PHYSICS GCE Advanced Subsidiary Level and GCE Advanced Level 9702 Aims

1. PHYSICSGCE Advanced Subsidiary Level andGCE Advanced Level 9702Aims • 1/5. to provide, through well-designed studies, of experimental and practical science, to • 1.1 become confident citizens in a technological world and able to take or develop an informed interest in matters of scientific import; • 1.2 recognise the usefulness, and limitations, of scientific method and to appreciate its applicability in other disciplines and in everyday life; • 1.3 be suitably prepared for studies beyond A Level in Physics, in Engineering or in Physics-dependent vocational courses . • 2/5. to develop abilities and skills that • 2.1 are relevant to the study and practice of science; • 2.2 are useful in everyday life; • 2.3 encourage efficient and safe practice; • 2.4 encourage effective communication.

2. Aims…. • 3/5. to develop attitudes relevant to science such as • 3.1 concern for accuracy and precision; • 3.2 objectivity; • 3.3 integrity; • 3.4 the skills of enquiry; • 3.5 initiative; • 3.6 inventiveness. • 4/5. to stimulate interest in, and care for, the environment in relation to the environmental impact of Physics and its applications. • 5/5. promote an awareness • 5.1 that the study and practice of Physics are co-operative and cumulative activities, and are subject to social, economic, technological, ethical and cultural influences and limitations; • 5.2 that the implications of Physics may be both beneficial and detrimental to the individual, the community and the environment; • 5.3 of the importance of the use of IT for communication, as an aid to experiments and as a tool for the interpretation of experimental and theoretical results. • 6. stimulate students and create a sustained interest in Physics so that the study of the subject is enjoyable and satisfying

3. STRUCTURE OF THE PHYSICS SYLLABUS -the subject content of the syllabus is divided into Section Part AS (14 topics) A2 (20 topics) • I General Physics • 1. Physical Quantities and Units AS/A2 • 2. Measurement Techniques AS/A2 • II Newtonian Mechanics • 3. Kinematics AS • 4. Dynamics AS • 5. Forces AS • 6. Work, Energy, Power AS • 7. Motion in a Circle /A2 • 8. Gravitational Field /A2 • III Matter • 9. Phases of Matter AS • 10. Deformation of Solids AS • 11. Ideal Gases /A2 • 12. Temperature /A2 • 13. Thermal Properties of Materials /A2 • IV Oscillations and Waves • 14. Oscillations /A2 • 15. Waves AS • 16. Superposition AS

4. V Electricity and Magnetism • 17. Electric Fields AS/A2 • 18. Capacitance /A2 • 19. Current of Electricity AS • 20. D.C. Circuits AS • 21. Magnetic Fields /A2 • 22. Electromagnetism /A2 • 23. Electromagnetic Induction /A2 • 24. Alternating Currents /A2 • VI Modern Physics • 25. Charged Particles /A2 • 26. Quantum Physics /A2 • 27. Nuclear Physics AS/A2 • VII Gathering and Communicating Information • 28. Direct Sensing /A2 • 29. Remote Sensing /A2 • 30. Communicating Information /A2

5. 1. Physical Quantities and Units • 1. Content • 1.1 Physical quantities • 1.2 SI Units • 1.3 The Avogadro constant • 1.4 Scalars and vectors • Learning Outcomes • (a) show an understanding that all physical quantities consist of a numerical magnitude and a • unit. • (b) recall the following base quantities and their units: mass (kg), length (m), time (s), • current (A), temperature (K), amount of substance (mol). • (c) express derived units as products or quotients of the base units and use the named units • listed in this syllabus as appropriate. • (d) use base units to check the homogeneity of physical equations. • (e) show an understanding of and use the conventions for labelling graph axes and table • columns each. • (k) add and subtract coplanar vectors. • (l) represent a vector as two perpendicular components.

