x) r sr s s rstt ymax =1
2a = a + a
strs trs rtr r trr
s ss t s t r sr sr ss ssrr q
t r str s r tr stt tr rs tr a a+ s s tr t rrt r tr s s s ss
ts ss s s s qtr rtr rt
rs rs s q s r rr r s s
r tr tr tr s rs sts s sst
strr sss ss rt ss rss s str trr
str ss r r r str trr
s s r rtr s
-
strs sttsts
ymax =2
a+ a =1
a r s q s r str rtr
r tr sttst rt r tr ss str trr
=a6
a s rtr q
rtr rs 0, 1 A s r r rrt i rt tr tr s sst strr rtr
rst rt uap(i) ss s rtrsts trss rtr q t s r st s rss
rrtt r rrt rt tr
tr rrt tr rtr
rtr sr str trr rr rrst s s s
rs st 2a = 2 0, 1 A a = 0, 1 A ss r q
=a6=
a6=
0, 1 A6
= 0, 04 A
tr s sst strr rtr q r rrt
tr i = 0, 75 A r rrt rt tr sr rss rrtt
i = (0, 75 0, 04) A
qtr rs 0, 02 mm s r r tr d st s rsts trs r 8, 40 mm 8, 42 mm 8, 40 mm 8, 44 mm 8, 42 mm r d rt u(d) ss s s trs tr d s t rtr r S =
1
4d2 r S r s t rt r uc(S) rt u(d) rt uap(d) ss s rtrsts trss qtr rt ue(S) r q t 95% s rss rrtt r r s t
r d tr d
d =5
i=1
di5=
8, 40 mm+ 8, 42 mm+ 8, 40 mm+ 8, 44 mm+ 8, 42 mm
5= 8, 4160 mm
s s r rtr s
-
str trr rtr
r d
i di (mm) d2i (mm
2)
8, 40 70, 560
8, 42 70, 896
8, 40 70, 560
8, 44 71, 234
8, 42 70, 896
ts
di = 42, 080
d2i = 354, 146
s r r tr d s t
rt tr sr s t s r
d q s strs s s rt s strsssrs r s r d ss r r s r sr
u(d) = =1
5(5 1)
5i=1
d2i 1
5
(5
i=1
di
)2=
1
5
1
5
(354, 1464 mm2 1
542, 0802 mm2
)
=1
5
1
5(354, 1464 mm2 354, 1453 mm2) = 0, 00297 mm
r S r s t sr
S = 14d2 = 1
4(8, 4160 mm)2 = 55, 629 mm2
qtr sr str rtr rr rrst s rs st
2a = 0, 02 mm ss r q rt trs qtr sr
uap(d) =a3=
0, 02 g
23
= 0, 00577 mm
rt r uc(S) r q sr
u(S) =
(S
d
d=d
)2[u2(d) + u2ap(d)
]=
(1
2 d
)2[u2(d) + u2ap(d)
]
=
(1
28, 4160 mm)2
[(0, 00297 mm)2 + (0, 00577 mm)2
]= 0, 08579 mm2
str ss q r s n = 5 t rt ue(S) sr str t tt str q t = 2, 776 r 95% r r = n 1 = 5 1 = 4 ss s rt sr
ue(S) = tuc(S) = 2, 776 0, 08579 mm = 0, 2381 mm2 rssr rt s 1 rs st t s rrr rt r ue(S) = 0, 2 mm
2 s srr q rt st rr
s q rt trs ss s rt ss
s r r S = 55, 629 mm2 rst trs ss s ss s q r ss sr rr t r s Prtt rsst
sr
S = S ue(S) = (55, 6 0, 2) mm2
s s r rtr s
-
strs sttsts
rs
s rt ss s rs rs s str
rtr trr
ttr s
tr
Pqtr
Pqtr t
trs
rtr
r r rs 1 mm s r r rr x rt y rt rt rst s s trs
x (mm)
y (mm)
s rr x rt y rt rt
s rs s x y s rts u(x) u(y) sss s s trs rr x rt y rt rt rtr r S = xy r S r rt rt rt r uc(S) s rts u(x) u(y) s rts uap(x) uap(y) sss rtrsts trss r r rt ue(S) r q t 95% s rss rrtt r r rt rt
