Discover PHYSICS for GCE ‘O’ Level Science
Unit 1: Measurement
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
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
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
Figure 1.1 What is Physics - a pictorial overview
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.2 Physical Quantities and SI units
In this section, you’ll 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
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.2 Physical Quantities and SI units
What is a Physical Quantity?
A physical quantity is a quantity that can be measured. Itconsists of a numerical magnitude and a unit.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
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
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.2 Physical Quantities and SI units
All other physical quantities can be derived from theseseven base quantities. These are called derived quantities.
Table 1.2 Some common derived quantities and units
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.2 Physical Quantities and SI units
Some common SI prefixes are listed in the table below.
Table 1.3 Common SI prefixes
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.2 Physical Quantities and SI units
Worked Example 1.1
Donovan Bailey broke the 100 m sprint world recordat the 1996 Atlanta Olympics, with a time of 9.84 s. In contrast, a dog runs at a speed of 30 km h–1. Ifthe dog chases Donovan Bailey, will the dog catchup with him?
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.2 Physical Quantities and SI units
Solution
First, we calculate the average speed of Donovan Bailey.
1sm10.2
s9.84
m100
timedistancespeedAverage
-=
=
=
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.2 Physical Quantities and SI units
Solution (Continued)
In order to make meaningful comparisons of speed,the units must be the same. So Bailey’s speedshould be converted to km h–1.
Since Bailey’s speed of 36.7 km h– 1 > 30 km h– 1, Bailey will outrun the dog over a distance of 100 m.
11
hkm36.7
h1min60×
min1s60×
m1000km1×
s1m1×10.2
sm1×10.2sm10.2
=
=
=- -
1-
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
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
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
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 world’s smallest playable guitar is 13 μm long. Express the length in standard form.
1.2 Physical Quantities and SI units
Figure 1.6 Nanoguitar
Figure 1.5 Quarter Pounder
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.2 Physical Quantities and SI units
Solutions
1.
g113.3=
kg1g1000
×lb2.205
kg1×lb4
1lb4
1=
2. 13 μm = 13 ×
10-6 m= 1.3 ×
10-7 m (in standard form)
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
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
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
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.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.3 Measurement of Length
Some of the common instruments that we use tomeasure lengths are the:• Metre rule• Tape measure• Calipers• Vernier Calipers• Micrometer screw gauge
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
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 measurethe depth of a pond
Figure 1.10 Using a tape measureto measure the width of a pond
Figure 1.9 Tape measure
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.3 Measurement of Length
Precision of an Instrument
The precision of an instrument is the smallest unitthat the instrument can measure.
What is the precision of the metre rule? The smallestunit the metre rule can measure is 0.1 cm or 1 mm.Hence, we say that the metre rule has a precision of0.1 cm.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.3 Measurement of Length
Avoiding Reading Errors
When using the metre rule, position your eye directlyabove the markings to avoid parallax errors. Bytaking several readings and taking the average, youwill minimise reading errors.
Figure 1.12(a) No parallax errors Figure 1.12(b) Inaccurate measurement due to parallax errors
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.3 Measurement of Length
Calipers – An instrument for measuring the diametersof cylinders or circular objects.
Figure 1.13(a) Inverting the jaws of the calipers to measureinner diameters
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.3 Measurement of Length
Figure 1.13(b) Calipers used to measure outer diameters.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.3 Measurement of Length
Vernier Calipers
A useful instrument to measure both internal andexternal diameters of objects. It consists of a mainscale and a sliding vernier scale.
The vernier calipers has a precision of 0.01 cm.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.3 Measurement of Length
Figure 1.14 Parts and uses of the vernier calipers
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.3 Measurement of Length
Using the Vernier Calipers
Before using the vernier calipers, it is important tocheck the instrument for zero error.
This is to check that the zero mark on the main scalecoincides with the zero mark on the vernier scalewhen not measuring anything between the jaws.
Table 1.4 of the textbook shows how to deal withzero errors.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
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.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.3 Measurement of Length
Table 1.4 Checking and correcting zero errors when using vernier calipers
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
Micrometer Screw Gauge
This instrument can measure to a precision of 0.01 mm. Itis used to measure the diameters of wires or ball bearings.
1.3 Measurement of Length
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.3 Measurement of Length
Figure 1.16 Step by step guide to using the micrometer screw gauge
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.3 Measurement of LengthTable 1.5 Checking and correcting zero errors when using the micrometer screw gauge
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.3 Measurement of Length
Key Ideas
1. Instruments with their range and precision.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.3 Measurement of Length
2. Errors to take note for each instrument
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
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 yourvision is placed directly above the needle so that theimage of the needle coincides with the needle. Thishelps to reduce parallax error.
1.3 Measurement of Length
Figure 1.17 Voltmeter scale with mirror mounted under the needle
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
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 cmStep 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
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.3 Measurement of Length
3. The diameter of a wire is measured using a micrometerscrew gauge. A student takes an initial zero readingand then a reading of the diameter. What is thecorrected 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 mmThe diameter reading D = 3.87 mmHence the corrected diameter reading: Dcorrected = D – Z = 3.87 – (+0.02)
= 3.85 mm
Therefore the answer is B.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.4 Measurement of Time
In this section, you’ll be able to:• Describe how to measure periods of time using the
pendulum, stopwatch and other appropriate instruments.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.4 Measurement of Time
Using a Pendulum to Measure Time
A simple pendulum consists of a bob attached to astring.• 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.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.4 Measurement of Time
Instruments for Telling Time
All instruments use some kind of periodic motion totell time e.g. mechanical watches or clocks use theoscillations of springs, quartz watches use thenatural 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 0.3–0.5 s.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.4 Measurement of Time
Experiment 1.1
Objective: To calibrate a simple pendulum to measuretime in seconds.
Apparatus: pendulum, stopwatch, metre rule, retort stand and clamp
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.4 Measurement of Time
Procedure:
1. Fasten the metre rule vertically.
2. Tie the pendulum to the clamp and measure the length of thestring, l in metres.
3. Measure the time taken t for thependulum to make 20 oscillations.
4. Vary the length l between60 cm and 100 cm.
Figure 1.24
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.4 Measurement of Time
Complete the table below.
Plot a graph of period T/s against l/m and find thelength of pendulum with a period of one second.Plot also a graph of T2/s2 against length l/m.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.4 Measurement of Time
Results:
The length of pendulum with a period of 1 second can beread off the graph.
Figure 1.25(a) Graph of T/s vs. l/m Figure 1.25(b) Graph of T2/s2 vs. l/m
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.4 Measurement of Time
Question 1: Why do we need to take the averagetime of 20 oscillations?
Answer: We take the average to account for humanreaction time. Human reaction time is about 0.3 s formost people. It would not be accurate to stop astopwatch to measure the time taken for just oneoscillation.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
1.4 Measurement of Time
Question 2: What can you observe about thegraph of T/s vs. l/m?
Answer: The period of the pendulum, T, increaseswith length l, but not linearly.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
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 againstl/m. By extending the straight line graph, we can easily predict the period of the pendulum for lengthsthat are not included in the graph we have plotted.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
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.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
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,recordthe time on your watch when you board the bus. Record thetime when you alight the bus. The difference between thetwo times is the time taken for the journey. Repeat steps 2-3 over the course of the week until Friday. Take theaverage of the time taken during the journey over the 5 days.
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
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 whenthe swing is at one end of its motion. Stop thestopwatch 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 =2
(t1 + t2 )
20t
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
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
s434×3T
3 sT43
==
=
28 April 2010Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.
Top Related