6. …. • (f) use the following prefixes and their symbols to indicate decimal sub-multiples or multiples of both base and derived units: pico (p), nano (n), micro (μ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G), tera (T). • (g) make reasonable estimates of physical quantities included within the syllabus. • (h) show an understanding of the significance of the Avogadro constant as the number of atoms in 0.012 kg of Carbon-12. • (i) use molar quantities where one mole of any substance is the amount containing a number of particles equal to the Avogadro constant. • (j) distinguish scalar and vector quantities and give examples

7. Physical Quantities & Units • Physics is the study of how the universe/world behaves and how the laws of nature operate • Physics is a mathematical science. The underlying concepts and principles have a mathematical basis.

8. Physical Quantities • Physics involves the study of physical quantities and its measurement • Accurate measurement is very important in science particularly physics, known as the ‘scientific method’ • Scientific method: observe, measure, collect data & analyse to discover a pattern to make it a theory, and then law otherwise repeat or reject • A physical quantity is a quantity that can be measured e.g. length, mass or time of fall • Physical quantities have a numerical value and unit but not always • Some quantities have no units e.g. pi, ratios, radian, strain • A physical quantity can be divided into base quantities and derived quantities

9. Base Quantities • Base quantities are the quantities that are conventionally accepted as functionally independent of one another. • It is a quantity that cannot be defined in terms of other physical quantities nor is it derived from other units, i.e. it is independent of other units.

10. Common language of measurement units • Same as spoken languages, different systems of measurement evolved throughout the world • Examples: foot, furlongs, cubit, gantang, pounds, carats, grains, kati etc • Foot is the length of King Henry VII’s foot • Although units of measurement can be converted between systems it is cumbersome and far better to have just one system • Hence the System International (SI) system was born in 1960

11. 7 base quantities The Systême International (SI) is based on 7 fundamental or base quantities and its units are given below: Quantity Name of unit Unit symbol • Length metre m • Mass kilogram kg • Time second s • Electric current Ampere A • Temperature Kelvin K • Amount of substance mole mol • Luminous intensity candela cd (not in syllabus)

12. Beware ! • A distance of thirty metres should be written as 30 m and not 30 ms or 30 m s • The letter ‘s’ is never included in a unit for the plural • If a space is left between 2 letters, the letters denote different units • So, 30 m s would mean thirty metre seconds and 30 ms would mean 30 milliseconds

13. Derived quantities and derived units • A derived quantity is a physics quantity that consists of some combination of base units • It is a quantity which is derived from the base quantities and is a combination of base units through multiplying and/or dividing them, but never added or subtracted • All derived units are expressible as products or quotients of the base units e.g N  kg m s-2 and J  kg m2 s-2. • SI derived units are units of measurement defined in the International System of Units (SI). • They are derived from the seven base units and can be expressed in base-unit equivalents • Most derived units have a special name • The names of all SI units are written in lowercase. The unit symbols of units named after persons are always spelled with an initial capital letter (e.g., hertz, Hz; but meter, m). • The exception is degrees Celsius, which refers to degrees on the Celsius temperature scale.

14. Derived quantity & equations • A derived quantity has a defining equation which defines the quantity in terms of other quantities. • It enables us to express a derived unit in terms of base-unit equivalent. Example: F = ma ; Newton = kg m s-2 P = F/A ; Pascal = kg m s-2/m2 = kg m-1 s-2

15. Some derived units Derived quantity Base equivalent units _______Symbol • area square meter m² • volume cubic meter m³ • speed, velocity meter per second m/s or m s-1 • acceleration meter per second squared m/s/s or m s-2 • density kilogram per cubic meter kg m-3 • amount concentration mole per cubic meter mol m-3 • force kg m s-2 Newton • work/energy kg m2 s-2 Joule • power kg m2 s-3 Watt • pressure kg m-1 s-2 Pascal • frequency s-1 Hertz

16. Avogadro’s Constant • The Avogadro constant, NA, is the number of atoms in 0.012 kg of Carbon-12 or the number of particles in one mole of any substance. • The substance may be in a solid, liquid or gaseous state, and its basic fundamental unit may either be atomic, molecular or ionic in form. • NA equals to 6.02 x 10²³ per mole. • A molar quantity is the amount per mole unit (6.02 x 10²³ particles) e.g molar volume of a gas at s.t.p. is 22.4 dm³. • E.g the number of atoms in 6 g of Carbon-12 is 6/12 x 6.02 x 10²³ or 3.01 x 10²³.

