Tuesday, 27 March 2012

The Scientific Method

(Updated on 2/10/2013 to include latest SPM 2012 questions)

Analysing Scientific Investigations
·        Before the time of Galileo Galilei (1564 ~ 1642), natural phenomena were commonly explained by pure thinking alone – for this reason, physics was then also known as natural philosophy.

·        However, this pure thinking or philosophical approach had led to many false beliefs - among which were that:
·        Our Earth was flat;
·        Our Earth was the centre of the universe;
·        A heavier object would fall freely faster than a lighter object…

·        Galileo adopted the approach that all hypothesis put forth to explain a natural phenomenon must be systematically investigated by experiments to prove its validity before it can be accepted as a law of nature or theory of physics – this systematic approach in verifying the validity of a hypothesis by experiments was, in essence, the scientific method.  Galileo was thus regarded by many including Albert Einstein as the father of experimental physics and of modern science.

·        Using the scientific method, Galileo proved that all objects – heavy or light – would fall freely from the same point with the same acceleration, g, which depends on the gravitational field strength at that point. Earlier authoritative “pure thinking theory on free-falling objects” was therefore proven wrong.

·        Laws of nature and physic are formulated by an inductive process – that is, from hypotheses on specific cases which have been proven right by scientific experiments. (As a simple illustration: This is how the law of nature which states that “the Sun rises in the east” may come about by an inductive process:

Man noticed that each time he looks at sunrise, the Sun seems to rise in a particular direction. He noticed from his compass the direction is east. So, he offers the hypothesis that “the Sun always rises in the east”. In all subsequent occasions that he or others look at sunrise, the Sun is still observed to rise in the same eastern direction. Hence, his hypothesis is accepted as a law of nature.)

·        Once accepted as a law of nature or physics law, the law can be applied to make deductions or predictions for subsequent specific instances. (Thus, when lost in the jungle, Man can deduce that the direction in which the Sun rises must be the east because the accepted law of nature is that “the Sun rises in the east”.)

The Scientific Method – The Main Steps:

1.      Making Observation (of a natural phenomenon or event that interests us) using our 5 senses of sight, hearing, smell, taste and touch – for example, observing movement of a swing in a playground.

2.      Making Inference – i.e. making early conclusion or recognition on the existence of a relationship between 2 variables observed in the phenomenon – For example, after careful observation, concluding that the time taken for a swing to make a complete swing depends on the length of the swing - there is a relation between the variable length and the variable time of the swing. The former is known as the independent or manipulated variable and the latter, the dependent or responding variable.

3.      Identifying Problem – i.e. asking questions based on the inference made: For example, what exactly is the nature of the inferred relationship? How does the length of the swing affect the period of its swing? A scientific report on an experiment usually begins with the problem statement or aim of the experiment which is usually worded as follows: “To study (or investigate) how one variable ( the manipulated variable, say, the length of the pendulum) affects another variable (the responding variable,say, the period of its oscillation)”.

4.      Making Hypothesis – i.e. making an early intelligent guess or sensible general statement about the exact nature of the inferred relationship between the 2 variables. There are at least 2 different ways to state the same hypothesis. Take the pendulum swing for example again:
a)    the period of oscillation increases as the length of the pendulum increases – i.e. hypothesizing how the responding/dependant variable changes as the manipulated/independant variable changes; or,
b)   as the length of the pendulum increases, the period of oscillation increases – stating the changes in the manipulated/independent variable first before hypothesizing how the values of the responding/dependant variable will be affected.

5.      Identifying Variables – i.e. identifying all other variables that may affect the responding/dependant variable other than the variable already identified (i.e. the manipulated/independent variable) so that all other variables that can affect the responding/dependent variable are fixed, controlled or kept constant. Therefore, a scientific experiment must identify all 3 sets of variables:
a.       Manipulated/Independent Variables
b.      Responding/Dependent Variables
c.       Fixed Variables

(2009 P1 Q3 pg. 186 - Test on understanding of the 3 variables)
(2010 P1 Q2 pg. 230 - Test on understanding of the 3 variables)

6.      Controlling Variables – i.e. planning and deciding:
               i.            how to manipulate the independent variable;
             ii.            how to measure the responding/dependent variable; and
            iii.            how to keep the fixed variables constant.

