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BASIC MEASUREMENT AND UNCERTAINTY
Helny Lydarisbo*), Andi Lisra Andriani Hasrat, Nurul Angelita, Sitrah Nurdini Irwan
Basic Physic Laboratory, Chemistry Education ICP FMIPA UNM 2015
Abstract. Measurements have been carried out activities entitled "Basic Measurement and Uncertainty". This measurement activity is divided into three parts, the measurement of length, mass measurement and the measurement of time and temperature. Objects measured in lab activities that beam cube and small balls (marbles). At length measurement used ruler, vernier caliper and micrometer screw while mass measurements using three kinds of balance sheet ohauss ohauss ie 2610 grams, 311 grams ohauss balance, balance ohauss 310 grams then for time and temperature measurement used a stopwatch and thermometer. The first activity undertaken by the practitioner that the length measurement. In this activity 3 alternately between the practitioner to measure and record the measurement results. In the measurement of the cube beam is measured in length, width and height of the beam cube which has the same length but in this lab turns out there are some differences in the length measurement on the ruler, calipers, and micrometer screw. Then focus on the measurement of the ball diameter. Measuring the diameter of the ball using a ruler can not be done because of the uneven surface of the ball, so it can not be measured. Then for measurements with calipers or a micrometer screw can be done because these tools have a special function, making it easier to measure the diameter. Furthermore, for both activities and the activities of the three is also done by 3 people praktikan which alternately measure and record the measurement results. The conclusion of the experiment was done by is that for the measurement of length in greater detail is a micrometer a screw it can be seen from the value of DK ( degrees the truth ) on the results of direct observation that was the great it is present in a measuring instrument a micrometer a screw, while for the measurement of mass in greater detail were the balance of ohaus 311 grams with precision 0.005 grams/scale, and to activities the measurement of temperature can be concluded that along with increase in time, temperature is large.
Keywords: Measurement, micrometer screw, ohaus balance, temperature, varnier calipers.
FORMULATION OF THE PROBLEM1. How to use a measuring instrument basic ?2. How to determine the uncertainty in a single measurement and repetitive?3. How to use the numbers mean?
PURPOSE1. Able to use measuring tools.2. Being able to determine the uncertainty in a single measurement and repetitive.3. Able to understand the numbers mean.
BRIEF THEORIMeasurement is part of the Science Process Skills which is a collection of
information both quantitatively and qualitatively. By performing the measurement, can be obtained magnitude or value of a quantity or qualitative evidence. In Physics science learning, an educator not only convey only a collection of facts but should teach science as a process (process approach). Therefore, doing science experiments or experiments in Physics is very important. Conduct experiments in the laboratory, means deliberately evoke natural phenomena then take measurements.
The precision (accuracy), if a quantity is measured several times (multiple measurements) and produce prices are spread around the measurement sebenarnyamaka price said to be "accurate". In these measurements, the average price closer to the actual price.
Accuracy, if the measurement results centered in a specified area then called the measurement precision (the price of each measurement is not much different). Important figure is the number obtained by measurements given (read at the gauge) and the last digit is estimated.
a. All non-zero numbers are significant figures.b. Zeros are located between nonzero digits including significant figures
Example: 25.04 A contains four significant figuresc. The zero on the right number is not zero, including significant figures, unless
there are other explanations, such as a line under the last digit is still considered important. Example: 22.30 m containing four significant figures
d. Zeros are located on the left digit is not zero, either on the right or the left of the decimal point does not include significant figures. Example: 0.47 cm containing two significant figures
Uncertainty (error) applying will cause any results obtained deviate from actual results. Sources of uncertainty include applying:
1. Calibration error2. Zero point error (ZPE) 3. Demage to equipment components4. Friction 5. Parallax error6. Errors due to the current state of work, conditions in different calibration tool
with the condition at the condition at the time of the tool works.This error comes from the symptoms may not be controlled or overcome such
changes take place so quickly that the controlling and regulating beyond capabilities. This uncertainty causes the measurement falls slightly to the left and to the right of the actual value. Sources of random uncertainties, among others.
random uncertainties include :1. The error estimating section scale.
The first source of uncertainty in the measurement is limited scale measuring instrument. The price is less than the value of the smallest scale measuring instrument can no longer be read, so be estimated. that is to say, an uncertainty has infiltrated the measurement results. There are three determinants in terms of assessment, namely:• Distance physical (physical distance) between two adjacent scratches• Smooth or rough needle• Power split (resolving power) of the human eye
2. The state of fluctuating, meaning the rapidly changing circumstances of the time. For example, strong electrical currents and other sources always changing irregularly.
