laporan dasar pengukuran dan ketidakpast

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


=500 g5

=100g


=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


=200 g2

=100g


=100 g10

=10g


=10g10

=1g


=1,0 g100

=0,01g


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|



=200 g2

=100g


=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


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 = 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 = 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


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


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


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

laporan dasar pengukuran dan ketidakpast

Documents