7.      Planning Experiment – means determining:
a.       what apparatus, instruments and materials to use;
b.      the procedure of the experiment;
c.       the method of collecting data;
d.      the ways to analyse and interpret the collected data.

8.  Collecting Data – means
               i.      making observation and description of qualitative data; or
             ii.      taking measurement of quantitative data; and, recording the data systematically by tabulation:
a.       Top Row of Table Must Contain: 1) Name of Variable, 2) Symbol and 3) Unit of Measurement
b.      First Column Contains: Values of Manipulated Variable at Uniform Intervals & in Ascending or Descending Order
c.       Second Column (with sub-colums for repeated measurements and average values) for: Measured Values of Responding Variables
d.      Third Column, if any, for Values Derived From Responding Variables for Use in Plotting Graph
e.       Values in Each Column Must Be Stated to the Same Number of Significant Numbers or Decimal Places; But Derived Values May Have an Additional Number of Decimal Places.

9.  Interpreting Data – this is the part that involves the study of the recorded data, the making additional calculations where necessary and the drawing of graphs to see whether the relationship between the 2 variables is as originally hypothesized. Discussion is usually involved. The six common graphs, their meanings and how they look like:
               i.            Responding Variable Increases as Manipulated Variable Increases:
             ii.            Responding Variable Decreases as Manipulated Variable Increases
            iii.            Responding Variable Increases Linearly with Manipulated Variables
           iv.            Responding Variable Decreases Linearly with Manipulated Variable
             v.            Responding Variable is Directly Proportional to Manipulated Variable
           vi.            Responding Variable is Inversely Proportional to Manipulated Variable (i.e. Responding Variable is Directly Proportional to the Inverse or Reciprocal of Manipulated Variable)

(SPM 2006 P1 Q2 Pg. 48 on graph for F = kx)

(SPM 2012 P3 Q1(d) & (e) pg 375: Plot the graph of x against 1/a (as in x = λD/a) and state the relationship between x and 1/a )
* Any graph of y against 1/x - or x against 1/a as in the above SPM 2012 P3 Q1 -  which is a straight line with a positive gradient must not be described as "y is directly proportional to 1/x" because such a straight line graph will never pass through the origin as 1/x will never be zero (in the case of the SPM question, 1/a will never be zero). For such a graph, the relationship is: y increases linearly with 1/x (or, x increases linearly with 1/a in the case of the SPM 2012 P3 Q1(e))

1  10.  Making Conclusion – this involves making a statement on the findings of the experiment:
a.       Whether the inference made was correct; and,
b.      Whether the hypothesis put forth is valid or to be rejected.

1  11.  Writing Report – Writing a report on the whole experiment so that:
a.       Its findings can be critically evaluated by others; and, if necessary, the experiment can be repeated to verify its findings;
b.      The findings are recorded for understanding, use or application by others.

Relevant Past-Year Questions: Most Paper 3 questions are related to scientific method of investigation - of direct relevance to Form 4 Chapter 1 are:
  • SPM 2010 Paper 3 Q1 at Pg. 268
  • SPM 2009 Paper 3 Q1 at Pg. 220
  • SPM 2008 Paper 3 Q1 at Pg. 174

Measurements in Science

Understanding Measurements

1.      Nature of Measurement: To measure a physical quantity is to make an acceptable estimate of the true and actual value of the quantity.

2.      All measurements in science are Man’s attempts to determine the true and actual value of the relevant physical quantities.

