laporan dasar pengukuran dan ketidakpast
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Contoh Data Dan Analisys Data Unit Dasar Pengukuran Dan Ketidakpastian
HASIL EKSPERIMEN DAN ANALISIS DATA
Hasil Pengamatan
1. Pengukuran Panjang
NST Mistar : BatasUkurJumlah Skala
=1cm10
=¿0,1 cm= 1 mm
NST Jangka Sorong :
NST Mikrometer Sekrup :
Tabel 1. Hasil pengukuran panjang
N
o
Benda
yang
diukur
Besaran
yang
diukur
Hasil Pengukuran (mm)
Mistar Jangka Sorong Mikrometer Sekrup
1. Balok
Panjang
|17,0±0,5| |16,10±0,05| |16,910±0,005|
|17,0±0,5| |17,00±0,05| |16,770±0,005|
|17,0±0,5| |17,10±0,05| |16,270±0,005|
Lebar
|14,0±0,5| |15,50±0,05| |15,960±0,005|
|14,0±0,5| |15,40±0,05| |15,500±0,005|
|14,0±0,5| |15,50±0,05| |15,520±0,005|
Tinggi |23,0±0,5| |24,10±0,05| |23,460±0,005|
20 SN =39 SU
20 SN =39 (1 mm)
20 SN = 39 mm
SN = 1,95 mm
NST = 2 mm – 1,95 mm = 0,05 mm
NST SU = BatasUkurJumlah Skala
= 5mm
10= 0,5
mm
NST Skala Putar = BatasUkur
Jumlah SkalaPutar
¿ 0,5mm50
|23,0±0,5| |23,15±0,05| |23,530±0,005|
|23,0±0,5| |24,05±0,05| |23,260±0,005|
2.
Bola Diameter
|17,0±0,5| |16,20±0,05| |16,310±0,005|
|17,0±0,5| |16,30±0,05| |16,020±0,005|
|17,0±0,5| |16,45±0,05| |16,010±0,005|
2. Pengukuran MassaNeraca Ohauss 2610 gram
Nilai Skala lengan 1 : BatasUkurJumlah Skala
=100 g10
=10g
Nilai Skala lengan 2 : BatasUkurJumlah Skala
=500 g5
=100g
Nilai Skala lengan 3 : BatasUkurJumlah Skala
=10g100
=0,10 g
Massa beban gantung : -
Tabel 2. Hasil pengukuran massa dengan Neraca Ohauss 2610 gram
Benda Penunjuk
lengan 1
Penunjuk
lengan 2
Penunjuk
lengan 3
Beban
gantung
Massa benda (g)
Balok
Kubus
0
0
0
0
0
0
4,00
4,00
3,90
-
-
-
|4,00±0,05|
|4,00±0,05|
|3,90±0,05|
Bola 0
0
0
0
0
0
5,60
5,65
5,55
-
-
-
|5,60±0,05|
|5,65±0,05|
|5,55±0,05|
Neraca Ohauss 311 gram
Nilai Skala lengan 1 : BatasUkurJumlah Skala
=200 g2
=100g
Nilai Skala lengan 2 : BatasUkurJumlah Skala
=100 g10
=10g
Nilai Skala lengan 3 : BatasUkurJumlah Skala
=10g10
=1g
Nilai Skala lengan 4 : BatasUkurJumlah Skala
=1,0 g100
=0,01g
Tabel 3. Hasil pengukuran massa dengan Neraca Ohauss 311 gram
Benda Penunjuk
lengan 1
Penunjuk
lengan 2
Penunjuk
lengan 3
Penunjuk
lengan 4
Massa benda (g)
Balok
Kubus
0
0
0
0
0
0
3,000
3,000
3,000
0,875
0,850
0,870
|3,875±0,005|
|3,850±0,005|
|3,870±0,005|
Bola 0
0
0
0
0
0
5,000
5,000
5,000
0,550
0,500
0,530
|5,550±0,005|
|5,500±0,005|
|5,530±0,005|
Neraca Ohauss 310 gram
Nilai Skala lengan 1 : BatasUkurJumlah Skala
=200 g2
=100g
Nilai Skala lengan 2 : BatasUkurJumlah Skala
=100 g10
=10g
Nilai Skala Putar : BatasUkurJumlah Skala
=1g10
=0,1g
Jumlah Skala Nonius : 10 skala
NST Neraca Ohauss 310 gram : 1,9 SP = 10 SN
0,19 SP = SN
NST = NSP-NSTN= 0,2-0,19 = 0,01 g
Tabel 4. Hasil pengukuran massa dengan Neraca Ohauss 310 gram
BendaPenun.