3. The random motion (motion brown) air molecules. This motion causes the needle designation of a measuring instrument that is very smooth to be disturbed.
4. The foundation of a vibrating5. Noise, ie interference with the electronic device in the form of rapid fluctuations
in voltage due to increased temperature component tool works.6. Radiation background cosmic radiation from outer space.
Measurement is always accompanied by uncertainty. Some of the causes of these uncertainties include Smallest Scale Value (NST) calibration errors, zero point error, parallax error, friction, fluctuations in measurement parameters and environment affect each other as well as well as the skills of the observer.
Single measurement is a measurement performed one time only. Limitations scale measuring instruments and limited ability to observe as well as many other sources of error, the result would always be considered the uncertainty of measurement.coat Δx is the absolute uncertainty. For single single measurement taken wisdom:
∆x = 12 NST Alat
Where Δx is the uncertainty of a single measurement. Number 2 in the formula have the meaning of the scale (values between the two nearest scratches) can each be divided into two partially clearly by eye. Δx value measurement reported in a standardized manner as follows:
X = ( x ±∆x ) [X]information :X = symbol magnitudes measured(X ± Δx) = measurement results and uncertainty[X] = unit mass x (in units of S1)Absolute uncertainty in the value of [X] and give an idea of the quality of measuring instruments used. The better the quality of the measuring instrument, the smaller Δx obtained. By using better quality measuring instrument, it is expected that the results obtained are also more precise, therefore absolute uncertainty stated accuracy of measurement results. The smaller the absolute uncertainty, the more precise the measurement results
Comparison between the results of measurements of absolute uncertainty Δx / x is called the relative uncertainty on the value of {x} is often expressed in% (multiplied by 100%. The uncertainty relative express the degree of accuracy of measurement results. The smaller the relative uncertainty, the higher accuracy achieved in the measurement . Repeated measurements (Multiple). By holding the repetition of knowledge about the actual value (x) be the better. Deviation is the difference between each result between each measurement results of the average value. Deviation (deviation) or the largest average deviation is reported as Δx So :
{x} = x , average measurementsΔx = δ max = δ averagewith:
x = x₁+x₂+x ₃
3and :
∆x = δ ₁+δ ₂+δ ₃
3
δ ₁=¿ x₁−x |δ ₂=¿|x₂−x|δ ₃=¿ |x₃−¿ x| [1]
EXPERIMENT METHODS
Tools and materials
Toolsa. Rulerb. Vernier Caliperc. Screw Micrometerd. Stopwatche. Thermometerf. Ohaus Balanceg. Beaker glassh. Tripodi. Gauzej. Bunsen burner
Materialsa. Iron beam b. Ballsc. Water
Identification of variabel1st activity (Length Measurement)
Control VariableBalance of measuring instrument
Manipulation Variable Length, width, height, diameters
Respon VaribleEach object that measured (balls or iron beams) has length, width, height, diameters differently and own measuring instrument has a different precision
2ndactivity (Mass Measurement) Control Variable
Balance of measuring instrument Manipulation Variable
Mass of each object that used
Respon Variable Eeach object that measured has a different mass accordance with materials that compound the object
3rdactivity (Time and Temperature Measurement) Control Variable
Burner Manipulation Variable
100 ml water Respon Variable
If the water heated more longer, so that the temperature of water will be high
Operational Definition of Variables1st activity
Length is the size of that began from the left to the right object of use measuring instrument length namely ruler, calipers and micrometer screw expressed in a unit of m or mm.
Width is the size of that began from the front end of the an object to the rear end of or otherwise use measuring instrument length namely ruler, calipers and micrometer screw expressed in a unit of m or mm.
Height is the size of that began from the top an object to point the bottom or commonly called a pedestal or otherwise use measuring instrument length namely ruler, calipers and micrometer screw expressed in a unit of m or mm.
Diameter is the size of that began from the other side to the other side through a point the center of a circle an object use measuring instrument length namely ruler, calipers and micrometer screw expressed in a unit of m or mm.
2ndactivity Mass is the size of the what owned by an object measured by a measuring
instrument mass namely the balance ohaus 310, balance ohaus 2610 and balance ohaus 311 grams expressed in a unit of grams.
3rdactivity Temperature is the increases of value that showing in the thermometer. Time is interval between the two the state or can be expressed as long of an
event.
