All YOU NEED TO KNOW:
SCIENCE
( P H YS I C S ) FOR GCE ‘O’ LEVEL
Lawrence Lau • Josephine Fong
Published by Alston Publishing House Pte Ltd 745 Toa Payoh Lorong 5, #01-07, Singapore 319455 enquiry@alstonpublishinghouse.com www.alstonpublishinghouse.com Š 2013 Alston Publishing House Pte Ltd All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the copyright owner. First published 2013 ISBN 978-981-4437-28-8 Publisher: Sim Wee Chee Editor: Melanie Sim Design Team: Anna Gallenero, Eric Sto Domingo, Melissa Lee, Raymond Tan Printed in Singapore
CONTENTS Read Me First!: How to Study Science (Physics)
v
How to Use This Study Guide
vii
Practical Skills
viii
General Tips on Answering Questions
xvi
CHAPTER 01 Physical Quantities
1
CHAPTER 02 Kinematics
19
CHAPTER 03 Dynamics and Pressure
36
CHAPTER 04 Mass, Weight and Density
53
CHAPTER 05 Turning Effects of a Force
61
CHAPTER 06 Energy, Work and Power
75
CHAPTER 07 Kinetic Model of Matter
85
CHAPTER 08 Transfer of Thermal Energy
93
CHAPTER 09 Thermal Properties of Matter
107
CHAPTER 10 General Wave Properties
117
CHAPTER 11 Light
129
Contents
iii
iv
CHAPTER 12 Electromagnetic
153
CHAPTER 13 Sound
162
CHAPTER 14 Static Electricity
175
CHAPTER 15 Current Electricity
184
CHAPTER 16 D.C. Circuits
198
CHAPTER 17 Practical Electricity
215
CHAPTER 18 Magnetism and Electromagnetism
231
Essential Formula List
253
Glossary
256
Answers
265
All You Need to Know: Science (Physics) for GCE ‘O’ Level
Read Me First!: How to Study Science (Physics) Welcome to the world of Science (Physics)!
Suitable for 5116 and 5117 syllabus
Physics is slightly different from Chemistry or Biology, because if you learn it properly by making sense of what you are learning, it needs less memory work. However, if you study it the wrong way by memorising everything, this can become the most difficult subject you have ever taken up. First things first: Science (Physics) is NOT Mathematics!
Rather, Physics studies the known universe – from the smallest subatomic particles to the universe itself, and looks for the simplest laws that explain their behavior. These laws are often (but not always) expressed in mathematical formulae. So Physics uses Mathematics as a tool, but it is not the same as Mathematics. (An analogy: You use a calculator as a tool, but you are not a calculator). Science (Physics) CANNOT be learnt by memorisation alone!
Among the subjects you are taking, Science (Physics) is probably the subject that requires the least amount of memorisation, but the greatest amount of understanding. You cannot learn Science (Physics) by memorising solutions to worked examples! Science (Physics) requires you to make sense of what you are learning, not just be able to reproduce all the examples you encounter. The study approach you adopt for Science (Physics) will determine the grades you will achieve: Common study approaches and their usual outcome: Study approach
Usual outcome
Read the textbook and notes like a storybook
Fail
Reading the textbook and comparing it constantly with your OWN notes
Pass
Memorise every definition, formula and solutions to worked examples, memorise written explanations
Average pass
Understand the concepts: see the common idea behind the worked examples in the same topic, and know how these ideas are interconnected with one another
High distinction!
How to Study (Science) Physics
v
Learning Science (Physics) is about MAKING SENSE.
