Discover PHYSICS for GCE

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Discover PHYSICS for GCE O Level Science

• Unit 1 Measurement

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1.1 What is Physics?

• Physics is the study of Matter and Energy.
• This includes sub-topics like
• General Physics
• Thermal Physics
• Light
• Waves
• Sound
• Electricity
• Magnetism

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• Figure 1.1 What is Physics - a pictorial overview

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1.2 Physical Quantities and SI units

• In this section, youll be able to
• understand that all physical quantities consist
  of a numerical magnitude and a unit
• recall the seven base quantities and their units
• use prefixes and symbols to indicate very big or
  very small SI quantities

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1.2 Physical Quantities and SI units

• What is a Physical Quantity?
• A physical quantity is a quantity that can be
  measured. It
• consists of a numerical magnitude and a unit.

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1.2 Physical Quantities and SI units

• The 7 base quantities and 7 base SI units are
  shown in
• the table below.

Table 1.1 The seven base quantities and their SI
units
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1.2 Physical Quantities and SI units

• All other physical quantities can be derived from
  these
• seven base quantities. These are called derived
  quantities.

Table 1.2 Some common derived quantities and units
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1.2 Physical Quantities and SI units

• Some common SI prefixes are listed in the table
  below.

Table 1.3 Common SI prefixes
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1.2 Physical Quantities and SI units

• Worked Example 1.1
• Donovan Bailey broke the 100 m sprint world
  record
• at the 1996 Atlanta Olympics, with a time of 9.84
  s.
• In contrast, a dog runs at a speed of 30 km h1.
  If
• the dog chases Donovan Bailey, will the dog catch
• up with him?

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1.2 Physical Quantities and SI units

• Solution
• First, we calculate the average speed of Donovan
  Bailey.

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1.2 Physical Quantities and SI units

• Solution (Continued)
• In order to make meaningful comparisons of speed,
• the units must be the same. So Baileys speed
• should be converted to km h1.

Since Baileys speed of 36.7 km h 1 gt 30 km h
1, Bailey will outrun the dog over a distance of
100 m.
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1.2 Physical Quantities and SI units

• Key Ideas
• A physical quantity has a numerical magnitude and
  a unit.
• The are seven base quantities length, mass,
  time, electric current, temperature, luminous
  intensity and amount of substance.
• The units of these seven base quantities are
  known as the SI base units
• m, kg, s, A, K, cd, mole

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1.2 Physical Quantities and SI units

• Test Yourself 1.2
• 1. Express the weight of a Quarter Pounder in
  grams, given that 2.205 pounds (lb) is equal to 1
  kilogram (kg).
• 2. The worlds smallest playable guitar is 13 ?m
  long. Express the length in standard form.

Figure 1.5 Quarter Pounder
Figure 1.6 Nanoguitar
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1.2 Physical Quantities and SI units

• Solutions
• 1.

2. 13 ?m 13 ? 10-6 m
1.3 ? 10-7 m (in standard form)
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1.3 Measurement of Length

• In this section, you will be able to
• Have a good sense of the orders of magnitude
• Describe how to measure a variety of lengths
  using the appropriate instruments (e.g. metre
  rule, vernier calipers, micrometer)
• Use a vernier scale

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1.3 Measurement of Length

• The SI unit for length is the metre (m).

Figure 1.7 There is a wide range of lengths in
the natural world.
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1.3 Measurement of Length

• Some of the common instruments that we use to
• measure lengths are the
• Metre rule
• Tape measure
• Calipers
• Vernier Calipers
• Micrometer screw gauge

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1.3 Measurement of Length

• Metre rules can measure lengths up to 1 m.
• Tape measures can measure lengths up to a few
  metres.

Figure 1.11 Using a metre rule to measure the
depth of a pond
Figure 1.10 Using a tape measure to measure the
width of a pond
Figure 1.9 Tape measure
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1.3 Measurement of Length

• Precision of an Instrument
• The precision of an instrument is the smallest
  unit
• that the instrument can measure.
• What is the precision of the metre rule? The
  smallest
• unit the metre rule can measure is 0.1 cm or 1
  mm.
• Hence, we say that the metre rule has a precision
  of
• 0.1 cm.

