Discover PHYSICS for GCE ‘O’ Level Science - …lawzchiasciphy.wikispaces.com/file/view/Unit+1+-+Measurement.pdf• A physical quantity has a numerical magnitude and a unit. •

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


Figure 1.1 What is Physics - a pictorial overview


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



What is a Physical Quantity?

A physical quantity is a quantity that can be measured. Itconsists of a numerical magnitude and a unit.



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



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



Some common SI prefixes are listed in the table below.

Table 1.3 Common SI prefixes



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?



Solution

First, we calculate the average speed of Donovan Bailey.

1sm10.2

s9.84

m100

timedistancespeedAverage

-=

=

=



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-



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


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.


Figure 1.6 Nanoguitar

Figure 1.5 Quarter Pounder



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)


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



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

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



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



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



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.



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



Calipers – An instrument for measuring the diametersof cylinders or circular objects.

Figure 1.13(a) Inverting the jaws of the calipers to measureinner diameters



Figure 1.13(b) Calipers used to measure outer diameters.



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.



Figure 1.14 Parts and uses of the vernier calipers



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.



Guide to Using Vernier Calipers

Figure 1.15 Using the vernier calipers to measure the diameter of a ball bearing.



Table 1.4 Checking and correcting zero errors when using vernier calipers


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.




Figure 1.16 Step by step guide to using the micrometer screw gauge


1.3 Measurement of LengthTable 1.5 Checking and correcting zero errors when using the micrometer screw gauge



Key Ideas

1. Instruments with their range and precision.



2. Errors to take note for each instrument


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.


Figure 1.17 Voltmeter scale with mirror mounted under the needle



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



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.


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.



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.



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.



Experiment 1.1

Objective: To calibrate a simple pendulum to measuretime in seconds.

Apparatus: pendulum, stopwatch, metre rule, retort stand and clamp



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



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.



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



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.



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.



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.



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.



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.



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



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

==

=


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Discover PHYSICS for GCE ‘O’ Level Science - …lawzchiasciphy.wikispaces.com/file/view/Unit+1+-+Measurement.pdf• A physical quantity has a numerical magnitude and a unit. •