3.      Errors in Measurements
·        No measurement is without error because:
o       No measuring instruments is perfect;
o       No handling of measuring instrument (i.e. technique of measurement) is perfect; and,
o       No environment of measurement is perfectly stable or error-free.

·        An error in measurement is the difference between the actual value of the physical quantity and the value obtained in the measurement.

·        The 2 main types of errors:
Systematic Errors                                       Random Errors
-         Tend to shift all measurements             - Fluctuate from 1 measurement to the
            in a particular direction - the mean         the next – the mean from measurements
            from measurements is displaced            is close to the actual true value
            from the actual true value
-         Are due to:                                           - Are due to:
o       Incorrect calibration of                    * Personal error e.g. parallax error
equipment – Zero errors.                * Natural errors e.g. changes in wind,
o       Improper use of equipment.               temperature, humidity, magnetic field,
o       Forgetting to account for                    gravity, etc. while experiment is on
some effects                                   * Use of wrong technique while
-         To find-out systematic errors                     taking measurements – e.g. excessive
o       Use different instrument                       pressure in turning micrometer
o       Compare data                                    screw gauge
-         To correct zero error:
o       Adjust zero adjustment screw         - To minimize random errors:
o       In the case of vernier calipers            * Take many readings & find mean
      and micrometer screw gauge,            * Ensure no parallax error
Correct Reading = Reading               * Minimise natural errors
Obtained – Zero Error

(2012 P2 Q1 at pg. 346 on: Vernier calipers with zero error.)

Sensitivity, Consistency (Precision) & Accuracy
1.      Sensitivity of Measuring Instrument
·        Sensitivity of a measuring instrument is defined as the capability of that instrument 1) to respond and/or 2) to register small amounts or differences of the targeted stimuli (e.g. heat) or physical quantity (e.g. temperature) respectively.

·        Sensitivity depends on:  (2007 P1 Q3 pg. 92 - Which balance is more sensitive?)
o       The smallest division on its scale – the finer, the more sensitive (e.g. the smallest division on the thimble scale of micrometer screw gauge is 0.01mm whereas that on the vernier scale of the vernier calipers is 0.01cm);
o       The design of the instrument – e.g. the finer the capillary tube or the wall of the bulb of the thermometer, the more sensitive it is; (2011 P1 Q2 at pg. 280)
o       The choice of the responding material - e.g. alcohol is more sensitive (expands more) to heat than mercury but it is colourless.

·        Generally, measurements of large quantities do not require sensitive measuring instrument. It is in the measurements of small quantities that sensitive instruments are needed or the margins of errors can be significant.

2.      Consistency (Precision) in Measurement
·        Measurements are said to be consistent when the values of the measurements are close to each other – meaning, the deviation (i.e. the difference) of each measured value from the mean value (of all measured values) is small and the spread (i.e. the difference between the 2 outermost values) is small. (2005 P1 Q2 Pg 3) / (2008 P1 Q2 Pg. 140)

·        Therefore, high consistency means:
o       Small deviation from the mean value; and,
o       Small spread between the 2 outmost values.

·        Consistent measurements are considered precise but not necessarily accurate – they are only accurate if their mean value is close to the true and actual value.

·        Consistent measuring instrument is one with ability to register the same or nearly the same readings when a measurement is made repeatedly.

·        To improve consistency:
o       Avoid parallax errors;
o       Exercise greater care and consistency in taking readings;
o       Avoid using defective measuring instrument

3.      Accuracy in Measurement
·        Accuracy is the degree of how close a measurement is to the true and actual value of the physical quantity.

·        When repeated readings are involved, all the values of the measurement must be consistent and close to the true and actual value:
o       The mean value must be almost the same as the actual value;
o       The deviation from the mean value is small and
o       The spread is also small.

·        No measurement or measuring instrument is 100% accurate.

·        An error represents the difference between the measured value and the actual value. High accuracy means small error.

