MEASUREMENT
TECHNIQUES
Prepared by Mr. Akpan
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MEASUREMENT TECHNIQUES
In Physics, different instruments are used to measure physical
quantities. The major quantities we measure in lab are:
1. Length
2. Mass
3. Time
4. Current
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MEASUREMENT OF LENGTH
Length can be measured in the laboratory using different
apparatus base on its nature.
1. Metre rule / Measuring tape
2. Vernier Caliper
3. Micro Screw Gauge
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METRE RULE
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POSSIBLE ERRORS WHEN USING METRE RULE
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REDUCTION OF PARALLAX ERROR
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POSSIBLE ERRORS WHEN USING METRE RULE
REDUCTION OF ZERO ERROR
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POSSIBLE ERRORS WHEN USING METRE RULE
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VERNIER CALIPER
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MAJOR PARTS OF VERNIER CALIPER
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READING ON VERNIER CALIPER
Vernier Caliper Reading = Main Scale Reading + Vernier Scale Reading
SOLUTION
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MICRO SCREW GAUGE
Micro Screw Gauge is use to measure dimension of objects up to
Maximum of about 50mm. It measures up to 0.01mm.
Micro Screw gauge is used to measure diameter of wire.
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MAJOR PARTS OF MICRO SCREW GAUGE
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READING ON MICRO SCREW GAUGE
= Main Scale Reading + Micro Screw Gauge
Scale Reading
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PRECAUTION READING ON MICRO SCREW GAUGE
a.
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PRECAUTION READING ON MICRO SCREW GAUGE
b.
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EXAMPLE
1.
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EXAMPLE
Solution
2.
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EXAMPLE
Solution
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MEASUREMENT OF MASS
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MEASUREMENT OF MASS
The Top-Pan Balance work base on a pressure sensor under the
pan. The mass is measured directly, and value is displayed on a
digital reading scale. The sensitivity for digital scale is 0.01g
while analogue scale is 1g.
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MEASUREMENT OF MASS
Spring Balance work base on the principle of Hooke’s law. It
measures the weight of a body directly.
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MEASUREMENT OF MASS
The Lever/Beam Balance work base on the principle of moment
of force. The unknown mass is balance by a slider along a bar
that is calibrated in mass unit. The balance point give the value
of the unknown Mass.
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MEASUREMENT OF TIME
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MEASUREMENT OF TEMPERATURE
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Sensitivity of Commonly Used Measuring Instrument
INSTRUMENT
METRE RULE
SENSITIVITIY
1mm or 0.1cm
EXAMPLES
543mm
54.3cm
0.543m
Vernier Caliper
0.1mm or 0.01cm
60.3mm
6.03cm
Micro Screw Gauge
0.01mm or 0.001cm
1.42mm
0.142cm
Digital Stop Watch
Analogue
0.01sec
0.1sec
9.85sec
9.8sec
Electronic balance
Analogue
0.01g
1g
4.25g
4g
Protractor
0.5°
32.5°
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ERRORS IN MEASUREMENT
ERROR REDUCTION
NOTE THIS:
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ERRORS IN MEASUREMENT
HOW TO MINIMIZE SYSTEMATIC ERROR
CAUSES OF SYSTEMATIC ERRORS
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EXAMPLE
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YOUR TURN
1.
2.
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ACCURACY AND PRECISION
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PRECISION
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DIFFERENCE BETWEEN PRECISION AND ACCURACY
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EXAMPLE
1.
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EXAMPLE
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YOUR TURN
2.
3.
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UNCERTAINTY
EXAMPLE
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HOW TO CALCULATE THE EFFECT OF RANDOM
UNCERTAINTY
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EXAMPLE
SOLUTION
a.