Work Procedure1st activity : length measurement
In this measure, we measure the length, wide, high beams and diameter of on the ball . An instrument used a ruler, vernier caliper and micrometer screw. After prepared all tools which will be used, first determine SSV each tools. Began measuring for length, width and hight the iron beam each three times by using three tools that is a ruler, vernier caliper and micrometer screw, then measuring the diameter of the ball each three times too by using a ruler, vernier caliper and micrometer screw. And we must write down on the obeservation result table with the uncertainty.
2ndactivity : measuring the amount of massIn this practicum we measure mass manually by using three types of the balance
ohaus that is the balance ohaus 2610 grams, 310 grams, 311 grams. After prepared all tools, first determine SSV each tools and then make the balance balanced by means of burden sliding is at the zero point, put the objeck in platter the balance, made balance by moving burden sliding on where the most appropriate, after balanced those are mass objects. So mass objects equal to the mass that indicated by each burden sliding on an arm of the balance, write down the mass that shown by burden sliding on the outcome of the measurement of arms the balance.
3rdactivity : measurement of temperature and timeIn this practicum we measure time and temperature by using stopwatch and
thermometer,first, we prepared tools and material and then determine SSV of thermometer and stopwatch, turn on the burner bunsen (spiritus) right down a beaker glass and then measuring the temperature first, stopwatch on, write down changes of temperature occurring every one minute each six times.
EXPERIMENTAL RESULTS AND DATA ANALYSIS
Experimental Result
Measurement of Length
a. Ruler
SSV Ruler ¿Limit of measurement
Number of scale= 30cm
300 scale = 0.1 cm = 1 mm
x = 12 × SSV =
12
× 1 mm = 0.5 mm
Measurement result ( HP ) = ¿ x± ∆ x∨¿
Table 1. the result of measurement for lenght with rulerMeasured object Magnitude is Measure The measurement results (mm)
Length
|18,5± 0,5|
|18,5± 0,5|
|18,0 ± 0,5|
Iron beam Width
|18,5± 0,5|
|18,5± 0,5|
|18,5± 0,5|
Hight |18,0 ± 0,5|
|18,0 ± 0,5|
|18,5± 0,5|
Ball Diameter
|23,0 ± 0,5|
|24,0 ± 0,5|
|24,0 ± 0,5|
b. Varnier caliperSSV Varnier caliper20 nonius scale = 39 main scale
∑main scale
∑ nonius scale=
3920
=1.95 mm
SSV ¿2−1.95=0.05 mmx¿1×0.05=0.05 mmMeasurement result ( HP ) = ¿ x± ∆ x∨¿
Table 2. the result of measurement for lenght with varnier caliperMeasured object Magnitude is Measure The measurement results (mm)
Length|18,90± 0,05|
|18,90± 0,05|
|19,05± 0,05|
Iron beam Width
|19,95± 0,05|
|19,85± 0,05|
|19,50± 0,05|
Hight
|19,05± 0,05|
|19,10± 0,05|