·        To improve accuracy:
o       when small values are to be measured:
·        use sensitive instrument
·        use technique which minimizes starting and ending errors – e.g. instead of measuring the time for just 1 oscillation, measure time for say 20 oscillations and then divide this time by 20;
o       take repeated readings to get average value to minimize random errors
o       avoid parallax error
o       avoid or adjust for ‘zero errors’

4.      Measurement of Length
·        There are different instruments to measure length: measuring tape, metre-rule, vernier calipers, micrometer screw gauge.

·        The choice of the instrument depends on
o       The size of the length to be measured; and,
o       The accuracy needed (or, the margin of error allowed):
Accuracy                Length to be Measured Instrument
0.01 mm                 0.1 mm ~ 2.5 cm                      Micrometer screw g.
0.01 cm (0.1mm)    1 cm ~ 12 cm diameter Vernier calipers
0.1 cm (1mm)         Several cm ~ 100 cm                Metre rule
1 cm (10mm)          Several metres                          Measuring tape

·        At Form 4 level, you should be familiar with the use of vernier calipers (2011 P1 Q1 at pg. 280) and micrometer screw gauge – verify your proficiency (2005 Paper 1 Q1 at Pg 3). You should be able to deal with zero errors in both instruments – verify by attempting questions on this.

Micrometer Screw Gauge

Ratchet exerts correct amount of pressure on the object to be measured. 

How to take reading from micrometer screw gauge?

5.      Measurement of Time Interval
·        Time interval is measured by using stopwatch.

·        There are 2 types of stopwatches depending of the accuracy needed:
Accuracy Needed              Type of Stopwatch Used
0.1 s ~ 0.2 s                       Analogue (mechanically-operated)
0.01 s                                 Digital (electronically-operated)

·        When small time interval is to be measured and the digital stopwatch is not available (say, when the period of oscillation of a pendulum is to be measured), higher accuracy or lower margin of error can be achieved by measuring the time for, say, 20 oscillations 2 or 3 times (instead of measuring the time for just 1 complete oscillation). Then take the average time for 20 oscillations and divide it by 20 to give the mean period for 1 complete oscillation.

     (2010 Paper 2 Q1 at Pg. 246)

6.      Measurement of Temperature
·        There are a number of instruments to measure temperature. But the most commonly used in laboratory is the mercury thermometer.

·        There are 2 types of mercury thermometers used in laboratory:
Accuracy Needed              Temperature Range of Thermometer
1` C                                   -10` C ~ 110` C
2` C                                   0` C ~ 360` C

·        To measure body temperature, there is another mercury thermometer with the range of 35` C – 42` C. A temperature above 37` C means having fever.

·        Both mercury and alcohol expand uniformly with temperature changes. In fact, alcohol is more sensitive to heat changes than mercury. However, alcohol is colourless whereas mercury is not which is why mercury is used in thermometer.

·        Other functional features of thermometer are:
o       the thin-walled bulb which allows for quick heat transfer between heat source and the mercury for its expansion;
o       the small-diameter of the capillary tube which amplifies small expansion of mercury in the bulb into large linear expansion along the fine calibrated capillary tube allowing changes in temperature to be measured.

7.      Measurement of Electric Current & Voltage
·        Electric current (I) flowing through a point in an electric circuit is measured by the instrument ammeter or milliammeter. Both have scales calibrated in SI unit for electric current, I - ampere (A). (2005 P2 Q1 Pg. 16)

·        The choice between ammeter and milliammeter depends on the size of the current to be measured and the accuracy needed:
Current Size                       Accuracy                                  Instrument
Small (less than 1 A)           0.1 mA ~ 0.2 mA                     Milliammeter
1 A ~ a few A                    0.1 A ~ 0.2 A                          Ammeter

·        Ammeter or milliammeter is connected in series at a point in the circuit – draw diagram.

·        Voltage, V, (or potential difference) between any two points in an electric circuit is measured by a voltmeter which is connected in parallel across the two points in the circuit.