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1.3 Measurement of Length

• Avoiding Reading Errors
• When using the metre rule, position your eye
  directly
• above the markings to avoid parallax errors. By
• taking several readings and taking the average,
  you
• will minimise reading errors.

Figure 1.12(a) No parallax errors
Figure 1.12(b) Inaccurate measurement due to
parallax errors
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1.3 Measurement of Length

• Calipers An instrument for measuring the
  diameters
• of cylinders or circular objects.

Figure 1.13(a) Inverting the jaws of the calipers
to measure inner diameters
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1.3 Measurement of Length
Figure 1.13(b) Calipers used to measure outer
diameters.
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1.3 Measurement of Length

• Vernier Calipers
• A useful instrument to measure both internal and
• external diameters of objects. It consists of a
  main
• scale and a sliding vernier scale.
• The vernier calipers has a precision of 0.01 cm.

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1.3 Measurement of Length
Figure 1.14 Parts and uses of the vernier calipers
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1.3 Measurement of Length

• Using the Vernier Calipers
• Before using the vernier calipers, it is
  important to
• check the instrument for zero error.
• This is to check that the zero mark on the main
  scale
• coincides with the zero mark on the vernier scale
• when not measuring anything between the jaws.
• Table 1.4 of the textbook shows how to deal with
• zero errors.

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1.3 Measurement of Length

• Guide to Using Vernier Calipers

Figure 1.15 Using the vernier calipers to
measure the diameter of a ball bearing.
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1.3 Measurement of Length
Table 1.4 Checking and correcting zero errors
when using vernier calipers
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1.3 Measurement of Length

• Micrometer Screw Gauge
• This instrument can measure to a precision of
  0.01 mm. It
• is used to measure the diameters of wires or ball
  bearings.

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1.3 Measurement of Length
Figure 1.16 Step by step guide to using the
micrometer screw gauge
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1.3 Measurement of Length

• Table 1.5 Checking and correcting zero errors
  when using the
• micrometer screw gauge

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1.3 Measurement of Length

• Key Ideas
• 1. Instruments with their range and precision.

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1.3 Measurement of Length

• 2. Errors to take note for each instrument

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1.3 Measurement of Length

• Test Yourself 1.3
• 1. Figure 1.17 shows a voltmeter with a strip of
  mirror mounted under the needle and near the
  scale. Suggest how this may help to reduce errors
  when taking a reading.
• Answer When taking a reading, ensure that your
• vision is placed directly above the needle so
  that the
• image of the needle coincides with the needle.
  This
• helps to reduce parallax error.

Figure 1.17 Voltmeter scale with mirror mounted
under the needle
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1.3 Measurement of Length
2. Vernier calipers are used to measure the
diameter of a ball bearing. What is the reading
of the vernier scale? Answer Step 1
Main scale reading 2.5 cm Step 2 Vernier
coincides with 3rd line. Vernier reading
is 0.03 cm. Step 3 Reading of diameter 2.5
0.03 cm 2.53 cm
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1.3 Measurement of Length

• 3. The diameter of a wire is measured using a
  micrometer
• screw gauge. A student takes an initial zero
  reading
• and then a reading of the diameter. What is
  the
• corrected diameter of the wire in mm?
• A 3.37 B 3.85 C 3.89 D 3.87
• Answer
• The zero reading Z 0.02 mm
• The diameter reading D 3.87 mm
• Hence the corrected diameter reading
• Dcorrected D Z 3.87 (0.02)
• 3.85 mm
• Therefore the answer is B.

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1.4 Measurement of Time

• In this section, youll be able to
• Describe how to measure periods of time using the
  pendulum, stopwatch and other appropriate
  instruments.

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1.4 Measurement of Time

• Using a Pendulum to Measure Time
• A simple pendulum consists of a bob attached to a
• string.
• A complete to-and-fro motion from R to S and back
  to R is one complete oscillation.
• The period T is the time taken for one complete
  revolution.