Each chapter in Science (Physics) is made up of a number of main ideas or concepts. These concepts are usually very fundamental (basic) ways that describe how the world works – they apply to every situation. This is different from simpler ideas you may already have (eg, “All moving things will eventually stop” – not true). These concepts are usually illustrated by a few worked examples, and it is the common idea behind each example. From these worked examples, try to find the same concept or the ‘common idea’. In other words, the more you make sense, the better you will do in the subject. One way to know if you have understood a concept, is to re-state the concept/a related observation in your own words, and then check with your teacher. Another way is to draw a concept map for every topic. A concept map not only helps you to organise what you learn, it can also be used as an easy examination revision tool. A good concept map can also expose problems with your concepts, so that you can fix them in time. For a start, you can use a search engine to look for “images of science concept maps” and learn how to make your own. Studying Science (Physics) requires you to BELIEVE what you are learning.
It is difficult to learn a concept in Science (Physics) and, at the same time, believe that the world actually works in some other way. Trying to do so will cause you to apply wrong ideas when stressed, such as during a national examination. Try your best to relate what you learn into your daily experiences, and they should agree with each other. You may become more confused at first, as what you learn in Science (Physics) may seem to disagree with your daily experiences. Keep going – your confusion will start to clear up as you replace more and more of the wrong ideas with the correct ones. (A good example is again “All moving things will eventually stop”. You will find that it contradicts the idea of inertia and the formula F = m × a. You will learn later that moving things stop because of friction.) Brush up on your English!
Physics depends a lot on whether you can comprehend what the teacher and the textbook are saying, and on whether you can express your ideas across to the marker. If you have been failing your English or have trouble understanding what your teacher is saying – work on it AS MUCH AS YOU CAN.
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All You Need to Know: Science (Physics) for GCE ‘O’ Level
How to Use This Study Guide This study guide is not a textbook. So it will take the shortest path to get all the concepts across. It will not be as interesting as a textbook which can develop ideas more fully and clearly, and show how the concepts apply to everyday life. Below are the features of this book and how you can make full use of it: 1) The important concepts are listed in bulleted format for an uncluttered view. This includes all the necessary definitions and formulae. 2) We have included loads of worked examples – they are set such that you can see how the concept is being applied. Not only should you study how the solutions are arrived at, you should also take note of how the solutions are presented! 3) Each chapter is peppered with notes that we feel are important to you in your learning. These notes include the Introduction, which gives you important examination pointers such as the type of questions likely to appear from a particular chapter. Clarify Your Concept! points out possible misconceptions or common mistakes students make, while Tip gives tips on steps to answer a particular type of question. 4) Questions at the end of each chapter are for you to test your understanding. The questions are modelled after past year papers. 5) We also have a list of formulae for your quick reference. 6) Lastly, a glossary is included for those who need to look up the terms used in this book. Not everything in this guide is equally important: Concepts are more important than formulae (if any), which are more important than worked examples. Make sense of the concepts from the examples given. Test your understanding of the concepts by trying the exercises at the end of each chapter. If you: • don’t know how to answer them… • get some questions correct and some wrong (not caused by miscalculation)… • get all questions correct (aside from miscalculations):
…you didn’t understand the concept, or your concept is inaccurate. Go back to the concept again and ask your teacher about how it works. …you probably have the correct concept!
Once you are sure that you get the concept, try out the questions from past year papers without referring to any material. You should get all of them correct (aside from misspellings and miscalculations). Any further mistakes are caused by an incomplete understanding of the concept, or you may have switched back to your old, wrong ideas. FIX THEM. Good luck!