s s r rtr s
-
t
rs s rs
tr
r r q str r tr s rs s
s s rs st rs tr s r r r
s qts t tr ss r t sr r r rstr s
s rts Ps r q r strt t r rr
ss q s s s s r s rr srs r r
ts s ts rts trr r q r s st s rt ss
sss ts r ss r r rtr rr st s ss
srr trs s rt s sr q sr
rrt tr s rs s rtr s s rs s
s s rt s s r qr ss sss t
str rs
s rrs ss q sr ss str rs s
r tt s s st q r s rs s
srr s s rs s rs rrsts ss rsts s
rt sss r t st r s rs s
ss rtr rt r r t
s q t rr
s sr ss r r s t
srs tr rs ts sts s rs 1 2 4 5
s t rs sr tr
sr ss ts q rs s ts sr r s rt rs
s ts q rrst s s rts r r t t s
rst q st rs s s s ts sr t ss
trs r sr r r
sr ss ts q rst r q t r rtt s s
s ssr s s rrsts s ts rts sr s s r
s
s s r rtr s
-
rs s rs
ts s ts rts str rs r rst trr r st
rs ssr sr ts s ts t ss q r ss r t
r ss ssr q r t rr tr t t
rt
str str r rtt rtr r
r s qs rrs rt rt rs sr t rt
s s rrs rr sr sss rrs r stt s
rts sss t rt rstt rss
s rs Ps tr s rsts sts s r sss
s rt s rts trs t rt s sts trs
strs sttsts tr r n s r r r r t rt sr t s s rs s
r r
rst r r r rt y = ax+b s tsr b r a
str s rts rtr r rt s
ts qrs rrst s s rts s srs s rts s
rt r rt t rrst r q r sr r
r x r y
s rs
s rs s qs s qs s rs s st rs r
t
y = ax+ b
t r t r t r rrs
rt s y/x qt q t r t trs rt y r x = 0 sr srs s ts q rt trr ststs rtr s s rts
s s r rtr s
-
ts tr s ts a b
ts tr s ts a b
r sr q sr rrt tr
s rs s rtr rt rs s rs rr
s s qs ts r st sts ss qs sr rr tt
sr trs rs ss r tr sq rst
s ts r trr st r rtr s rts q ss rtt
r rtt tr q sts s s s ts trs trtr s s
s s s
t r
ss t rr q s t r r ts rts (n > 10) st rqr s ss t s s stt s rtrs
rt q r s st s ts rts rtr tr r (x , y) sssts strs sr r
x = 1n
ni=1
xi y = 1n
ni=1
yi
s s rs s s rs x y rstt
rt rt rt q ss r st t r qtr qrts
s st rt t s ts rts st
trr qrt t s Pr s str rt q r s st s ts
rts s t s sr t (x , y) s r trsrtrs r tr t (x , y) t q rt 84% s ts q r trr qrt s qt s qrt
tr s ts a b t r
rt tr sss s t amax rt s r rt ss rt trt y r x = 0 tr t r bmin t s t (x , y) r r t q rt 84% s ts q r trr qrt s qt s qrt rt tr sss
s t amin rt s r rt ss rt trt y r x = 0 tr t r bmax srs q r ts rts ts rt 68% s ts rts q sstt t s r st s sss srs
s s r rtr s
-
rs s rs
rt q r s st sr s ts rts rt q r trr
tr s rts s ts r a r b rt ss rts u(a) u(b) s ts r
a =1
2(amax + amin) b =
1
2(bmax + bmin)