|19,05± 0,05|
Ball Diameter
|25,85± 0,05|
|25,85± 0,05|
|26,00± 0,05|
c. Micrometer screw
SSV Horizontal scale = Horizontal scale value
N = 5
10 = 0.5
SSV Micrometer screw ¿Horizontal scale
turnscale ¿0,550 = 0.01 mm
∆x = 12 × 0,01 mm = 0,005 mm
Measurement result ( HP ) = ¿ x± ∆ x∨¿
Table 3. the result of measurement for lenght with micrometer screwMeasured object Magnitude is Measure The measurement results (mm)
Length
|18,250± 0,005|
|18,250± 0,005|
|18,250± 0,005|
Iron beam Width
|18,790± 0,005|
|18,780 ± 0,005|
|18,780± 0,005|
Hight
|19,380± 0,005|
|19,380± 0,005|
|18,875± 0,005|
Ball Diameter
|25,430± 0,005|
|25,430 ± 0,005|
|25,410 ± 0,005|
Measurement of Mass
a. Ohaus Balance of 2610 gramsValue scale arm 1 = 10 gramsValue scale arm 2 = 100 gramsValue scale arm 3 = 0,1 gramsThe mass of the hanging load = 0 kg
SSV = 10
100 = 0,1 gram
∆x = 12
×SSV
= 12
×0,1 gram
= 0,05 gram
Tabel 4. Result Mass Measurement with Balance Ohauss 2610 gram
Object Appointment Arm 1
Appointment Arm 2
Appointment Arm 3
Hanging Burden
Mass Load (g)
Iron Beam
50 0 4,10 0 |54,10±0,05|
50 0 3,95 0 |53,95±0,05|
50 0 3,85 0 |53,85±0,05|
Ball
60 0 6,90 0 |66,90±0,05|
60 0 6,90 0 |66,90±0,05|
60 0 6,85 0 |66,85±0,05|
b. Ohaus Balance of 311 grams
Value scale arm 1 = 100 gramsValue scale arm 2 = 10 gramsValue scale arm 3 = 1 gramValue scale arm 4 = 0.01 gram
SSV = 1
100 = 0.01 g
∆ x = 12
× SSV
= 12
× 0.01
= 0.005 g
Table 5. Result Mass Measurement with Balance Ohauss 311 gram
Object Appointment Arm 1
Appointment Arm 2
Appointment Arm 3
Appointment Arm 4
Mass Load (g)
Iron Beam
0 50 4 0,245 |54,245±0.005|
0 50 4 0,245 |54,245±0.005|
0 50 4 0,255 |54,255±0.005|
Ball
0 60 6 0,865 |66,865±0.005|
0 60 6 0,840 |66,840±0.005|
0 60 6 0,820 |66,820±0.005|
c. Ohaus Balance of 310 grams
Value scale arm 1 = 100 gramsValue scale arm 2 = 10 grams
Turn the scale value = 0.1 scaleNumber Nonius scale = 10 scaleSSV = 0.20 - 0.19 = 0.01 g∆ x = 1 x VSS = 1 x 0,01 = 0.01
Table 6. Result Mass Measurement with Balance Ohauss 310 gram
ObjectAppointment
arm 1Appointment
arm 2Designation Rotate Scale
Designation Nonius Scale
Mass Load (g)
Iron Beam
0 50 4,23 0,06 |54,31±0.01|
0 50 4,20 0,07 |54,27±0.01|
0 50 4,20 0,07 |54,27±0.01|
Ball
0 60 6,70 0,04 |66,74±0.01|
0 60 6,70 0,03 |66,73±0.01|
0 60 6,70 0,03 |66,73±0.01|
Time and Temperature MeasurementSSV thermometer = 10/10 = 10C
∆ x=12
× 1=0.5
Temperature at first = |31±0,5| 0C SSV stopwatch = 1/10 = 0.1 s / scale
Table 7. Result of Time and Temperature Measurement
No. Time (s) Temperature (˚C) Temperature Change (˚C)
1 60 |31±0,5| |0,0±0,5|
2 120 |34±0,5| |3,0±0,5|
3 180 |37±0,5| |3,0±0,5|
4 240 |40±0,5| |3,0±0,5|
5 300 |43±0,5| |3,0±0,5|
6 360 |46±0,5| |3,0±0,5|
Data Analisys
1. Length MeasurementBeama. Ruler