How to Use This Study Guide
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Practical Skills There are only a few themes that can appear in the Science (Physics) Practical Examination: Theme
Laboratory skills needed
Measurement
• d e t e r m i n i n g p e r i o d o f a swinging pendulum
• using a stopwatch • counting complete oscillations
Mechanics
• determining the density of an object or liquid • using the Principle of Moments • determining the CG of a lamina • investigating the stability of an object • i n v e s t i g a t i n g t h e e ff e c t o f friction on an object • investigating the temperature changes when mixing hot and cold liquids • investigating the processes of melting or boiling • investigating reflection of light from a mirror • inve stigating refract io n o f light through a (rectangular/ semicircular) glass block • investigating the relationship between object and image characteristics of a thin converging lens • investigating the relationship p.d ∝ current • investigating the relationship resistance ∝ 1/current ∝ length of resistance wire
• u s i n g v e r n i e r c a l i p e r s o r micrometer screw gauge • using a measuring cylinder to measure volume of a solid or liquid • operating an electronic balance • balancing a metre rule • using a plumb line • r e a d i n g f r o m a l a b o r a t o r y thermometer
Thermal Physics
Light
Electricity and Magnetism
Table A
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Experiment might involve
The different themes for the Practical
All You Need to Know: Science (Physics) for GCE ‘O’ Level
• using optical pins • using a protractor • focusing an image from a lens onto a screen
• connecting components correctly to form a circuit as indicated in a circuit diagram • reading from an ammeter and voltmeter • using a jockey or a crocodile clip on a wire correctly
For a more complete list, refer to the syllabus available from the SEAB website. Other Skills Tested Besides the laboratory skills listed in Table A, the Practical also tests you on other skills: Other skills Presenting Data Handling Data
Sources of Errors Table B
Details • Expressing the recorded data in the appropriate number of decimal places (d.p) or significant figures (s.f.) • Tabulating the recorded data clearly • Carrying out operations on the data recorded and expressing them in the appropriate number of d.p. or s.f. • Presenting the data in a graph - with an appropriate scale and range (if not given) - as plotted points with a best-fit line (line can be a straight line or a curved line) • Make inferences from the graph by - determining the gradient of the straight line - determining the vertical or horizontal intercepts - taking a reading off a graph - making extrapolations • State a source of error • Suggest an improvement to the experiment
Other Skills
Reading the Practical Paper
It is very tempting to start doing the experiment straight away. Hold on! You should actually be READING the instructions from the start till the end – yes, till the last word of the last part of the question. This will not only calm you (a bit) before you plunge into action, it will also give you a good overall view of the experiment, and you will not need to deal with surprises that spring your way at the end of the experiment. It may also help to underline or highlight key words/phrases (not sentences/ paragraphs) as you read through so that you can find them easily later. The experiment in the Practical may not be one of those listed in Table A, but it will involve the skills listed. If you encounter an experiment that is unfamiliar to you, just follow the instructions calmly.
AIM OF THE PRACTICAL The aim of the experiment is usually already given to you at the start of the experiment. It is usually easy to find the relationship between two variables — the independent variable (that you are controlling) and the dependent variable (that changes as you change the independent variable).
Practical Skills
ix
MAKING MEASUREMENTS The first part of the instructions will need you to make measurements. While carrying out the experiment, take precautions such that your readings are as accurate as possible. At the same time, be aware of the possible sources of errors in the experiment (page xiii). Some points to note: 1. The number and range of measurements is usually stated in the question. If not, you should usually take 5—6 readings with the widest practical range of values. If the experiment set-up is fixed, like in the case of an electrical circuit, or balancing the rule, or even using the converging lens, it might not hurt to obtain a few extra readings to confirm your results. Example In the following instructions, x is the independent variable, while t is the dependent variable.
Determine the value of t when the angle x is 40°. Repeat the experiment with 4 other readings of x between 30° and 70°.
This means that there is a total of 5 sets of readings for x and t, with x ranging from 30° to 70°, including x = 40°. 2. The spread of the measurements will depend on the following cases: – If an intercept is needed, obtain more readings near the intercepts. – If you need to read off the line, make sure the value is included in the range. 3. Usually a table is given to you. If not, construct it before making measurements. This will take any surprises out of the procedure and keep you more in control. To do this, you have to read the whole procedure of the experiment. The next section, Presenting Data, will advise you on how to make such a table. 4. Record the measurements to the appropriate number of decimal places (d.p.). The number of d.p. reported depends on the size of the smallest division of the instrument used.
Example (a)
(b)
Reading is 18.0 cm. Reason: The smallest division is 0.1 cm.
x
Figure A
Reading is 18 cm. Reason: The smallest division is 1 cm.
The ‘.0’ shows that ruler (a) is more precise than ruler (b).