lengan 1
Penun.
lengan 2
Penun.
skala
putar
Penun.
skala
Nonius
Massa benda (g)
Balok
Kubus0
0
0
0
0
0
3,90
4,00
3,90
5
7
7
|3,95±0,01|
|4,07±0,01|
|3,97±0,01|
Bola 0
0
0
0
0
0
5,50
5,50
5,50
8
7
7
|5,58±0,01|
|5,57±0,01|
|5,57±0,01|
3. Pengukuran Waktu dan Suhu
NST termometer : BatasUkurJumlah Skala
=10℃10
=1℃
Temperatur mula-mula (To) : |33℃±0,5|
NST Stopwatch : BatasUkurJumlah Skala
=1 sekon10
=0,1 sekon
Tabel 5. Hasil pengukuran waktu dan suhu
No.Waktu (s) Temperatur (℃¿
Perubahan
Temperatur
(℃)
1. |60,0±0,1| |35,0±0,5| |2,0±1|
2. |120,0±0,1| |37,0±0,5| |2,0±1|
3. |180,0±0,1| |40,0±0,5| |3,0±1|
4. |240,0±0,1| |43,0±0,5| |3,0±1|
5. |300,0±0,1| |46,0±0,5| |3,0±1|
6. |360,0±0,1| |49,0±0,5| |3,0±1|
ANALISIS DATA
Pengukuran Panjang
Benda I Balok
Rambat Ralat Volume
V = P × L × T
δv=|δvδp|∆P + |δvδl |∆L + |δvδt |∆T
δv = |δ (p× l× t)δp |∆P + |δ (p× l× t)
δl |∆L + |δ (p× l× t)δt |∆T
∆vv
=|l ×tv |∆P + | p× t
v |∆L + | p× lv |∆T
∆vv
=| l ×tp×l×t|∆P + | p×t
p× l× t|∆L + | p× lp× l× t|∆T
∆vv
=|∆Pp |+ |∆ L
l | + |∆Tt |
∆ v=|∆ Pp |+ |∆ L
l | + |∆Tt |v
Mistar
Panjang
P=17,0mm+17,0mm+17,0mm
3 = 17,0 mm
δx =|Px−P|δ1 =|17,0−17,0|mm= 0 mm
δx =|17,0−17,0|mm= 0 mm
δx =|17,0−17,0|mm= 0 mm
∆ P = δmax = 0,5 mm.
KR = ∆ PP
× 100%
KR = 0,5
17,0 × 100% = 2,9% ( 3 AB )
PF : |P±∆ P| = |17,0±0,5| mm
Lebar
L=14,0mm+14,0mm+14,0mm
3 = 14,0 mm
δx =|Lx−L|δ1 =|14,0−14,0|mm= 0 mm
δx =|14,0−14,0|mm= 0 mm
δx =|14,0−14,0|mm= 0 mm
∆ L = δmax = 0,5 mm.
KR = ∆ LL
× 100%
KR = 0,5
14,0 × 100% = 3,5% ( 3 AB )
PF: |L±∆ L| = |14,0±0,5| mm
Tinggi
T=23,0mm+23,0mm+23,0mm
3 = 23,0 mm
δx =|T x−T|
δ1 =|23,0−23,0|mm= 0 mm
δx =|23,0−23,0|mm= 0 mm
δx =|23,0−23,0|mm= 0 mm
∆ t = δmax = 0,5 mm.
KR = ∆TT
× 100%
KR = 0,5
23,0 × 100% = 2,1% (3 AB)
PF : |T ±∆T| = |23,0±0,5| mm
Vbalok = P × L × T
Vbalok = 17,0 mm × 14,0 mm× 23,0 mm
Vbalok = 5.474 mm3
∆ v=|∆ Pp |+ |∆ L
l | + |∆Tt |v
∆ v=| 0,5mm17,0mm|+ | 0,5mm
14,0mm| + | 0,5mm23,0mm|5.474 mm3
∆ v=|0,029|+ |0,035| + |0,021|5.474 mm3
∆ v=|0,085|5.474 mm3
∆ v=¿ 465,29 mm3 0,5 cm3
v=¿ 5.474 mm3 5,5 cm3
KR = ∆vv
× 100%
KR = 0,5cm3
5,5cm3 × 100% = 9 % ( 2 AB )
PF: |V ±∆V| =│5,5 ±0,5│cm3
Jangka Sorong
Panjang
P=16,10mm+17,00mm+17,10mm
3 = 16,73 mm
δx =|Px−P|δ1 =|16,10−16,73|mm= 0,63 mm
δx =|17,00−16,73|mm= 0,27 mm
δx =|17,10−16,73|mm= 0,37 mm
∆ P = δmax = 0,63 mm.