Length of ruler
p=p1+ p2+p3
3 =
18,5+18,5+18,03 = 18,3 mm
δ 1=|p1−p| = |18,5−18,3| = 0,2δ 2=|p2−p|= |18,5−18,3| = 0,2δ 3=|p3−p| = |18,0−18,3| = 0,3δ max=0,3
ℜ=∆ PP
×100%
ℜ= 0,318,3
×100 %=1,64 % (3 AB )
Physics Report :Hp = |p ±⧍ p|mmHp = |18,3 ± 0,3|mm
Width of ruler
l=l1+ l2+l3
3 =
18,5+18,5+18,53 = 18,5 mm
δ 1 = |l1−l| = |18,5−18,5| = 0,0
δ 2 = |l2−l| = |18,5−18,5| = 0,0
δ 3 = |l3−l| = |18,5−18,5| = 0,0
δ max=0,5
ℜ=∆ ll
×100 %
ℜ= 0,518,5
×100 %=0,0270 % (4 AB)
Physics Report : Hp =|l ±⧍ l|mm Hp = |18,50 ± 0,50|mm
Height of ruler
t=t1+t 2+ t3
3 =
18,0+18,0+18,53 = 18,2 mm
δ 1 = |t 1−t| = |18,0−18,2| = 0,2
δ 2 = |t 2−t| = |18,0−18,2| = 0,2
δ 3 = |t 3−t| = |18,5−18,2| = 0,3
δmax=0,3
ℜ=∆ tt
×100 %
ℜ= 0,318,2
×100 %=1,65 %(3 AB)
Physics Report : Hp = |t ±⧍ t|mm Hp = |18,2 ± 0,30|mm
Volume of iron beamV = p̅ x l̅ x t̅ = 18,3 x 18,5 mm x 18,2 mm = 6161,61mm3
dV = │∂V∂ P │dp + │
∂V∂ l │dl + │
∂V∂ l │dt
dVV = │
¿plt │dp + │
ptplt │dl + │
plplt │dt
dVV = | l . t
p .l .t|dp + | p .tp .l .t| dl + | p . l
p .l .t| dt
dVV = │ 1
p│dp + │ 1
l│dl + │ 1
t│ dt
dVV =
dpp +
dll +
dtt
dV =│ dp
p ̅( + dl
l (̅ + dt
t (̅ │ V
ΔV = |∆ pp
+ ∆ ll
+ ∆ tt | V
ΔV = | 0,318,3
+ 0,518,5
+ 0,318,2|6161,61
ΔV = 369,0804 mm3
RE = ∆ VV
X 100 %
RE = 369,08046161,61
X 100 %
RE = 5,99 % (2AB)
DK = 100 % - RE
DK = 100% - 5,99%
= 94,01 %
Physics Report : Hp = │V ± ΔV│mm3
Hp = |6,2 ± 0,37| 103 mm3
b. Vernier caliperLength of Vernier caliper
p=p1+ p2+p3
3
p=18,90+18,90+19,053
=18,95 mm
δ 1=|18,90−18,95|=0,05δ 2=|18,90−18,95|=0,05δ 3=|19,05−18,95|=0,10δ max=0,10
RE = Δ pp
× 100 %
RE = 0,1018,95
×100 %
RE = 0,527 % (4 AB)
Physics Report :Hp = |p ±⧍ p|mmHp = |18,95 ± 0,10|mm
Width of Vernier Caliper
l=l1+ l2+l3
3
l=19,95+19,85+19,503
=19,76 mm
δ 1=|19,95−19,76|=0,16δ 2=|19,85−19,76|=0,09
δ 3=|19,50−19,76|=0,26δ max=0,26
RE = Δll
×100%
RE = 0,2619,76
×100 %
RE = 1,3157 % (3 AB)
Physics Report :
Hp = |l ±⧍ l|mmHp =|19,8 ± 0,26|mm
Height of Vernier caliper
t=t+t 2+t3
3
t=19,05+19,10+19,053
=19,07 mm
δ 1=|19,05−19,07|=0,02δ 2=|19,10−19,07|=0,03δ 3=|19,05−19,07|=0,02δ max=0,03
RE = Δtt
×100 %
RE = 0,0319,07
×100 %
RE = 0,1573 % (4 AB)
Physics Report :Hp =|t ±⧍ t|mmHp = |19,07 ± 0,03|mm
Volume of iron beam V = p x l x t = 18,95 mm x 19,76 mm x 19,07 mm = 7140,79 mm3
dV = │∂V∂ P │dp + │
∂V∂ l │dl + │
∂V∂ l │dt
dVV = │
¿plt │dp + │
ptplt │dl + │
plplt │dt
dVV = | l . t
p .l .t|dp + | p .tp .l .t| dl + | p . l
p .l .t| dt
dVV = │ 1
p│dp + │ 1
l│dl + │ 1
t│ dt
dVV =
dpp +
dll +
dtt
dV =│ dp
p ̅( + dl
l (̅ + dt
t (̅ │ V
ΔV = |∆ pp
+ ∆ ll
+ ∆ tt | V
ΔV = | 0,118,95
+ 0,2619,76
+ 0,0319,07|7140,79
ΔV = 141,69 mm3
RE = ∆ VV
×100 %
= 141,69
7140,79×100 %
= 1,98 % (3 AB)DK = 100 % - RE
= 100 % - 1,98 % = 98,02 %
Physics Report : Hp = │V ± ΔV│mm3