𝟐𝟎𝟗+𝟐𝟏𝟎+𝟐𝟎𝟗+𝟐𝟏𝟎+𝟐𝟎𝟎
Mean Length =
𝟓
b. Random Uncertainty =
𝟏𝟎𝟑𝟖
= 208mm
𝟓
=
Max. reading − Min Reading
𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒓𝒆𝒂𝒅𝒊𝒏𝒈
𝟐𝟏𝟎 −𝟐𝟎𝟎
=
= 2mm
𝟓
c. Length of Card = 208 ± 2 mm
± 2mm is the absolute uncertainty
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YOUR TURN
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EXPRESSION OF UNCERTAINTY
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RULE FOR STATING UNCERTAINTY
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COMBINATION OF UNCERTAINTY
1. ADDITION AND SUBTRACTION
a = 5.20±0.50
b = 3.50±0.30
Find the measurement of y with uncertainty
(a) y = a + b
(b) z = a – b
Solution
(a)
y = (a + b)±(∆a + ∆b)
= (5.20 + 3.50) ± (0.5 + 0..3)
= 8.70 ±0.80
(b)
Z = (a-b) ±(∆a + ∆b)
= 5.20 – 3.50 ± (0.5 + 0..3)
= 1.70±0.80
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EXAMPLE
SOLUTION
(∆𝐀 + ∆B)
(0.1 +0.1)
0.2 m³
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YOUR TURN
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20±1.0°C
Multiplication and Division
∆𝒙
=
𝟏𝟖.𝟐𝟎
a. X = ab
Uncertainty
∆𝒙 ∆𝒂 ∆𝒃
= +
𝑿
𝑨
𝑩
X = 5.20 x 3.50 = 18.20
∆𝒙 𝟎.𝟓𝟎 𝟎.𝟑𝟎
=
+
𝑿
𝟓.𝟐𝟎 𝟑.𝟓𝟎
∆𝒙
= 0.096 + 0.085
𝟏𝟖.𝟐𝟎
0.182
∆𝒙 = 0.182 x 18.20 = 3.30
𝟏𝟖. 𝟐 ± 𝟑. 𝟑
% Uncertainty
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∆𝒙
= x 100
𝑿
𝟑.𝟑𝟎
=
x 100
𝟏𝟖.𝟐
= 18%
EXAMPLE
∆𝒚 ∆𝒂 ∆𝒃
= +
𝒀
𝑨
𝑩
∆𝒚
𝟎.𝟓 𝟎.𝟑
= +
𝟏.𝟒𝟗 𝟓.𝟐 𝟑.𝟓
∆𝒚
= 0.182
𝟏.𝟒𝟗
∆𝒚 = 0.182 X 1.49
= 0.27
∆𝒚
𝒀
𝟎.𝟐𝟕
𝟏.𝟒𝟗
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YOUR TURN
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POWER AND EXPONENTS
∆z
𝒁
=
𝒂∆𝒃
𝒃
2. Y = 𝒂 =
𝟏∆𝒂
=
𝟐𝒂
, numbers, etc
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EXAMPLE
A cylinder of volume 15.0±0.5cm³ has a length of
20.0±0.1cm. Find the radius of the cylinder with uncertainty.
Solution
Volume of a cylinder V = 𝝅r²L
r=
𝑽
𝝅𝒍
=
𝟏𝟓
𝟑.𝟏𝟒𝟐 𝒙 𝟐𝟎
= 0.49
∆𝒓 ∆𝑽 ∆𝑳
= +
𝒓
𝑽
𝑳
∆𝒓 𝟎.𝟓 𝟎.𝟏
= +
𝒓
𝟏𝟓 𝟐𝟎
= 0.033 + 0.005 = 0.038
∆𝒓 = 0.49 x 0.04 = 0.0195 = 0.02
r = 0.49±0.02cm
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Percentage
Uncertainty
𝟎.𝟎𝟐
=
x 100
𝟎.𝟒𝟗
= 4%
YOUR TURN
1. In a circuit, a current of 2.50±0.05A flow through a
resistor of resistance 4.7±0.3Ω. What is the value off
voltage with its uncertainty?
2. A student finds the density of a liquid by measuring its
mass and its volume as follows:
Mass of empty beaker = (20 ± 1)g
Mass of beaker + liquid = (70 ±1)g
Volume of liquid = (10.0 ± 0.6)cm³
He correctly calculated the density of the liquid as
5.0g/cm³. What is the uncertainty of the value?
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11.75±.96 = 12 ±1v 5.0 ±0.3g/cm³
DETERMINATION OF SUITABLE INSTRUMENT FOR
VARIOUS MEASUREMENT
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CLASS WORK
1.
2.
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CLASS WORK
1.
2.
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CLASS WORK
3.
4.
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CLASS WORK
3.
4.
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CLASS WORK
5.
6.
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CLASS WORK
7.
8.
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ASK QUESTION
I WISH YOU ALL THE VERY BEST!
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