u(a) =1
2n(amax amin) u(b) = 1
2n(bmax bmin)
s s ts rts t rts rs rts s sr s r
t r s r t s rt t sss ss s rt
s rs rr rr t
t s s qrs
st rs t s s qrs rtt s trr t
r t rtr ss t s
st
R (a, b) =1
n
ni=1
(yi ycalculadoi
)2=
1
n
ni=1
(yi axi b)2
ss s rrs str s s (xi, yi) str q t q s ts a b r tr s rs yi s s rs y
calculadoi (xi) s r ss
q trs rs s rrr s rs a b q sts s s
af(a, b) =
bf(a, b) = 0
af(a, b) =
1
n
a
[ ni=1
(yi axi b)2]= 2
n
ni=1
(yi axi b)xi = 0
bf(a, b) =
1
n
b
[ ni=1
(yi axi b)2]= 2
n
ni=1
(yi axi b) = 0
ni=1
yixi + a
ni=1
x2i + b
ni=1
xi = 0 ni=1
yi + a
ni=1
xi + nb = 0
ss t q
ni=1
b = nb s sst qs r a b ts
a =
nni=1
xiyi ni=1
xi
ni=1
yi
nni=1
x2i (
ni=1
xi
)2 b =ni=1
x2i
ni=1
yi ni=1
xiyi
ni=1
xi
nni=1
x2i (
ni=1
xi
)2
s qs sr s rt r rr rsss s rrs
s s s s rs s s rs x y s s qs rr q trs
s s r rtr s
-
ts tr s ts a b
a =
nni=1
xiyi n2 x y
n
ni=1
x2i n2 x2=
n
[ ni=1
xiyi n x y]
n
[ ni=1
x2i n x2]
a =SxySxx
Sxy =ni=1
xiyi n x y
Sxx =
ni=1
x2i n x2
q s
Syy =
ni=1
y2i n y2
Pr tr s s s rs s s rs x y s s q rst
b =
n
ni=1
x2i y nni=1
xiyi x
nni=1
x2i n2 x2=
ni=1
x2i y ni=1
xiyi xni=1
x2i n x2
str tr n y x2 rr q s s qts
b =1
Sxx
[ni=1
x2i y ni=1
xiyi x+ n y x2 n y x2]
=1
Sxx
[y( n
i=1
x2i + n x2) x
( ni=1
xiyi + n x y)]
=1
Sxx
[ySxx xSxy
]= y Sxy
Sxxx
b = y a x s rs 2x
2y s rs x y s ts rts r cov(x, y) tr sss rs s ts sttsts rtts q sr s trs SxxSyy Sxy
2x =1
nSxx
2y =
1
nSyy cov(x, y) =
1
nSxy
s s r rtr s
-
rs s rs
tr t sttst rtts rqtt t t s s qr
t rr r trs Sxx Syy Sxy
r = a
SxxSyy
t rr r rst rt s rsts st s rs ts rrs tr r r r r tr 1 s sts rt r rst t s rt r rst t s r st
t r sr st rr i st sr rrst r srs s rt t rt r rt st st
i = yi ycalculadoi r s rrs S sr
S2 =Syy aSxy
n 2 = Sxx(1 r2n 2
)
r s rrs sr n 2 s n 1 rq st r trss s ts a b qt str ts st r srs q q s r2 = 1 t r s rrs r st ts sts rts tt rt st ss r s rrs St trrt rtt r s rt sr r s rts
r y trr s r q sss rts st s sts q tr tr st tr rrs y q st s s t
t s rts u(a) u(b) s ts st r sr s rtr q
u(a) =
S2Sxx
=|a|r
S2Syy
= |a|
1 r2(n 2)r2 u(b) = u(a)
1n
ni=1
x2i
Pr ts rts s rrrr t r
n = 5 r r s rs s ts r a r b s rts sss rtr s qs s rs tts s t sr sstts
rtt s rsss s rs s x y s s Sxx Syy Sxy
r a b
i xi yi x2i y
2i xiyi
ts
xi =
yi =
x2i =
y2i =
xiyi =
r s ts r a r b
t s s st stt Pr tr s
st st s rs t str s sts x t st t t r r xt r s ts rts