Hp = |7,14 ± 0,14| 103 mm3
c. Screw MicrometerLength of screw micrometer
p=p1+ p2+p3
3
p=18,250+18,250+18,2503
=18,250 mm
δ 1=|18,250−18,250|=0,00δ 2=|18,250−18,250|=0,00δ 3=|18,250−18,250|=0,00δ max=0,05
RE = Δ pp
× 100 %
RE = 0,05
18,250×100 %
RE = 0,274 % (4 AB)
Physics Report :Hp = |p ±⧍ p|mmHp = |18,25 ± 0,05|mm
Width of screw micrometer
l=l1+ l2+l3
3
l=18,790+18,780+18,7803
=18,783 mm
δ 1=|18,790−18,783|=0,007δ 2=|18,780−18,783|=0,003
δ 3=|18,780−18,783|=0,003δ max=0,007
RE = Δll
×100%
RE = 0,007
18,783×100 %
RE = 0,0372 % (4 AB)
Physics Report :Hp = |l ±⧍ l|mmHp = |18,78 ± 0,007|mm
Height of Screw micrometer
t=t+t 2+t3
3
t=18,875+19,380+19,3803
=19,212 mm
δ 1=|18,875−19,212|=0,337δ 2=|19,380−19,212|=0,168δ 3=|19,380−19,212|=0,168δ max=0,337
RE = Δtt
×100 %
RE = 0,33719,212
×100 %
RE = 0,0175 % (4 AB)
Physics Report :Hp = |t ±⧍ t|mmHp = |19,21 ± 0,337|mm
Volume of iron beamV = p x l x t = 18,250 mm x 18.783 mm x 19,212mm = 6585,6767 mm3
dV = │∂V∂ P │dp + │
∂V∂ l │dl + │
∂V∂ l │dt
dVV = │
¿plt │dp + │
ptplt │dl + │
plplt │dt
dVV = | l . t
p .l .t|dp + | p .tp .l .t| dl + | p . l
p .l .t| dt
dVV = │ 1
p│dp + │ 1
l│dl + │ 1
t│ dt
dVV =
dpp +
dll +
dtt
dV =│ dp
p ̅( + dl
l (̅ + dt
t (̅ │ V
ΔV = |∆ pp
+ ∆ ll
+ ∆ tt | V
ΔV = | 0,0518,250
+ 0,00718,783
+ 0,33719,212|6585,6767
ΔV = 135,7506 mm3
RE = ∆ VV
×100 %
= 135,7506
6585,6767×100 %
= 2,06 % (3 AB)
DK = 100 % - RE
= 100 % - 2,06 %
= 97,94 %
Physics Report : Hp = │V ± ΔV│mm3
Hp = |6,59 ± 0,135| 103 mm3
Balla. Ruler
δ 1=|23,0−23,67|=0,67δ 2=|24,0−23,67|=0,33δ 3=|24,0−23,67|=0,33δ max=0,67
x=x1+x2+ x3
3
x=23,0+24,0+24,03
x=23,67
r = 12
d
r = 12
x23,67
= 11,835
Volume of ball
V = 43
πr 3
V = 43
π (12
d)3
V = 43
x3,14 x 11,8353
= 6940,2189mm3
The propagation of ball
V = 43
πr 3
∆ vv = 3|∆ d
d |v
∆ v = 3| 0,6723,67|x 6940,2189
∆ v=589,3468
RE = ∆ vv
x 100 %
= 589,3468
6940,2189x100 %
= 8,4917% (2AB)
DK = 100% - RE
= 100% - 8,4917 %
= 91,5082 %
Physics Report :Hp = │V ± ΔV│mm3
Hp = |6,9± 0,59| 103 mm3
b. Vernier caliperδ 1=|25,85−25,90|=0,05δ 2=|25,85−25,90|=0,05δ 3=|26,00−25,90|=0,10δ max=0,10
x=x1+¿ x2+x3
3¿
x=25,85+25,85+26,003
x=25,90
r = 12
d
r = 12
×25,90
= 12,950
V = 43
πr 3
= 43 × 3,14 × 12,9503
= 9092,3823 mm3
For propagation of ball
V = 43
πr 3
∆ vv = 3|∆ d
d |× v
= 3| 0,125,90|× 9092,3823
∆ v=105,31716
RE = ∆ vv
×100 %
= 105,317169092,3823
×100 %
= 1,1583 % (3AB)
DK = 100% - RE
= 100% - 1,1583 %
= 98,84 %
Physics Report :Hp = │V ± ΔV│mm3
Hp = |9,09 ± 0,11| 103 mm3
c. Screw micrometer
δ 1=|25,430−25,423|=0,007δ 2=|25,430−25,423|=0,007δ 3=|25,410−25,423|=0,013δ max=0,013
x=x1+¿ x2+x3
3¿
x=25,430+25,430+25,4103
x=25,423
r = 12
d
r = 12
x25,423
= 12,71
Volume of ball
V = 43
πr 3
V = 43
x3,14 x 12,71
= 8599,2146 mm3
The propagation of ball