All You Need to Know: Science (Physics) for GCE ‘O’ Level
Table C shows the precision for common instruments you would usually encounter: Instrument
Units
Number of decimal places
Example
Metre rule
mm cm m
0 1 3
150 mm 15.0 cm 0.150 m
mm cm
2 3
6.48 mm 0.648 cm
Vernier calipers Micrometer screw gauge
mm cm
1 2
32.1 mm 3.21 cm
Stopwatch
s
2
10.48 s
Laboratory thermometer*
°C
1
48.5 °C
Ammeter* Voltmeter*
A V
Depends on the scale
—
Protractor
°
0
29°
Table C
Precision of common measuring instruments
(Instruments marked with an asterisk (*) usually have physically large divisions (> 1 mm), so you are required to estimate to half of the smallest division.)
5.
The unit must be appropriate. You need to note: – the unit the instrument is calibrated for – the prefixes, so that you can convert the measurements correctly
Example
18.0 cm = 0.180 m (not 0.018 m or 1.8 m)
Many students lose marks when they measure, say, in cm but do the wrong calculation to record in m or mm.
PRESENTING DATA In all Physics experiments, all data must be presented clearly in a table. Do note the following: 1. All data is presented in columns to allow quick checking of the decimal places of each reading. 2. Each column heading should have the symbol for the variable and the unit. The symbol used must be exactly the same one given in the instructions.
Example m/kg
W/N
d/cm
M/Ncm
3. The independent variable (that you are controlling) should be the first column (on the left). 4. There must be at least 5 sets of data (6 rows, including the heading).
Practical Skills
xi
PLOTTING A GRAPH You will be required to plot a graph to show the relationship between the independent and dependent variables. These are the things you need to note: Feature
Things to note
Axes
• The independent variable is usually represented by the horizontal axis. • The dependent variable is usually represented by the vertical axis. • Do not label the axes ‘x’ or ‘y’, unless the variables are actually called ‘x’ or ‘y’! The range on each axis depends on the question: • if you are required to find the horizontal (vertical) intercept, then you need to start the vertical (horizontal) axis from 0; • if you are required to find the gradient only, you don’t have to start the axes from the origin (0,0) at all.
Range of points
• You should choose a scale such that your actual graph occupies at least half of the graph paper vertically and horizontally (Figure 3). • You should note that (a) each axis can have a different scale, and (b) the scale should not be an awkward one (eg multiples of prime numbers).
Scale
Gradient of the best-fit line
xii
Figure 1
Figure 2
Ok! Figure 3
• All lines drawn on the graph (including the axes) should be in pencil, sharp and thin. • Draw a best-fit line/curve through the plotted points. Note the following: Dots Best-fit line Ok! (a) NEVER ‘join the dots’! (Figure 4) should not is not be joined balanced (b) The best-fit line does not necessarily pass through all the Figure 4 Figure 5 Figure 6 plotted points (Figure 6). (c) The best-fit line should look ‘balanced’, with a roughly equal number of plotted points on either side of the line. Eg Figure 6 looks more balanced than Figure 5.
Lines
Table D
Too small Too small on on both horizontal axes axis
• You need to (a) draw a large (dotted) triangle (Figure 8) (b) label the co-ordinates used to show how you determine the rise and the run of the line.
Features of a graph
All You Need to Know: Science (Physics) for GCE ‘O’ Level
Triangle too small
Ok!
Figure 7
Figure 8
TIP 1. The scale of the graph must be chosen such that all plotted points can be shown on the graph. Sometimes, the question that follows the graph needs you to take a reading that is outside the range of readings you have taken. Your scale must take this into account. That is why reading the WHOLE question at the start of the session is important.
For example, You have recorded a set of readings ranging from 30° to 70°. To make full use of your graph, your horizontal axis should start from ~ 20° and end at ~ 80°. However, if a question later needs you to find the y-intercept, then your horizontal axis needs to start from 0°; or if you are required to find the value of t when x is 90°, then your scale must allow for that.