s s r rtr s
-
ts tr s ts a b
s r s t s s qrs tr s ts r a r b rt q r s st s ts rts r rt rrst rx t t rr r s rts u(a) u(b) sss s ts ra r b r s rrs S
x (m) 5, 90 5, 10 3, 90 3, 10 1, 90
t (s) 1, 0 2, 0 3, 0 4, 0 5, 0
rs s sts x t st t t r
str r x t r s s
r xx s ts rts rs s r t q rs st s ts rs r t s s qrs
s s rtts r st strs
r a b
i ti (s) xi (m) t2i (s
2) x2i (m2) tixi (m s) 1, 0 5, 90 1, 0 34, 81 5, 9
2, 0 5, 10 4, 0 26, 01 10, 2
3, 0 3, 90 9, 0 15, 21 11, 7
4, 0 3, 10 16, 0 9, 61 12, 4
5, 0 1, 90 25, 0 3, 61 9, 5
ts
ti = 15
xi = 19, 9
t2i = 55
x2i = 89, 25
tixi = 49, 7
r s ts r a r b
rtr s rr s sts s
t = 15, 05
= 3, 0 s x = 19, 95
= 3, 98 m
s s r rtr s
-
rs s rs
Stt =ni=1
t2i n t2 = 55, 0 5 3, 02 = 10, 0 s2
Sxx =ni=1
x2i n x2 = 89, 25 5 3, 982 = 10, 048 m2
Stx =ni=1
tixi n t x = 49, 7 5 3, 0 3, 98 = 10, 0 m s
a =StxStt
=10, 010, 0
= 1, 0 m/s b = x a t = 3, 98 (1, 0) 3, 0 = 6, 98 m
r = a
SttSxx
= 1, 0
10, 0
10, 048= 0, 99761
s rs a b r r t sr ts rtt t r t str rt tr r x t q r s st ts rts srts u(a) u(b) sss s s s ts r a r b rstt sr trs rtr s qs st
u(a) = |a|
1 r2(n 2)r2 = | 1|
1 0, 9976123 0, 997612 = 0, 04 m/s
u(b) = u(a)
1n
ni=1
t2i = 0, 04
55
5= 0, 132665 m
r q r s rrs sr
S =
Sxx
(1 r2n 2
)=
10, 048
[1 (0, 99761)2
5 2]= 0, 1264 m
s tr s rrts ssrs s r q
a = (1, 00 0, 04) m/s b = (7, 0 0, 1) m
rs
t t r r ss M rs s rs trt s s sss t r ss r
q r rt x r r tr ~F sr r rstrr ~F rr rt r x st ~F = k~x k stt rtrst stt st Pr tstr
ss tr rssr r
rstrr
~F r rs rts rt r x str rst t r
x (cm) 1, 00 2, 00 3, 00 4, 00 5, 00 6, 00 7, 00 8, 00 9, 00 10, 00 11, 00
F (N) 8, 11 21, 8 29, 1 40, 5 49, 8 60, 1 69, 7 80, 6 88, 8 102, 0 108, 1
rs s rts r x s rs rstrrs ~Frrsts
s s r rtr s
-
ts tr s ts a b
r F x r s ts s r s t rtr s ts r a r b rsts rts rt q r s sts ts rts sr q r F = ax+ b tr rt rrst r F x r q rt q F = kx rst rtrr r stt st k s s rts tr sts r a r b ss rr
tr r sst s r sr t ts s
rs trt stt t sst st r r r sr
t rt r r tr t r rts sts
rr sr tr r stt t
x (cm) 7, 0 10, 0 11, 0 16, 0 18, 0 20, 0
t (s) 0, 61 0, 87 0, 96 1, 40 1, 57 1, 75
rs s sts x rr sr tr r trs t t rrsts
r x t r s ts s r s t ss qrs tr s ts r a r b rsts rts rtq r s st s ts rts sr q r x = at+b tr rtrrst r x t r q rt q x = x0+ vt rst tr t rt r r trr r v s x0 rr tr r s s rts tr s ts ra r b ss rr tr t rt r
s t r q r q r
~A rr r~F sr r st