V = 43
× π r3
∆ vv = 3|∆ d
d |× v
∆ v = 3| 0.01325,423|× 8599,2146
∆ v=13,1915
RE = ∆ vv
×100 %
= 13,1915
8599,2146×100 %
= 0,1534 % (4 AB)
DK = 100% - RE
= 100% - 0,1534 %
= 99,8466 %
Physics Report :Hp = │V ± ΔV│mm3
Hp = |85,99 ± 0,13| 102 mm3
Measurement of Mass
Beam (m)1. Ohaus Balance 2610 gramm1=|54,10 ± 0,05|g
m2=|53,95 ± 0,05|g
m3=|53,85 ± 0,05|g
m=53,97 g
δ 1=|54,10−53,97|=0,13 g
δ 2=|53,98−53,97|=0,02 g
δ 3=|53,85−53,97|=0,012 g
δ max=0,13 gδ max=∆ m=0,13 g
ℜ=0,24% (4 AB)
Hp=|53,97 ± 0,13|g
Density of Beam on Balance Ohauss 2610 grams
Volume that measured by Rulerm=|53,97 ± 0,13|gv=|6161,61 ±369,2469|mm3
ρ= 53,976161,61
ρ=0,0087
∆ ρ=|∆ mm
+ ∆ vv |ρ
∆ ρ=| 0,1353,97
+ 369,24696161,61 |0,0087
∆ ρ=|0,00024+0,0599|0,0087
∆ ρ=0,00054
ℜ=∆ ρρ
×100 %
¿ 0,0005 40,0087
×100%
¿6,2% (2 AB)
DK = 100% - REDK=100 %−5,88 %
¿93,8 %
Hp=|ρ± ∆ ρ| gmm3
Hp=|8,7 ±0,54| 10-3 g/mm3
Volume that measured by Vernier Caliper
m=|53,97 ± 0,13|gv=|7140,79 ±141,691|mm3
ρ=0,0075 gmm3
∆ ρ=0,00017 gmm3
ℜ=2,27 % (3 AB)DK=97,73 %
Hp=|ρ± ∆ ρ| gmm3
Hp=¿7,50 ± 0,17∨¿ 10-3 g/mm3
Volume that measured by Micrometer screwm=|53,97 ± 0,13|g
v=|6585,6767 ± 119,7276|mm3
ρ=0,0082 gmm3
∆ ρ=0,00017 gmm3
ℜ=2,07 % (3 AB)DK=97,93 %Hp=¿8,2 ± 0,17∨¿ 10-3 g/mm3
2. Ohauss Balance 311 gram
m1=|54,245 ± 0,005|g
m2=|54,245 ± 0,005|g
m3=|54,255 ± 0,005|g
m=54,248 g
δ 1=|54,245−54,248|=0,003 g
δ 2=|54,245−54,248|=0,003 g
δ 3=|54,255−54,248|=0,007 g
δ max=0,007 g
δ max=∆ m=0,007 g
ℜ=0,01 %(4 AB)
Hp=|54,25 ± 0,007|g
Density of Beam on balance ohauss 311 grams
Volume that measured by ruler
m=|54,25 ± 0,007|gv=|6161,61 ±369,2469|mm3
ρ=0,0088 gmm3
∆ ρ=0,00053 gmm3
ℜ=6,01 % (2 AB)DK=93,98 %Hp=¿8,8 ± 0,53∨¿ 10-3 g/mm3
Volume that measured by Vernier Caliper
m=|54,25 ± 0,007|gv=|7140,79 ±141,69|mm3
ρ=0,0076 gmm3
∆ ρ=0,00015 gmm3
ℜ=2,00 % (3 AB)DK=98,00 %Hp=¿7,60± 0,15∨¿ 10-3 g/mm3
Volume that measured by Micrometer Screw
m=|54,25 ± 0,007|gv=|6585,6767 ± 119,7276|mm3
ρ=0,0082 gmm3
∆ ρ=0,00015 gmm3
ℜ=1,83 % (3 AB)DK=98,17 %Hp=¿|8,2 ± 0,15| 10-3 g/mm3
3. Ohauss Balance 310 gramm1=|54,31± 0,01|g
m2=|54,27± 0,01|g
m3=|54,27 ± 0,01|g
m=54,28 g
δ 1=|54,31−54,28|=0,03 g
δ 2=|54,27−54,28|=0,01 g
δ 3=|54,27−54,28|=0,01 g
δ max=0,03 g
δ max=∆ m=0,03 g
ℜ=0,055% (4 AB)
Hp=|54,28 ± 0,03|g
Density of Beam on Balance Ohauss 310 grams
Volume that measured by Ruler
m=|54,28 ± 0,03|gv=|6161,61 ±369,2469|mm3
ρ=0,0088 gmm3
∆ ρ=0,00053 gmm3
ℜ=6,02 % (2 AB)DK=93,8 %Hp=¿8,8 ± 0,53∨¿ 10-3 g/mm3
Vernier Caliperm=|54,28 ± 0,03|g
v=|7140,79 ±141,69|mm3
ρ=0,0076 gmm3
∆ ρ=0,00015 gmm3
ℜ=2,03% (3 AB)DK=97,96 %Hp=¿|7,60 ± 0,15| 10-3 g/mm3
Micrometer Screwm=|54,28± 0,03|g
v=|6585,6767 ± 119,7276|mm3
ρ=0,0082 gmm3
∆ ρ=0,00015 gmm3
ℜ=1,83 % (3 AB)DK=98,17 %Hp=¿8,2 ± 0,15∨¿ 10-3 g/mm3