KR = ∆ PP
× 100%
KR = 0,63
16,73 × 100% = 3,7% ( 3 AB )
PF : |P±∆ P| = |16,7±0,6| mm
Lebar
L=15,50mm+15,40mm+15,50mm
3 = 15,47 mm
δx =|Lx−L|δ1 =|15,50−15,47|mm= 0,03 mm
δx =|15,40−15,47|mm= 0,07 mm
δx =|15,50−15,47|mm= 0,03 mm
∆ L = δmax = 0,07 mm.
KR = ∆ LL
× 100%
KR = 0,07
15,47 × 100% = 0,4% ( 4 AB )
PF : |L±∆ L| = |15,47±0,07| mm
Tinggi
T=24,10mm+23,15mm+24,05mm
3 = 23,76 mm
δx =|T x−T|δ1 =|24,10−23,76|mm= 0,34 mm
δx =|23,15−23,76|mm= 0,61 mm
δx =|24,05−23,76|mm= 0,29 mm
∆ t = δmax = 0,61 mm.
KR = ∆TT
× 100%
KR = 0,61
23,76 × 100% = 2,5% (3 AB )
PF : |T ±∆T| = |23,7±0,6| mm
Vbalok = P × L × T
Vbalok = 16,7mm × 15,47mm× 23,7 mm
Vbalok = 6.122,87 mm3
∆ v=|∆ Pp |+ |∆ L
l | + |∆Tt |v
∆ v=| 0,616,7|+ | 0,07
15,47| + | 0,623,7|6.122,87 mm3
∆ v=|0,035|+ |0,004| + |0,025|6.122,87 mm3
∆ v=|0,064|6.122,87 mm3
∆ v=¿ 391,86 mm3 0,4 cm3
v=¿ 6.122,87 mm3 6,1 cm3
KR = ∆vv
× 100%
KR = 0,4c m3
6,1cm3 × 100% = 6,5 % ( 2 AB )
PF: |V ±∆V| =│6,1 ±0,4│cm3
Mikrometer Sekrup
Panjang
P=16,910mm+16,770mm+16,270mm
3 = 16,650 mm
δx =|Px−P|δ1 =|16,910−16,650|mm= 0,260 mm
δx =|16,770−16,650|mm= 0,120 mm
δx =|16,270−16,650|mm= 0,380 mm
∆ P = δmax = 0,380 mm.
KR = ∆ PP
× 100%
KR = 0,380
16,650 × 100% = 2,2% ( 3 AB )
PF : |P±∆ P| = |16,6±0,3| mm
Lebar
L=15,960mm+15,500mm+15,520mm
3 = 15,660 mm
δx =|Lx−L|δ1 =|15,960−15,660|mm= 0,300 mm
δx =|15,500−15,660|mm= 0,160 mm
δx =|15,520−15,660|mm= 0,140 mm
∆ L = δmax = 0,300 mm.
KR = ∆ LL
× 100%
KR = 0,300
15,660 × 100% = 1,9% ( 3 AB )
PF: |L±∆ L| = |15,6±0,3| mm
Tinggi
T=23,460mm+23,530mm+23,260mm
3 = 23,416 mm
δx =|T x−T|δ1 =|23,460−23,416|mm= 0,044 mm
δx =|23,530−23,416|mm= 0,114 mm
δx =|23,260−23,416|mm= 0,156 mm
∆ t = δmax = 0,156 mm.
KR = ∆TT
× 100%
KR = 0,156
23,416 × 100% = 0,6 % ( 3 AB )
PF : |T ±∆T| = |23,4 ±0,1| mm
Vbalok = P × L × T
Vbalok = 16,6mm × 15,6mm× 23,4mm
Vbalok = 6059,6 mm3
∆ v=|∆ Pp |+ |∆ L
l | + |∆Tt |v
∆ v=| 0,316,6|+ | 0,3
15,6| + | 0,123,4|6059,6 mm3
∆ v=|0,018|+ |0,019| + |0,004|6059,6 mm3
∆ v=|0,041|6059,6 mm3
∆ v=¿ 248,4 mm3 0,24 cm3
v=¿ 6059,6 mm3 6,05 cm3
KR = ∆vv
× 100%
KR = 0,26,0
× 100% = 3,9 % ( 3 AB )
PF : |V ±∆V| = |6,05±0,24| mm
Rambat Ralat Volume Bola
v=16π d3
dv=|∂v∂d|dd
dv=|∂( 16π d3)
∂d |dddv=1
2π d2dd
∆ v=|12π d2∆d|
∆vv
=| 12πd2∆ d
16π d3 |
∆ v=|3∆dd |v
KR=∆ vv
x100%
Mistar
d=17,0mm+17,0mm+17,0mm
3 = 17,0 mm
δx =|d−d|
δ1 =|17,0−17,0|mm= 0 mm
δx =|17,0−17,0|mm= 0 mm
δx =|17,0−17,0|mm= 0 mm
∆ d = δmax = 0,5 mm.