17. Magnitude/size • Magnitudes of physical quantities range from very very large to very very small. • E.g. mass of sun is 1030 kg and mass of electron is 10-31 kg. • Hence, prefixes are used to describe these magnitudes. Common prefixes

18. Order of magnitude in metres • Earth to universe 1.4 x 1026 • Earth to Sun 1.5 x 1011 • Length of car 4 • Diameter of hair 5 x 10-4 • Diameter of an atom 3 x 10-10 • Diameter of a nucleus 6 x 10-15

19. Scientific notation • Large and small values are usually expressed in scientific notation i.e. as a simple number multiplied by a power of ten • A value expressed in the A x 10^ form where 1  A  10 is called the standard form scientific notation. • There is far less chance of making a mistake with the number of zeroes • E.g 154 000 000 would be written as 1.54 x 108 0.00034 would be written as 3.4 x 10-4

20. Conversions • Since there are so many base units and derived units, and orders of magnitudes, conversions from one unit to another is inevitable • Let us try some conversions; a) 30 mm2 = ? m2 b) 865 km h-1 = ? m s-1 c) 300 g cm-3 = ? kg m-3

21. a) 30 mm2 = ? m2

22. b) 865 km h-1 = ? m s-1

23. c) 300 g cm-3 = ? kg m-3

24. Conventions for symbols & units • Symbols & units when printed on paper, appear in different styles • At A/AS level and beyond, there is a special convention for labeling columns of data in tables and graph axes • The symbol is written first, separated by a forward slash from the unit • Then the data is presented in a column, or along an axis, as pure numbers as it is then algebraically correct

25. Equations • For any equation to make sense, each term involved in the equation must have the same base units • Look at this equation: 3 kg + 6 kg = 9 m The numbers are correct but the units make it nonsense • A term in an equation is a group of numbers and symbols, and each of the terms is added to, or subtracted from other terms • In any equation where each term has the same base units, the equation is said to be homogeneous or balanced • An equation is homogeneous if quantities on BOTH sides of the equation have the same unit. • e.g. s = ut + ½ at2 LHS : unit of s = m RHS : unit of ut = m s-1 x s = m unit of at2 = m s-2 x s2 = m Unit on LHS = unit on RHS, hence equation is homogeneous • A homogeneous equation may not be physically correct but a physically correct equation is definitely homogeneous e.g. a) s = 2ut + at2 is homogeneous but not physically correct (correct equation is s = ut + ½ at²), b) F = ma is homogeneous and physically correct (try it!)

26. Dimension analysis • The ‘dimensions’ of a physical quantity shows the relation between that quantity to the ‘base’ quantities e.g the dimensions of ‘area’ are Length x Length hence area is the product of Length². • Dimension analysis is defined as a technique or method in which the dimensions of physical quantities can be expressed in terms of a combination of basic quantities. • Dimensions are physical quantities which can be treated as algebraic quantities. • e.g. dimension of length is L, mass is M, time is T etc • Dimensional analysis is used • to determine the unit of the physical quantity. • to determine whether a physical equation is correct or not dimensionally by using the principle of homogeneity. • but not if a formula is valid or not

27. a) To confirm if equation is homogeneous • E.g: The period of oscillation of a simple pendulum is dependent on the length l and acceleration of free fall, g. Is the equation; T = 2√(l/g) or T = 2√(g/l) ? Take the first equation T = 2√(l/g) LHS : unit of T = s RHS : unit of 2√(l/g) = [ m/(m s-2) ] ½ = s Equation is homogeneous since unit on LHS = RHS (try the 2nd formula!)