~A =1
M~F
stt rr 1/M st ss M r Pr tstr s t stt r
~A r rs rts r
~F s r ss M rt rtr r ss rss sr stt
str rst t r r A F r sts rsts rrs rr s r s t s s qrs
tr s ts r a r b rsts rts rt q r s sts ts rts sr q r A = aF + b tr rt rrst r AF r q rt q r trr r ss M r s s rts tr s ts r a r b ssr s t
F (N) 0, 150 0, 260 0, 350 0, 450 0, 550
A (m/s2) 0, 25 0, 01 0, 45 0, 02 0, 68 0, 03 0, 90 0, 04 1, 12 0, 05
rs r
~F q t r ssM s s rs ~A rrsts
s s r rtr s
-
rs s rs
s s r rtr s
-
t
rs s rs
s t str s s str r r rrst rqtt
rs s rs ts s sss s s s sr ts
rs t s ss s rs t 1/x 1/x sr ts r sss s sr s s rs s sts t t
s s str t s tr s qs q s t
t q rrs rt ss s r s s str r
t r q s t r ss rt r
rs t s t r r s rs
sr t tt ss rs ss rts r rt s s
ts sts tr t rtt r t
s s t y = f(x)
s s
sss s t st r r
y = kxm
k m s stts rt s s s q ts
log y = log k +mlog x
s s r rtr s
-
rs s rs
Y = B +AX
Y = log y B = log k A = m X = log x Ps strr r q s r tr tr s rs A B rtt rtr r Pr s ts rs r s rstts rt
s s x y tr r rtt y = f(x) t
r s r tr
rt rt q r s st s ts rs r str
ss s r s rs s ts r A r B sr ts rtt rt st
A =Y
X=
log y2 log y1log x2 log x1
Btrs rt Y r X = 0
s tsA B r sr ts t t t s s qrs tr s sts ss rtr s rs ts A B s trr stt k trs r k = 10B t m rtt m = A
s s strs r s rs x y rtt s r str r st
s r tr rt q r s st s ts r s
ts r A r B rtt rt tr t t t s sqrs
Pr r r s rrt rt x y srs sss rts st str t r s ts rrsts s
rts x y s r ts r r str rtstr st r rt q r s st s ts rts s ts r
A r B sr ts rtt rt r rr r Pr tr q s t s s qrs r sss ss ts ts
A = 2, 5 B = 0, 65 ss k = 10B = 4, 5 m = A = 2, 5 rr y = 4, 5x2,5
s s r rtr s
-
s rt
s r
r s r
ss ss rr s s rt t ss t
s trr sst trs q rqr rt ts s ts
rts trtt sss s sr sss q s s ss ss s
ss rts
s rt
str s rt st r s rt st rt rts
rrs s rs s rts s rs tr s a s tss s r s 10 ts rt s r tr ts 10sts 10n 10n+1 n r tr str s str srt s 10 ss s t x 10n r tr 10n 10n+1
t rt rt t r strr s rt s 10
ss r Lx st t x 10n r rr 10n L10 st tr 10n
s s r rtr s
-
rs s rs
10n+1 s rt s rt r tr sss sts s rs srts s ts rrsts rt st
L10log 10n+1 log 10n =
Lxlog ( x 10n) log 10n
L10log
(10n+1
10n
) = Lxlog x+ log 10n log 10n
L10log 10
=Lxlog x
log x =LxL10
q rt trr rt qqr r x s 10 rtr s strrt s tr e = 2, 781... s s a qqr ts rstt
ln x =LxLe
logax =LxLa
rtt r q r s rt rs r 100 = 1 s r t 10 t ss st rt rs ts s sss sr ts r strr s rt
P
