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. A wooden block

ii. A meter ruler

iii. A vernier caliper

iv. A boiling tube

v. A graduated cylinder

vi. A pebble

vii. A string (40 cm)

viii. A micrometer screw gauge A ball bearing

ix. A 20 cm copper wire SWG 16 (or lower)

x. 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

Mass/(kg)

(M M)

Length/

(m)

(L L)

Widht/

(m)

(W W)

Height/

(m)

(H H)

Volume/

(

(V V)

Density/(kg/

(

Wooden

Block (0.11

(9.9

)

(9.9

(1.8

(1.764

(623.50

Diameter/(m)

(D

Cooper

Wire (7.5

(0.208

1

(1.28 )

(2.667

(2801.64

72.71)

A ball

Bearing (3.52

(9.53

0.005

(4.532

(

A Pebble (0.0242

(1

(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

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

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 m

Volume = π

= π

=

=

= 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)