28. b) To find units of constant • E.g: Newton’s Universal Law of gravitation, says that the gravitational force between two objects is given by the formula F = GMm/r2 where F - force, G - Universal Gravitational constant, M, m - masses of objects, r - distance apart. Find the units of G. Solution To find units of G : Rearrange the equation. G = Fr2/Mm therefore unit of G = N m2 kg-2

29. Determining the dimension and unit • Determine the dimension and the S.I. unit for the following quantities: • Velocity • Acceleration • Linear momentum d. Density e. Force

30. Example solution for velocity ..... dimension Hence the S.I. unit of velocity is m s-1.

31. Exercises • Determine whether the following expressions are dimensionally correct a. where s, u, a and t represent the displacement, initial velocity, acceleration and the time of an object respectively. b. where s, u, v and g represent the displacement, initial velocity, final velocity and the gravitational acceleration respectively. c. where T, l and g represent the period of simple pendulum , length of the simple pendulum and the gravitational acceleration respectively.

32. Using homogeneity to find units of unknown quantities type questions • When an equation is homogeneous, then the balancing of base units provides a means of finding the units of an unknown quantity e.g. • 1. Use base units to show that the following equation, work done = gain in kinetic energy + gain in gravitational energy, is homogeneous • 2. The thermal energy Q needed to melt a solid of mass m without any change in temperature is given by the equation, Q = mL where L is a constant. Find the base units of L.

33. Scalars & Vectors • All physical units have a magnitude and a unit • For some quantities, magnitude and units alone do not give us enough information to fully describe the quantity • e.g we can calculate speed, if time and distance are given, but we cannot find out how far a car is from its starting point unless we know the direction of travel • In this case, the speed and direction must be specified • Hence, a quantity that can be fully described by giving its magnitude, is known as a scalar quantity whereas, • A vector quantity has magnitude and direction

34. Examples of scalar & vector quantities • Quantity Classification mass scalar speed scalar temperature scalar kinetic energy scalar volume scalar density scalar length scalar pressure scalar weight vector velocity vector acceleration vector force vector moment vector

35. Vector representation • One way to represent a vector is by an arrow and the length of the vector drawn to scale, as the magnitude

36. Addition of vectors • The addition of scalars with the same unit is not a problem as normal rules of addition are applied • e.g. a beaker of volume 250 cm³ and a bucket of volume 9.0 litres have a total volume of 9250 cm³ • In adding vectors we have to take into consideration magnitude as well as direction • If vectors are in the same direction i.e. if angle between the forces is 0º just add them e.g. 2 weights of 30 N & 20 N have a combined weight of 50 N since in the same direction i.e. downwards due to gravity • If vectors are in opposite directions i.e. angle between the forces is 180º we subtract them e.g. 2 vectors, one 30 N South and the other 20 N North, the resultant is 10 N South • For the above examples for all other angles between the direction of forces, the combined effect or resultant is some value between 10 N and 50 N which can be found by means of a vector triangle, scale diagram or trigonometry

37. Exercise • A ship is traveling due North with a speed of 12 km/h relative to the water. There is a current in the water flowing at 4 km/h in an Easterly direction relative to the shore. Determine the velocity of the ship relative to the shore by : • scale drawing • calculation • (ans: 12.6 km/h 18º East of North)

38. Exercise • A swimmer who can swim in still water at a speed of 4 km h-1, is swimming in a river. The river flows at a speed of 3 km h-1 Calculate the speed of the swimmer relative to the river bank when she swims: • downstream • upstream • (ans: 7 km/h, 1 km/h)

39. Coplanar vectors • When 3 or more vectors need to be added, the same principles apply, provided the vectors are all on the same plane i.e. coplanar • To subtract 2 vectors, reverse the direction i.e. change the sign of the vector to be subtracted, and add

40. Resolution of vectors • Since 2 vectors can be added together to give a resultant, it follows that a single vector can be resolved into 2 vectors or components • This method applies to all types of vector quantities • Consider a force of magnitude F acting at an angle of θ below the horizontal. so, F horizontal = F cos θ and, F vertical = F sin θ F θ

41. Exercise • An aircraft is travelling 35º East of North at a speed of 310 km h-1. Calculate the speed of the aircraft in (a) the Northerly direction (b) the Easterly direction (ans: 250 km/h, 180 km/h)