str s str rtr s rt t
r r s s ss s ss rt rt s
r rt Prtt ss rr s rs s rs t t
rtt sr s ss s ss r rt
sss rs s s s rt sr ts r rrstr ts
rts sss s rs ss Pr s s rs tr rs 0, 1 10 rr s s rs tr 0, 1 1 s s rs tr 1 10 s ss t s rt ss sss rr rr tr
0, 1 t s tr 0, 2 s rr tr 1 t s tr 2 ss r t rst 10 sss q t str ss 2 5 10 rts s s rts rs rst ss s t rs ss s rtr q r s s t 10 q r
Ps tr q r r r s rts s rs
2 0, 0148 s ss 10 qqr tr q s qr Pr ss s srr q qqr rt t rt L10 30 mm ss s rts L2 L1,48 s r ts
log 2 =L2L10
9, 0 mm30, 0 mm
0, 30
log 0, 0148 = log(1, 48 102) = log 1, 48 2 = L1,48
L10 2 5, 0 mm
30, 0 mm 2 1, 83
s s rts rstr rts ts s st s rrs
tr rts rts trs ts s ss s ss rsts
s s r rtr s
-
s s r s s
sts rs s s
s s r s s
srs q q s rs t Y = log y t X = log x s srts ss s q q s str r s rs rs (x, y) rtt ts rst rt s r q rr r
rr s t s Pr s ts rs s
rstts s s x y tr r rtt y = f(x) rtssr t
rt rt q r s st s ts rs r str
ss s r r t r A sr t rtt rt stss s ts rtrrs (x1, y1) (x2, y2)
A =Y
X=
log y2 log y1log x2 log x1
r t m t rtt m = A
stt s ts (x1, y1) = (0, 23; 0, 030) (x2, y2) = (1, 4; 7, 0) ss rtrrt sr rt st q ts
m = A =log 7, 0 log 0, 030log 1, 4 log 0, 23
0, 84 (1, 52)0, 15 (0, 64) 3, 0
s s r rtr s
-
rs s rs
r
r k q t r B sr tr rtt rt stss st q
m log x = 0 x = 1srs q st rst
log y = log k + 0 k = yss s q rt rt x = 1 st rst s r r k = y srt trs trs rt x = 1 rt st r srr q ss rr r y = k = 3, 0 Pr tr q rt rt x = 1 st rst s r trt sr r r k trs q s t rtrr (x1, y1) rt st ss s q r y1 = kx
m1
k =y1xm1
s t s ts ss t (x1, y1) = (1, 7; 15) t
s k =15
1, 73,0 3, 0 q r r trrt Prtt q r s rs x y st y = 3, 0x3,0
rtt r q t s s qrs t r sr s
q r r qqr s ts A B sss ts s s s ts rsrs sr ss t rs
s s
sss s t st r r
y = kemx
k m e = 2, 781... s stts rt s s s q ts
s s r rtr s
-
s s r s s
log y = log k +m (log e)x
Y = B +AX
Y = log y B = log k A = m (log e) X = x s s strr r q s r tr tr s rs A Brtt rtr r Pr s ts rs r s rstts
rt s s y tr r rtt y = f(x) t
r s r tr
t rt rt q r s st s ts rs r
str ss s r s rs s ts r A r B sr tsrtt rt st
A =Y
X=
log y2 log y1x2 x1
trs rt Y r X = 0
ts s ts A B r sr ts t t t s s qrs t r rtr s rs ts A B s trr stt k r r k = 10B t m rtt
m =A
log e
s s r s s
s str str rtr s rt t
r r s s s s s rt sr
ts r rrstr ts rts sss s rs ss
ss s rt r rt qt q s rt st
rt tr Prtt ss rr s rs s s rs
r t t rtt sr s ss
s s r rtr s
-
rs s rs
