Physics Laboratory Report
Experiment: No. 1 Title: Basic Measurement and Uncertainty
Prepared By:
Date: 4 November 2011
Liyana binti Hamdan (D20101037385)
Partner: Wan Nur Syuhada binti Wan Semail (D20101037366)
Lab Instructor: En Kamal Ariffin
Lab Section: Makmal Pakar 1A
Remarks by Grader:
Grade: Laboratory Instructor’s Initials:
Experiment 1:Basics measurement and uncertainty Objectives: 1. Expose the students to the simple understanding of the uncertainty, and the propagation of error. 2. Enable the students to identify and write the value of uncertainty that are associated to the measurement. 3. Develop the basics experimental skills including handling of measuring devices, taking measurements, using appropriate instruments and etc. 4. Determine the density of an object and its uncertainty.
Background Measuring some physical quantities is part and parcel of any physics experiment. It is important to realize that, not all measured values are exactly the same as the actual values. This could be due to the errors that we made during the measurement, or perhaps the apparatus that we used may not be accurate or sensitive enough. Therefore, as a rule, the uncertainty of a measurement must be taken and has to be recorded together with the measured value. The uncertainty of a measurement depends on the type of measurement and on how it is done. For a quantity x with the uncertainty x , the reading written as follows: x± x Furthermore, we can calculate, Relative uncertainty
=
and, Percentage of uncertainty,
x% = ×100%
1.1 Single Reading (a) If the reading is taken from a single point or at the end of the scale we use: x = x (the smallest division from the scale) (b) If the apparatus uses a vernier scale: x = 1 x (the smallest division from the vernier scale)
(c) If the readings are taken from two points on the scale: x=2 = the smallest division from the scale This applies to measurements made using electric meters, stopwatch, vernier calipers and micrometer screw gauge.
1.2 Repeated Readings For a set of n repeated measurements of x, the best value is the average value:
= where
n = the number of readings taken xi= the reading
The uncertainty is given by:
= The result should be written as:
= 1.3 Density The density, ρ of a substance is given by: = where,
m = mass of the substance V = volume of the substance
This may be determined experimentally by measuring the mass and volume of a given sample. The volume of regularly shaped object can be calculated from length measurements; for example:
(i) Cuboid V = × w× h
= where,
+
+
= length , w= width and h= height of the rectangle
(ii) Cylinder V=(
=2 Where
)
+
r = radius and = length of the cylinder
(iii) Sphere V=
=3 Where
r = radius of the sphere
The uncertainty of density is given by:
=
Apparatus: i. ii. iii. iv. v. vi. vii. viii. ix. x.
A wooden block A meter ruler A vernier caliper A boiling tube A graduated cylinder A pebble A string (40 cm) A micrometer screw gauge A ball bearing A 20 cm copper wire SWG 16 (or lower) A balance (preferably electronic balance)
Procedure: 1. Measure and record the dimension of wooden block including their uncertainties using meter ruler. 2. Vernier caliper was used to determined the thickness of the boiling tube wall including its uncertainties. 3. The density and the uncertainties of materials that are listed above was determined by: a) Use the electronic balance to obtain the mass (in grams). b) Use the micrometers gauge or vernier caliper to measure the diameter, length and other measurement of the wooden block, the ball bearing and cooper wire. Use the graduated cylinder to measure the volume of the pebble. c) Estimate the errors that are related to the measurement using the calculation and theory.
Data Analysis The Determination of the Density Description of Object Wooden Block
Mass/(kg) (M M) (0.11
Length/ (m) (L L) (9.9
Widht/ Height/ (m) (m) (W W) (H H) (9.9 (1.8
Volume/ ( (V V) (1.764
Density/(kg/ ( (623.50
)
Cooper Wire
(7.5
A ball Bearing
(3.52
A Pebble
(0.0242
(0.208 1
Diameter/(m) (D (1.28 )
(9.53 0.005
(2.667
(4.532
(1
(2801.64 72.71)
(
(2420
Uncertainty The uncertainty of every instrument used in this experiment must be determined before the process of measurement. Usually the uncertainty of the instrument had been writing at the instrument, but it is better to us to determine by calculation. They are the calculation for instrument: 1. Meter ruler =2
[
1]cm
= 0.1cm 2. Vernier caliper Main scale : centimeter (cm) Smallest unit for main scale : 0.1 cm Smallest unit for vernier scale :
cm
0.002 cm 3. Micrometer screw gauge Main scale : millimeter ( ) Smallest unit for main scale : 0.5 Thimble scale :
0.01 mm mm = 0.005 mm
4. Electronic Balance
0.002 cm
Calculation for data: Calculation for this experiment was determined by the theory that are provided. The density of the object was not same from one to other. It’s depend on the types of object. a) Wooden block By using meter ruler :
Volume = = = = =
Mass = = (109.51 =
=
176.42
= 1.337 = (1.337 = ( 1.337 V = (1.7642
)
=
Density =
=
=( = 4.78 kg Density,
b) Boiling tube Measured by using using vernier caliper : Outer = Inner Thickness
outer – inner
c) Pebble Mass weighed by using electronic beam balance
Volume measured using graduated cylinder = final volume of water – initial volume of water
=
Density
= = 243 kg
Density,
d) Copper wire Mass weighed by using electronic balance Length measured by using meter ruler Diameter measured by using micrometer screw gauge Diameter
Radius =
= (0.64
Volume = π
=π =
m
= = 3.3784
Density =
= = 2801.64
= =72.71 kg Density
= (2801.64
e) Ball Bearing Mass (electronic balance)
= (3.52
= (3.52
Diameter (Micrometer Screw Gauge)
= 9.5 mm + ( 3 = ( 9.53 0.005 ) mm = (9.53
Radius
= (4.765
Volume
= = = 4.532
=
= = 7.133 Density,
= = = 7766.99 kg = = =111.00 kg
Density,
= (5840.68
111.00) kg
Discussion: The experiment was carry out to determined the suitable instrument to measure the density of substance. Suitable instrument that are used for this experiment was very important to make sure we got the precise reading for the calculation. Calculation in this experiment was calculate refer to the theory provided. During the experiment was carry out, there are a few error that occurs.
Errors that occur : i.
There are parallax error that happen when the eyes does not directly proportional to the reading of the measurement.
ii.
Zero error that are at the instrument.
iii.
There are air resistance that are effect the mass of substance when the mass was taken by electronic balance.
iv.
The instrument used for the substance does not suitable, so the reading does not precise.
v.
The reading of the measurement does not repeated.
How to overcomes: i.
Make sure our eyes are directly proportional when taken the reading of measurement.
ii.
Adjust the instrument to decrease the zero error.
iii.
Make sure there are no air resistance when use the electronic balance.
iv.
Use the suitable and precise instrument for different substance.
v.
Take a few reading of measurement and calculate the average to get the accurate reading.
Conclusion: The density from this experiment will be more precise when the suitable instrument used. In order to
References: [1] http://physics.unc.edu/labs/sample report.php, retrieve Oct 3rd, 2011, [2] John D. Cutnell,Kenneth W.Johnson, Introduction to Physics, 8th Ed. John Wiley & Sons (Asia) Pte Ltd, 2010 [3] Christopher G. Deacon, “Error Analysis in the Introductory Physics Lab”, The Physics Teacher,vol 30, 368, (1998)