2. If you were asked to determine the gradient of the line, you would expect a straight-line graph! 3. If you have plotted a straight-line graph through the origin, then your variables are proportional to each other (Figure 9). Otherwise, the variables have a linear relationship (Figure 10 and Figure 11).
Figure 9
Figure 10
Figure 11
SOURCES OF ERROR AND SUGGESTIONS FOR IMPROVEMENT In these experiments, you may be asked to identify possible sources of error. Note that the sources of error are NOT errors you made, or errors you have avoided. They refer to errors that CANNOT be removed (or avoided) completely because of how the experiment was set up using the apparatus. The table below shows some examples of sources of error and what are not: The following are NOT sources of errors: 1. “The metre rule has a zero error.” (You can work around a zero error.)
2. “There was parallax error.” (Too vague – which measurement was affected?) 3. “There was parallax error when the length was measured.” (The error could have been avoided if the metre rule was used correctly.)
The following are possible sources of errors: 1. If the length of an object is supposed to be measured, but there is no way to put the scale of the metre rule against the object for some reason, then you can talk about the unavoidable parallax error. 2. If you are to measure the temperature of the water (in a beaker) heated by an electrical heater, the temperature you measure may be lower than expected because of thermal energy loss to the surroundings.
Practical Skills
xiii
Some sources of error have significant impact on the accuracy of an experiment, while other only have minor impacts. You must therefore prioritise on which ones to list first. Below is an example of an experiment and the possible sources of error that come with it. Example Aim To determine the specific heat capacity of a solid by the method of mixtures.
Apparatus Styrofoam cup brass mass glass rod Thermometer, 0–100 ºC
water beaker balance thread
Diagram 0—100 °C
xiv
Rod
Procedure 1. Weigh the brass mass (m0) on the balance. 2. Weigh the Styrofoam cup (m1) on the balance. 3. Half-fill the Styrofoam cup with tap water and weigh it again (m2). 4. Record the temperature (t0) of the water in the Styrofoam cup. 5. Boil some water in a beaker. Record the temperature (t1) of the boiling water. 6. Use the thread to tie a loop round the mass. Suspend it in the boiling water by means of the rod. Remove the brass mass; shake it briskly, and quickly transfer it into the Styrofoam cup. Gently stir the water continuously with the brass mass. Record the highest steady temperature (t2) reached. Question What are the sources of error in the above experiment?
Solution Some possible errors are listed below:
1. There is some boiling water left adhering to the bob and thread that is difficult to remove quickly. 2. The metal bob at 100°C cools down very quickly in room temperature, especially with water evaporating from its surface.
All You Need to Know: Science (Physics) for GCE ‘O’ Level
You will also be asked to suggest an improvement for the experiment. The suggestion you make – should be based on the source of error you have stated. – must not be a precaution. – must not be vague or general — you must explain how your suggestion would reduce your error. For example, for this experiment, insulating the cup with a layer of lagging or covering it with a lid will reduce thermal energy loss to the surroundings, and more of the energy from the ball will contribute to the temperature rise of the water.
Practical Skills
xv
General Tips on Answering Questions KNOWING THE SYLLABUS Before you even start studying for the examinations, have you read the syllabus? You need to know what is expected of you before you even attend the course! For a start, you can go to the Singapore Examination and Assessment Board (SEAB) website and download the Physics syllabus — 5116 or 5117 — you have signed up for. The syllabus will give you details like: a) the assessment objectives b) the structure of the paper – marks, weighting, duration, etc. c) the proportion of marks allocated to the different types of questions d) the quantities, symbols and units that you need to know e) the practical work that you should be familiar with f) glossary of terms used in Physics
THE ASSESSMENT OBJECTIVES AND THEIR WEIGHTING The assessment objectives for the theory paper are the skills and knowledge that are expected of you. These are broadly classified into two types: a) Knowledge with Understanding (60 %) Questions under this category require you to know the facts of the subject – you need to recall facts and explain observations. They usually start with these words: state, define, describe, explain, outline, etc.