PF: |d±∆d| = |17,0±0,5| mm
v=16π d3
v=16(3,14)(17,0)3
= 2571,13 mm3
∆ v=|3∆dd |v
∆ v=|3(0,5)mm17,0mm |2571,13mm3
∆ v=| 1,5mm17,0mm|x2571,13mm3
∆ v=0,08 x 2.571,13mm3
∆ v=205,69mm3 0,20 cm3
v=2.571,13mm3 2,57 cm3
KR=∆ vv
x100 %
KR=0,20cm3
2,57cm3 x 100 % = 7,7 % ( 2AB)
PF=|v ±∆ v| ¿|2,5±0,2| cm3
Jangka Sorong
d=16,20mm+16,30mm+16,45mm
3 = 16,31 mm
δx =|dx−d|δ1 =|16,20−16,31|mm= 0,11 mm
δx =|16,30−16,31|mm= 0,01 mm
δx =|16,45−16,31|mm= 0,14 mm
∆r = δmax = 0,14 mm.
PF : |d±∆d| = |16,31±0,14| mm
v=16π d3
v=16(3,14)(16,31)3
= 2.270,59 mm3
∆ v=|3∆dd |v
∆ v=|3(0,14)mm16,31mm |2.270,59mm3
∆ v=| 0,42mm16,31mm|x 2.270,59mm3
∆ v=0,025 x 2.270,59mm3
∆ v=56,76mm3 0,05 cm3
v=2.270,59mm3 2,27 cm3
KR=∆ vv
x100 %
KR=0,05cm3
2,27cm3 x 100 % = 2,2 % ( 3AB)
PF=|v ±∆ v| ¿|2,27±0,05| cm3
Mikrometer Sekrup
d=16,310mm+16,020mm+16,010mm
3 = 16,174 mm
δx =|dx−d|δ1 =|16,310−16,174|mm= 0,136 mm
δx =|16,020−16,174|mm= 0,154 mm
δx =|16,010−16,174|mm= 0,164 mm
∆r = δmax = 0,164 mm.
PF : |d±∆d| = |16,174±0,164| mm
v=16π d3
v=16(3,14)(16,174)3
= 2214, 27 mm3
∆ v=|3∆dd |v
∆ v=|3(0,164)mm16,174mm |2.214 ,27mm3
∆ v=| 0,492mm16,174mm|x2.214 ,27mm3
∆ v=0,030 x 2.214 ,27mm3
∆ v=66,428mm3 0,066 cm3
v=2.214 ,27mm3 2,214 cm3
KR=∆ vv
x100 %
KR=0,066cm3
2,214cm3 x 100 % = 2,9 % ( 3AB)
PF=|v ±∆ v| ¿|2,21±0,06| cm3
2. Pengukuran Massa
Rambat Ralat Massa jenis
ρ=mv
= mv-1
δρ=| δρδm|∆m + |δρδv|∆v
δρ=|mv−1
m |∆m + |mv−1
v |∆v
δρ=|v−1|∆m + |mv−2|∆v
∆ ρρ
=| v−1
mv−1|∆m + |mv−2
mv−1|∆v
∆ ρρ
=|∆mm | + |∆ v
v |∆ ρ=|∆m
m | + |∆ vv |ρ
Untuk balok :
v=5,5cm3+6,1cm3+6,05cm3
3 = 5,8 cm3
δx =|vx−v|δ1 =|5,5−5,8|cm3= 0,3 cm3
δx =|6,1−5,8|cm3= 0,3cm3
δx =|6,05−5,8|cm3= 0,25cm3
∆ v = δmax = 0,3 cm3
KR = ∆vv
× 100%
KR = 0,35,8
× 100% = 5,1% ( 2 AB )
PF=|v ±∆ v| ¿|5,8±0,3| cm3
Untuk bola :
v=2,5cm3+2,27cm3+2,21cm3
3 = 2,32 cm3
δx =|vx−v|δ1 =|2,5−2.32|cm3= 0,18cm3
δx =|2,27−2.32|cm3= 0,05cm3
δx =|2,21−2.32|cm3= 0,11 cm3
∆ v = δmax = 0,18 cm3
KR = ∆vv
× 100%
KR = 0,182.32
× 100% = 7,7% (2 AB)
PF=|v ±∆ v| ¿|2.3±0,1| cm3
Neraca Ohauss 2610 gram
Balok
m=4,00 g+4,00 g+3,90 g
3 = 3,96 g
δx =|m x−m|δ1 =|4,00−3,96|g= 0,04 g
δx =|4,00−3,96|g= 0,04 g
δx =|3,90−3,96|g= 0,06 g
∆ m = δmax = 0,06 g.