·        Voltmeter has accuracy of 0.1 V ~ 0.2 V.

Both the ammeter and voltmeter may have anti-parallax mirror to minimise parallax error.

·        Resistance (R) of a resistor in an electric circuit is found by using Ohm’s law where R = V/I. Hence, to find the resistance of a resistor in an electric circuit, we measure both the current flowing through the resistor and the potential difference or voltage across the resistor; we then use Ohm’s Law (R = V/I) to calculate the size of the resistance in ohms.


Segment Review Questions

1.         All measurements in science are Man’s attempts to make an acceptable estimate of the true and actual value of a physical quantity – True or False?

2.        The difference between the true and actual value of a physical quantity and the value obtained in a measurement is known as ________________.

3.        There are two main types of errors. State them, describe their differences and how each type of error may be minimised or avoided – give examples where appropriate.

4.        Attempts the following past year SPM questions:

a.         2007 P1 Q3 pg. 92 - Which balance is more sensitive?
b.         2011 P1 Q2 at pg. 280 on sensitivity in measurement
c.         2005 P1 Q2 Pg 3 on consistency and precision in measurement 
d.         2008 P1 Q2 Pg. 140 – consistency and precision
e.         2011 P1 Q1 at pg. 280 – on use of vernier calipers
f.           2005 Paper 1 Q1 at Pg 3 – on use of micrometer srew gauge
g.         2010 Paper 2 Q1 at Pg. 246 – on use of stopwatch to measure 20 oscillations of pendulum
h.         2005 P2 Q1 Pg. 16 – on use of ammeter, anti-parallax mirror, etc.

Updated on 24/01/2013 by

Scalar Quantities and Vector Quantities

Scalar Quantity:

1.      A scalar quantity has magnitude only (e.g. distance travelled – 1 km).

2.      Final scalar quantities can be found by simple additions and subtractions of like scalar quantities involved.

(Note: Pressure is a scalar quantity)

Vector Quantity 

1.      A vector quantity has both magnitude and direction (e.g. displacement – 1 km due East).

2.      Resultant vector quantities can be found by graphical methods to account for the magnitudes and directions of each individual like vector quantities involved.

3.      Vector variables (e.g. displacement, s) are written in bold.

4.      Examples of Scalar & Vector Quantities:

Scalar Quantities                   Vector Quantities
Length                                      Displacement
Mass                                        Weight (mg)
Time                                         Acceleration; Gravitational Acceleration, g;
            Temperature                             Momentum; Impulse
            Current                                     Force; Impulsive Force; Gravitational Force
            Speed                                      Velocity
            Pressure (acts in all directions in fluids)

Which one is a vector quantity?
2007 P1 Q2 pg. 92: A Energy; B Power; C Force; D Pressure? (Answer:: C)
2009 P1 Q2 pg 186: A Area; B Length; C Distance; D Displacement? (Answer: D)
2012 P1 Q3 pg. 332: A Energy; B Force; C Mass; D Speed? (Answer: B)


Segment Review Questions:

A)  Scalar Quantity and Vector Quantity

1.        State the main difference between a scalar quantity and a vector quantity.

2.        An object moves 40 km on a bearing of 090 from O to A in 20 minutes; it then immediately moves north 30 km also in 20 minutes to B. Find:

a.       The total distance travelled by the object from O to B
b.      The final displacement of the object in moving from O to B in terms of both magnitude and bearing from O.
c.       For the whole journey from O to B:
                                                               i.      The object’s average speed
                                                             ii.      The object’s average velocity

3.        Is pressure a scalar or vector quantity? Name 5 scalar quantities.

4.        Name 5 vector quantities and state their respective SI units of measurement.

Updated on 24/01/2013 by

Standard Form / Scientific Notation / Prefixes

Standard Form / Scientific Notation / Prefixes

1.      Scientists have developed a shorter method of expressing very large or very small numbers known as the standard form or scientific notation.