30 % of the marks are allocated to questions that need you to recall facts (definitions, laws, principles, etc). Do refer to the Summary of Key Quantities, Symbols and Units – they list the quantities and units whose definitions you need to recall.
The rest of the marks (30 %) is allocated to questions that need you to describe or explain (eg how an instrument such as a circuit breaker works, how earthing helps in preventing hazards, etc).
b) Handling Information and Solving Problems (40 %) Questions under this category require you to apply the knowledge you have learnt. The settings in these questions are usually not familiar to you, and you have to use the concepts you have learnt to solve problems. Such questions usually start with words such as: determine, predict, suggest, calculate, etc.
GLOSSARY OF TERMS USED This glossary is very useful if you do not know how much you need to include in your answer. For example, the terms ‘define’ and ‘what is meant by’ require you to give slightly different amounts of answer.
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All You Need to Know: Science (Physics) for GCE ‘O’ Level
ANSWERING PAPER 1 There are 40 Multiple Choice Questions (MCQ) in this paper of which the first 20 are Physics questions. There are different ways to approach answering the questions. The best way, of course, is to work out the answer and select the correct option. Here are some tips: 1. The proportions of the correct options are usually roughly equal. Thus, if you have an abnormally large proportion of A’s (eg 15 A’s), the chance of some of these answers being wrong is relatively high – and you should re-check your answers. 2. The same correct options rarely appear more than three times consecutively. This means that it is highly unlikely that, for example, there would be 4 consecutive B’s. 3. If you do not know the correct option right after reading the question, you can work it out. Based on what you know, eliminate as many options as you can, so that the chance of the correct option being left is higher. 4. Attempt the questions you know first, and skip the ones you do not know. Do not spend too much time (> 1 min) on one question at the expense of the rest. You can always go back to the ones you have skipped.
ANSWERING PAPER 2 Paper 2 consists of two sections: Section A (45 marks) and Section B (20 marks). There is a mix of recall, explanation and application questions according to the weighting. The marks indicated are a good guide of how much you need to answer: [1] for one concept point. The following, though not exhaustive, contains some tips on answering questions in this paper. 1. For explanation-type questions, the marker would be looking for detailed and clear explanations. –– Do not repeat a statement in the question – it takes up your writing space and will not earn you any marks. –– Adapt a general explanation so that it will be relevant to the actual situation set in the question. –– Use and include any specific information given in the question, rather than giving general statements. –– To help in your explanation, you can include calculations, or simple labelled diagrams/sketches (labels in the diagram help in your explanation too). –– You may also express your answers in bulleted form, if you are running out of time or find it difficult to express your ideas. Remember: some answer is better than no answer. –– The space provided should serve as a good guide as to how much you should answer.
General Tips on Answering Questions
xvii
2. For calculation-type questions, the marker would be looking for clear working. –– All calculations based on formulae should be presented in this format: • Quote the formula • Show substitution of values • Answer with the appropriate unit (if the unit is not given) If it takes a few stages to reach the answer, explain what you are calculating at each stage by using statements. –– All numerical answers should be between 2–3 significant figures (s.f.). –– Answers from calculations should not be expressed as fractions (unless instructed). Convert them into decimals. 3. For sketching/drawing-type questions, the marker would be looking for clear and neat sketches. –– All sketches must be made with a sharp pencil. –– All scales must be appropriate and stated if possible. –– The line for the graph must be sharp and clear, not ‘feathery’. –– If you need to extract information from the graph, show how it is done. For example, to obtain the gradient, you need to draw a large triangle or mark out two sets of coordinates, or to obtain a reading off the graph, indicate how you obtain it by using dotted lines. –– For graphical method of vector addition, make sure the scale is large enough. All arrows should be drawn and labelled. –– When drawing forces, make sure the force starts from the point of application, and is not hanging in the air!