Ball 1. Ohaus Balance 2610 gramm1=|66,90 ± 0,05|g
m2=|66,90 ± 0,05|g
m3=|66,85± 0,05|g
m=66,84 g
δ 1=|66,90−66,84|=0,06 g
δ 2=|66,90−66,84|=0,06 g
δ 3=|66,85−66,84|=0,01 g
δ max=0,06 g
δ max=∆ m=0,06 g
ℜ=0,09 % (4 AB)
Hp=|66,84 ±0,06|g
2. Ohaus Balance 311 gramm1=|66,865 ± 0,005|g
m2=|66,840 ± 0,005|g
m3=|66,820± 0,005|g
m=66,841 g
δ 1=|66,865−66,841|=0,024 g
δ 2=|66,840−66,841|=0,001 g
δ 3=|66,820−66,841|=0,021 g
δmax=0,024 g
δ max=∆ m=0,024 g
ℜ=0,036% (4 AB)
Hp=|66,841± 0,024|g
3. Ohaus Balance 310 gramm1=|66,74 ±0,01|g
m2=|66,73 ± 0,01|g
m3=|66,73± 0,01|g
m=66,73 g
δ 1=|66,74−66,73|=0,01 g
δ 2=|66,73−66,73|=0 g
δ 3=|66,73−66,73|=0 g
δ max=0,01 g
δ max=∆ m=0,01 g
ℜ=0,01 %(4 AB)
Hp=|66,73± 0,01|g
Calculate Volume of Ball1. Ruler
V=16
π d3=¿mm3
V=16
(3,14 ) (23,673 )=6940,2 mm3
dV =|δVδd |∆ d
dV =|δ (d3 )δd |∆ d
dV =|3 d2|∆ d
∆ VV
=|3d2
V |∆ d
∆ VV
=|3d2
d3 |∆ d
dVV
=3|∆ dd |
∆ V =3|∆ dd |V
∆ V =3| 0,6723,67|6940,2
∆ V =589,34mm3
ℜ=∆ VV
x100 %
ℜ=8,49 % (3 AB )
DK=100 %−KR
DK=91,5 %
Hp=¿6,94 ± 0,589∨¿103 mm3
2. Vernier Caliper
V=16
π d3=mm3
V=9092,38 mm3
∆ V =105,32mm3
ℜ=1,16 % (3 AB )
DK=98,8 %
Hp=|9,09± 0,105| 103 mm3
3. Micrometer Screw
V=16
π d3=mm3
V=8599,21mm3
∆ V =13,19 mm3
ℜ=0,15 % ( 4 AB )
DK=99,85 %
Hp=|85,99± 0,1319|102 mm3
EXPLANATION
Based on the data that has been obtained, it can be seen the volume of a cube beam using a ruler V = │6,16 ± 0,20│103 mm3, calipers V =│7,14 ± 0,14│103 mm3and micrometer screw V = │6,59 ± 0,12│103 mm3. The volume of the ball using the rule = │6,94 ± 0,59│103 mm3, calipers V =│9,09 ± 0,11│103 mm3, micrometer screw V = │85.99 ± 0,13│102 mm3. Also known density of beam cube using the ruler |8,7 ± 0,54 | 10-3 (g / mm3), calipers |7,50 ± 0,17| 10-3 (g / mm3) and micrometer screw = |8,20 ± 0,17| 10-3(g / mm3). Based on the data obtained by means of which have a high level of accuracy is the micrometer screw, because the smaller the relative uncertainty (RE), then the higher accuracy achieved in the measurement. As for the balance sheet, which has a high level of accuracy is the balance of 311 grams and 310 grams because it has relatively little uncertainty as well.
CONCLUSION
From the result experiment we can conclude that on the basis of lab measurements and uncertainties can be knotted that any measurement error can have different, depending on the state of the measuring instrument, differences in the level of accuracy of measuring instruments, measuring methods used in, and the ability of the measure. In this lab can distinguish between where the gauge is more accurate and precise in minimizing the time of measurement error.
REFERENCE
[1] Practice Guidebook 1 Unit Basic Physics Basic Physics Laboratory Department of Physics, State University of Makassar