Figure 1.22 A pendulum completes one full
oscillation when the bob moves from R to S and
back to R.
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1.4 Measurement of Time

• Instruments for Telling Time
• All instruments use some kind of periodic motion
  to
• tell time e.g. mechanical watches or clocks use
  the
• oscillations of springs, quartz watches use the
• natural vibrations of crystals.
• Stopwatches can measure time to a precision of
  0.1 s.
• Digital stopwatches can show readings to two
  decimal places of a second. However, human
  reaction time introduces an error of about
• 0.30.5 s.

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1.4 Measurement of Time

• Experiment 1.1
• Objective To calibrate a simple pendulum to
  measure
• time in seconds.
• Apparatus pendulum, stopwatch, metre rule,
  retort
• stand and clamp

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1.4 Measurement of Time

• Procedure
• 1. Fasten the metre rule vertically.
• 2. Tie the pendulum to the clamp
• and measure the length of the
• string, l in metres.
• 3. Measure the time taken t for the
• pendulum to make 20 oscillations.
• 4. Vary the length l between
• 60 cm and 100 cm.

Figure 1.24
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1.4 Measurement of Time

• Complete the table below.
• Plot a graph of period T/s against l/m and find
  the
• length of pendulum with a period of one second.
• Plot also a graph of T2/s2 against length l/m.

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1.4 Measurement of Time

• Results
• The length of pendulum with a period of 1 second
  can be
• read off the graph.

Figure 1.25(b) Graph of T2/s2 vs. l/m
Figure 1.25(a) Graph of T/s vs. l/m
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1.4 Measurement of Time

• Question 1 Why do we need to take the average
• time of 20 oscillations?
• Answer We take the average to account for human
• reaction time. Human reaction time is about 0.3 s
  for
• most people. It would not be accurate to stop a
• stopwatch to measure the time taken for just one
• oscillation.

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1.4 Measurement of Time

• Question 2 What can you observe about the
• graph of T/s vs. l/m?
• Answer The period of the pendulum, T, increases
• with length l, but not linearly.

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1.4 Measurement of Time

• Question 3 What does the plot of T2/s2 vs. l/m
  tell us?
• Answer It tells us that the square of the
  period, T2
• is directly proportional to the length, l. This
  gives rise
• to the straight line graph when we plot T2/s2
  against
• l/m. By extending the straight line graph, we can
  
• easily predict the period of the pendulum for
  lengths
• that are not included in the graph we have
  plotted.

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1.4 Measurement of Time

• Key Ideas
• Time intervals are measured by observing events
  that repeat themselves.
• Clocks can be used to measure time intervals in
  minutes or hours.
• Stopwatches can be used to measure time intervals
  to a precision of 0.1 s.
• The period T is the time taken for the pendulum
  to swing from one end to the other and back again
  to its starting position.

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1.4 Measurement of Time

• Test Yourself 1.4
• 1. How can you measure the average time taken by
  a bus to travel from home to school?
• Answer At the beginning of the week e.g.
  Monday,record
• the time on your watch when you board the bus.
  Record the
• time when you alight the bus. The difference
  between the
• two times is the time taken for the journey.
  Repeat steps
• 2-3 over the course of the week until Friday.
  Take the
• average of the time taken during the journey over
  the 5 days.

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1.4 Measurement of Time

• 2. How can you determine the period of the swing
  in the playground?
• Answer Start the swing in its to-and-fro motion.
• When the motion is steady, start the stopwatch
  when
• the swing is at one end of its motion. Stop the
• stopwatch after 20 oscillations. Record the time
  t1.
• Repeat steps 2-3 for another set of reading t2.
• Take average t
• The period T is given by T

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1.4 Measurement of Time

• 3. Figure 1.26 shows an oscillating pendulum. If
  the
• time taken for the pendulum to swing from A to
  C
• to B is 3 s, what is the period of the
  pendulum?
• Answer
• Moving from A to C to B only
• covers three-quarters of the
• oscillation. Hence,

Figure 1.26
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