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All You Need to Know: Science (Physics) for GCE ‘O’ Level
04
MASS, WEIGHT AND DENSITY
INTRODUCTION Questions from this chapter tend to be straightforward. Questions on mass and weight are usually tested along with concepts from other chapters, such as moments and dynamics. It is important to distinguish between mass and weight.
MASS AND WEIGHT • Mass is a measure of the amount of substance in a body. –– SI unit: kilogram (kg) –– Measured by beam balance • Inertia is a reluctance of the mass of a body to change from its state of rest or motion. –– A heavier object (higher mass) has more inertia and needs more force to change its motion • A gravitational field is a region in which a mass experiences a force due to gravitational attraction. –– Gravitational field strength g is gravitational force per unit mass g = 10 N/kg (near the surface of the Earth) • Weight is the gravitational force acting on an object. –– W = mg where m: mass of the object g: gravitational field strength –– SI unit: Newton (N) –– Measured by spring balance • Difference between mass and weight: Mass
A measure of the amount of substance SI unit: kg
Constant and does not depend on its position Table 4. 1
Weight
Force acting on a mass due to gravitational field SI unit: N
Varies according to position
Distinguishing mass and weight
Clarify Your Concept!
Gravitational field is not a physical quantity, and so no units are associated with it. Chapter 4 | Mass, Weight and Density
53
Worked Example 4. 1 What is the weight of a boulder of mass 500 kg on (a) the Earth [2] (b) the Moon? [2] Given: g on Earth is 10 N/kg; g on the Moon is 1.6 N/kg Solution m = 500 kg (a) Earth: g = 10 N/kg (b) Moon: g = 1.6 N/kg W = mg = 500 × 10 [1] W = mg = 500 × 1.6 [1] = 50 000 N [1] = 800 N [1] The weight of the boulder on Earth The weight of the boulder on the Moon is 5000 N. is 800 N.
Worked Example 4. 2 A baseball travels in the direction indicated below immediately after being hit by a bat. As it travels in the air, what is the effect on its speed and the direction of its path?
Effect on speed
Effect on direction
A
Changing
Changes direction
B
Changing
Remains in a straight line
C
Remains the same
Changes direction
D
Remains the same
Remains in a straight line
Solution A Clarify Your Concept!
The baseball travels in the gravitational field of the Earth. A mass in the gravitational field will experience a force acting on it. Since F = ma, the baseball will experience acceleration or a change in speed – in both magnitude and direction.
DENSITY • Density r of an object is its mass per unit volume.
–– r =
m V
where m: mass of the object; V: volume of the object –– SI unit: kg/m3
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All You Need to Know: Science (Physics) for GCE ‘O’ Level
–– Graph of m vs V: Mass
Gradient = density Volume
Figure 4.1 Graph of m vs V • The density of a material is unique. –– Density of water is 1 g/cm3 or 1000 kg/m3
Worked Example 4. 3 A lead cylinder as shown in the diagram below has a mass of 2.22 kg. Determine the density of lead. [3] (Take p = 3.14) Solution
2.5 cm
10 cm
m = 2.22 kg = 2220 g Radius r = 25 cm
Height h = 10 cm m
Density r = V =
2220
196.25
Volume V = p r2h = p (2.5)2(10) [1]
= 11.3 g/cm3 (3 s.f.) [1]
= 196.25 cm [1] 3
TIP
The answer to the density can also be expressed in non-SI unit g/cm3, unless the question specifically states that SI unit is required.
The density of lead is 11.3 g/cm3.
Chapter 4 | Mass, Weight and Density
55
Worked Example 4. 4 Samantha wants to find the density of an object she found in her room. She finds out the following information:
Mass of object: 250 g
Volume of object: 100 cm3
Calculate the density of the object. [2] Solution Density of object =
Mass
Volume
=
250 100
[1]
= 2.5 g/cm3 [1]
The density of the object is 2.5 g/cm3.