2.      By this method, all numbers are expressed in the form of: A x 10N, where A is an integer or decimal number such that 1 ≤ A < 10 (A is equal to or greater than 1 but less than 10) and N is an integer (i.e. positive and negative whole numbers including zero). Hence,
o       for a number equals to A (where 1 ≤ A < 10), N equals to zero;
o       for a number ≥ 10 (equals to or greater than 10), N is a positive integer; and
o       for a number < 1 (less than 1), N is a negative integer.
o       for a number which is negative, just insert a negative sign in front of the notation.
(What about the number 0? Can it be defined by scientific notation? Answer: NO!)

3.      A prefix is a letter placed before a unit of measurement to act as the multiplier of the unit – for example, 2000 metres or 2 x  103 metres (in standard form) can be written as 2 kilometres (2 km) where the prefix kilo (k) acts as 1000 or 103

4.      Other prefixes, their symbols and the multipliers they represent are as follows:
Prefix         Symbol            Multiplier          Value of Multiplier
tera-           T                      1012              1 000 000 000 000
giga-           G                     109                1 000 000 000
mega-         M                    106                1 000 000
kilo-           k                      103                1 000
hecto-        h                      102                100
deca-         da                    10                  10
deci-          d                     10-1               0.1
centi-          c                     10-2               0.01
milli-           m                    10-3               0.001
micro-         µ                     10-6               0.000001
nano-         n                      10-9                0.000000001
pico-          p                      10-12              0.000000000001

Solving Problems Involving Conversion of Units of Measurements – Sound Understanding of the Prefixes and Some Basic Mathematical Skills Are Needed.

(2006 P1 Q3 pg. 48 - convert 102.3 Mhz to Hz in standard form)
(2007 P1 Q1 pg. 92 - convert 470 pF to F in standard form)
(2008 P1 Q1 pg. 140 - convert 3.1 km/h to m/s)
(2009 P1 Q1 pg. 186 - given lengths in different prefixes - choose the longest) 
(2010 P1 Q1 pg. 230 - pick prefixes in ascending order)
(2012 P1 Q2 pg. 332 - Which value is equal to 3 500 000 W? Answer: B 3.5 MW)
(2013 P1 Q4 - What is the volume of 2.5 cm3 in m3 ?


Segment Review Questions:

A)  Standard Form / Scientific Notation / Prefixes:

1.    Express each the following physical quantities in its SI unit and in scientific notation to 3 significant figures:

a.    Acceleration due to gravity, g = 9.783 ms-2
b.    Speed of light in vacuum, c = 298,000 kms-1
c.    Length of an onion cell, L = 0.000 028 m
d.    Charge of an electron = -1.6 x 10-7 pC (pico coulombs)

2.    For each of the following symbol of prefixes, state its name and its numerical value in index form (i.e. in power or exponential form):
a.    da
b.    h
c.    k
d.    M
e.    G
f.      T
g.    d
h.    c
i.      m
j.      µ
k.    n
l.      p

3.    Identify the largest and the smallest measurements from the following values:

A.     3.14 x 103 km
B.     3.14 x 108 nm
C.     3.14 x 1010 µm
D.     3.14 x 10-2 cm

4.    Convert:

a.       Density of sea water from 1.05 x 103 kg m-3 to g cm-3
b.      Velocity of cyclist from 5.6 m s-1 to km h-1
c.       Radio frequency from 102.3 MHz to Hz
d.      470 pF to F in standard form to 3 significant figures
e.       0.0006 Gm to Mm
f.        26 µm to mm

1a) g = 9.78 ms-2 (3 sf)
  b) c = 2.98 x 108 ms-1 (3 sf)
  c) L = 2.8 x 10-5 m (3 sf)
  d) e = -1.6 x 10-19 (3 sf)

Updated on 24/01/2013 by