KR = ∆mm
× 100%
KR = 0,063,96
× 100% = 1,5 % ( 3 AB )
PF: |m±∆m|g=|3,96±0.06|g
Bola
m=5,60g+5,65g+5,55 g
3 = 5,60 g
δx =|m x−m|δ1 =|5,60−5,60|g= 0 g
δx =|5,65−5,60|g= 0,05 g
δx =|5,55−5,60|g= 0,05 g
∆ m = δmax = 0,05 g.
KR = ∆mm
× 100%
KR = 0,055,60
× 100% = 0,8% ( 3 AB )
PF: |m±∆m|g=|5,60±0.05|g
Neraca Ohauss 311 gram
Balok
m=3,875g+3,850g+3 ,870 g
3 = 3,865 g
δx =|m x−m|δ1 =|3,875−3,865|g= 0,010 g
δx =|3,850−3,865|g= 0,015 g
δx =|3 ,870−3,865|g= 0,005 g
∆ m = δmax = 0,015 g.
KR = ∆mm
× 100%
KR = 0,0153,865
× 100% = 0,3% (4 AB)
PF : |m±∆m| = |3,865±0,015| g
Bola
m=5,550g+5,500 g+5,530 g
3 = 5,526 g
δx =|m x−m|
δ1 =|5,550−5,526|g= 0,024 g
δx =|5,500−5,526|g= 0,026 g
δx =|5,530−5,526|g= 0,004 g
∆ m = δmax = 0,026 g.
KR = ∆mm
× 100%
KR = 0,0265,526
× 100% = 0,47% ( 4 AB )
PF: |m±∆m| = |5,526±0,026| g
Neraca Ohauss 310 gram
Balok
m=3,95g+4,07 g+3,97 g
3 = 3,99 g
δx =|m x−m|δ1 =|3,95−3,99|g= 0,04 g
δx =|4,07−3,99|g= 0,08 g
δx =|3,97−3,99|g= 0,02 g
∆ m = δmax = 0,08 g.
KR = ∆mm
× 100%
KR = 0,083,99
× 100% = 2 % (3 AB)
PF : |m±∆m| = |3,99±0,08| g
ρbalok=mv
ρbalok=(3,99 g)(5,8cm3)
ρbalok=¿ 0,68 g/cm3
∆ ρ=|∆mm | + |∆ v
v |ρ∆ ρ=|0,08
3,99| + |0,35,8| 0,68 g/cm3
∆ ρ=|0,020| + |0,051| 0,68 g/cm3
∆ ρ=¿ 0,04 g/cm3
KR = ∆ ρρ
× 100%
KR = 0,04 g/cm3
0,68 g/cm3 × 100% = 5,8 % (2 AB)
PF: |ρ±∆ ρ| = |0,68±0,04| g/cm3
Bola
m=5,58g+5,57g+5,57g
3 = 5,57 g
δx =|m x−m|δ1 =|5,58−5,57|g= 0,01 g
δx =|5,57−5,57|g= 0 g
δx =|5,57−5,57|g= 0 g
∆ m = δmax = 0,01 g.
KR = ∆mm
× 100%
KR = 0,01g5,57g
× 100% = 0,1% ( 4 AB )
PF : |m±∆m| = |5,570±0,010| g
ρbalok=mv
ρbalok=5,570 g
2,3c m3
ρbalok=¿ 2,421 g/cm3
∆ ρ=|∆mm | + |∆ v
v |ρ
∆ ρ=|0,010 g/cm3
5,570g /cm3| + |0,1cm3
2,3cm3| 2,421 g/cm3
∆ ρ=|0,001| + |0,043| 2,421 g/cm3
∆ ρ=¿ 0,106 g/cm3
KR = ∆ ρρ
× 100%
KR = 0,106 g/cm3
2,421g /cm3 × 100% = 4,3 % (3 AB)
PF: |ρ±∆ ρ| = |2,42±0,10| g/cm3
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