tr rs tts
srs q q r t Y = log y rt qt q r t X = x r ss s q q s str r s rs rs (x, y)rtt ts rst rt s r q
rr r rr s t s Pr s ts rs
s rstts s s x y tr r rtt y = f(x) rts sr t
sts rs s s r
rt rt q r s st s ts rs r s
tr ss s r r t r A sr t rtt rt stss s ts rtrrs (x1, y1) (x2, y2) sstts q
stt s ts (x1, y1) = (0, 3; 6, 0) (x2, y2) = (1, 3; 200) ss rtrrt sr rt st q ts
A =log 200 log 6, 0
1, 3 0, 3 2, 300 0, 77
1, 0 1, 53
ss q r stt m r m =A
log e 1, 53
0, 43 3, 6 r k q t r B sr tr rtt rt stss st q
m (log e)x = 0 x = 0srs q st rst
log y = log k + 0 k = y
s s r rtr s
-
s s r s s
ss r k = y sr t trs trs rt x = 0 rt st r srr q ss rr r y = k = 1, 9 Pr tr q rt rt x = 0 st rst s r trt sr r r k trs q s t rtrr (x1, y1) rt st ss s tsy1 = ke
mx1
k =y1emx1
s t s ts ss t (x1, y1) = (0, 3; 6, 0)
ts k =6, 0
e3,60,3 2, 0 q r rt r trrt Prtt q r s rs x y st y = 1, 9e3,6x
t s rs rs t s s qrs t r
sr t q r r s ts r A r B sss ts s s s ts rs rs sr ss t rs
rs
t q r s t t rt rt
r t q r rr rt y srr q ss t
y = y0 + v0yt+1
2gt2
g r r t v0 = 0 tr y = h rtr s y0 = 0 q trs
h =1
2gt2
h (m) t (s)
0, 200 0, 1593
0, 250 0, 1831
0, 300 0, 2046
0, 350 0, 2238
0, 400 0, 2432
0, 450 0, 2593
0, 500 0, 2750
0, 550 0, 2912
0, 600 0, 3056
0, 650 0, 3202
0, 700 0, 3336
0, 750 0, 3468
0, 800 0, 3599
s q t r rts sts q r
stt rst q s tr r rs
rr q tr t q r ss rtr t
rs stt s ts q t t rs r
rts sts q r str rst rt t
r rq sss ts tr rt q r s st s
s s r rtr s
-
rs s rs
ts rts r r g rs stt rst r ss rr q t q r t
t rt rt r stq
tr r tr s trs rss rsss ss st rsss
s s st t ttr s t r rs
trstr s q r rr sts rsss
sst r t t tr trss r tr t
t R0 t t R ts s trssr tr sssr t s tr r
R = R0et
t r t tt q s rsss tr t tr
t (mm) 1, 22 2, 21 3, 10 4, 32 5, 31 6, 53 7, 28 8, 50 9, 91
R (CPS) 9, 32 8, 83 8, 46 8, 27 8, 38 8, 15 7, 90 7, 63 7, 46
s ts r rts sssrs
t str r tr r rr tr trt
137Cs55 s t t ts r s Pr rss sssrs s ss tr str rst rt
t ss r rq sss ts tr rt q r s
st s ts rts t t Al r
s s r rtr s
-
r
rs rrt r ss rsr rs s
rs s Prs rs r rrt rs 3a
st r st rs sr t rt s r
PP t t rss rtt srt
rrt rrt trt rt r trt
r r Prs rtt srt Prt
ts tr rrs r r t
rss rt srt r rts
rr tt ts sttst Prt rst Prss
sst st sttst
s r r str ttrtt t r
rrt rrrs Pr s Ps r
t tt r s tr r r t srt
t t t rss rtt srtst rs P
t s Prt ss rsr rs s
t st tttrrstqrsttt
t s sts s s r
s s s P
s s r rtr s