Worked Example 4. 5 Some water is heated from 0 °C to 100 °C. The graph below shows how the volume of the water changes with temperature. Volume
0 °C 4 °C
Temperature
Based on the above graph, which of the following conclusions can be made about the density of water? The density of water is
.
A highest at 4 °C B highest at 100 °C
C lowest at 4 °C D lowest at 0 °C
Solution A
Clarify Your Concept!
56
m
The mass of the water is constant in the volume-temperature graph. Using the formula r = V , r is highest when V is lowest at 4 °C.
All You Need to Know: Science (Physics) for GCE ‘O’ Level
QUESTIONS Section A
1. Which of the following physical quantities will not change when an astronaut lands on a satellite orbiting the Earth?
I
Mass of the astronaut
II Weight of the astronaut
III Gravitational force of the Earth on the astronaut A I only
B I and II only
C I and III only
D II and III only 2. A crate of weight 1000 N on Earth will have a weight of
.
(Take gearth as 10 N/kg; gmoon as 1.67 N/kg) A 1.67 N on the Moon B 16.7 N on the Moon C 167 N on the Moon
D 1670 N on the Moon
3*. Two objects, M and N, of the same dimensions are each placed on a top-pan balance. Which of the 1 with higher density2 and inertia? following shows the correct objects
M
N
0
0
kg
A B C D
kg
Higher density
Higher inertia
N N
M N
M3 M
X
M N
Y
Z
Chapter 4 | Mass, Weight and Density
57
4. Which of the following is correct about weight and mass?
A B C D
Weight
Can vary Can vary Constant Constant
Mass
Can vary Constant Can vary Constant
5. An object is attached to the end of a spring balance and the reading on the balance is 14.0 N. Which of the following shows its correct mass, given that the gravitational field strength is 10 N/kg?
A 140.0 kg
C 4.0 kg
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B 24.0 kg D 1.4 kg
All You Need to Know: Science (Physics) for GCE ‘O’ Level
Section B
6. A solid P is submerged totally into water.
If the solid P of mass 10.7 g displaces 10.5 cm3 of water when submerged in water, calculate its density. [3]
Water P
7. A 1.2 kg mass was placed on top of a spring. It compresses the spring and is at rest.
(a) On the diagram, draw an arrow to indicate the direction and the line of action of the force acting on the mass due to the
(i) Earth’s gravitational field.
1.2 kg mass Spring
(ii) compressed spring.
Write down the name of each of the above forces next to the respective arrow. [2]
(b) State one effect of a force on the spring. [1]
(c) (i) State the resultant force acting on the mass.
(ii) Given that the gravitational field strength is 10 N/kg, determine the values of the two forces in (a). [2]
(d) Given that the mass has dimensions of 13.1 cm by 19.8 cm by 10.7 cm, determine the density of the mass in g/cm3. [3]
8*. A pipe is sealed on both ends. It has an internal cross-sectional area of 4 cm2 and a length of 40 cm. It is filled 34 full with water.
(a) Given that the density of water is 1 g/cm3, calculate the mass of water in the pipe. [2]
40 cm Water
(b) Determine the weight of the water. [1]
(c) Hence, determine the pressure of the water at Point X. [2]
9*. A truck and a car are moving along the expressway with the same speed.
Ă— X
Both drivers see an obstacle along the expressway in front of them and apply the same braking force on their vehicles at the same time. They are able to stop some distance away from the obstacle. State and explain which vehicle is closer to the obstacle after they are stopped. [4]
Chapter 4 | Mass, Weight and Density
59
10. The Curiosity rover is a robotic rover that landed on Mars in 2012. It has a mass of 900 kg. The gravitational field strength on Earth is 10 N/kg and on Mars is 3.7 N/kg respectively.
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(a) Explain what is meant by gravitational field strength of 3.7 N/kg. [2] (b) Calculate the weight of the rover
(i) on Earth [2] (ii) on Mars [2]
(c) How do your answers in (b) explain the difference between mass and weight? [3]
All You Need to Know: Science (Physics) for GCE ‘O’ Level
Curiosity rover