H1.01. 2022 Measurement Notes

CJC H1 PHYSICS LECTURE NOTES JC1 2022 1(1) 1 Measurement Main concept(s) 1. Physical quantities & SI units 2. Uses of SI base units 3. Estimation 4. Errors and Uncertainties 5. Vectors Learning Outcome(s) Candidates should be able to: (a) recall the following base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol). (b) state that one mole of any substance contains 6.02 × 10 23 particles and use the Avogadro number NA = 6.02 × 1023 mol–1 (c) express derived units as products or quotients of the base units and use the named units listed in ‘Summary of Key Quantities, Symbols and Units’ as appropriate. (d) use SI base units to check homogeneity of physical equations. (e) show an understanding of and use the conventions for labelling graph axes and table columns as set out in the ASE publication Signs, Symbols and Systematics (The ASE Companion to 16–19 Science, 2000) (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) distinguish between scalar and vector quantities, and give examples of each (i) add and subtract coplanar vectors (j) represent a vector as two perpendicular components (k) show an understanding of the distinction between systematic errors (including zero errors) and random errors. (l) show an understanding of the distinction between precision and accuracy. (m) assess the uncertainty in a derived quantity by simple addition of actual, fractional or percentage uncertainties or by simple numerical substitution (a rigorous statistical treatment is not required). Introduction Physics is an experimental science in which measurements are made. Evidence from measurements is the ultimate authority in establishing physics theories. Precise measurements enable the checking of experimental data against theoretical prediction. Accurate measurements allow us to overcome the unreliability of our human s enses and for the purpose of standardisation. Precise measurements made possible many applications e.g. study of the structure of matter, from geophysics to astronomy, in the medical industry where development of measuring instruments provides data that ar e crucial in informing clinical decisions. In this chapter, you will not only learn concepts

CJC H1 PHYSICS LECTURE NOTES JC1 2022 1(2) associated with measurements , but also vectors to represent physics quantities, and enable us to compute quantities and solve problems. Essential Questions • Why is there a need for standards in measurements and how are the standards of measurements defined or established? • Why are uncertainties inherent in all measurements and how can uncertainties be reduced? • Why do we need to know the uncertainty of a measurement? • How is the skill of making approximations of particular physical quantities useful in science? 1. 1.1 QUANTITIES AND UNITS 1.1.1 Physical Quantities • Quantities which can be measured. • Examples: length, density, time, force, pressure, velocity, energy, temperature, magnetic field strength, wavelength, frequency, etc. • Stated with a numerical value, and, its unit. For example, mass of man is 65 kg. • The standard system of measure adopted in Physics is the International System of Units (SI). [Be familiar with the ‘Summary of Key Quantities, Symbols and Units’ listed in the Appendix at the end of this Module Notes.] 1.1.2 Base Quantities & Base Units • A set of quantities chosen by scientists, which , by convention, cannot be defined in terms of any other base quantities. • These are the quantities by which all other physical quantities are defined. • There are seven base quantities: Base quantity SI Base unit Symbol Length metre m Mass kilogram kg Time second s Temperature kelvin K Electric current ampere A

CJC H1 PHYSICS LECTURE NOTES JC1 2022 1(3) Amount of substance mole mol Luminous intensity candela cd Quiz Spot the odd one out: 1.1.3 The mole & Avogadro’s Number One mole is defined as the amount of substance that contains as many elementary particles as there are atoms in 0.012 kg (12 g) of carbon-12 isotope. The Avogadro constant NA is the number of atoms in 0.012 kg of carbon -12 isotope, and has been determined to have a value of 6.02  1023 mol-1. Hence, one mole of a substance contains 6.02  1023 particles. The mass of 1 mole of substance is known as the molar mass of the substance expressed in g mol-1. Since there are NA particles in 1 mol e of any element, the mass of an atom for a given element is atom A molar massm= N As such, molar quantities refer to physical quantities associated with 1 mole of a substance. As an example, the molar volume of CO2 means the volume occupied by 1 mole of CO2 and so on. Example 1 The Hope Diamond and the Rosser Reeves Ruby The Hope diamond is almost pure carbon which has a mass of 44.5 carats. The Rosser Reeves ruby is primarily aluminium oxide (Al2O3) which has a mass of 138 carats. One carat is equal to a mass of 0.200 g. kilogram length mass temperature time

CJC H1 PHYSICS LECTURE NOTES JC1 2022 1(4) Determine (i) the number of Al2O3 molecules in the ruby, and (ii) the number of moles of carbon atoms in the diamond. Solution: (i) Mass of the Rosser Reeves ruby = 138  0.2 = 27.6 g Molar mass of Al2O3 molecules = 2  27 + 3 16 = 102 g mol-1 No. of moles of aluminium oxide, massn= molar mass = mol 0.271102 27.6 = No. of aluminium oxide molecules in the Rosser Reeves ruby, N = nNA = 0.271  6.02  1023 = 1.63  1023 molecules (ii)Try it yourself! Mass of the Hope diamond = 44.5 x 0.200 g = 8.90 g Molar mass of carbon atoms = 12 g mol-1 No. of moles of carbon atoms, n = mass of sample molar mass = 0.742 mol No. of carbon atoms in the Hope diamond = N = nNA = (0.742) x (6.02 x 1023) = 4.47  1023 atoms

CJC H1 PHYSICS LECTURE NOTES JC1 2022 1(5) 1.1.4 Derived Quantities & Derived Units • Derived quantities are all other physical quantities other than the base quantities. • Derived units are obtained by using the defining equation of that derived quantity. • Derived units are called SI units if they are constructed from the 7 base units. • In calculations, square brackets, “[ ]”, denote “units of”. Example 2 Derived quantity Defining equation How the base units are found SI units SI base units Velocity Velocity = displacement moved / time v = s / t [v] = [s] / [t] = m / s = m s-1 m s-1 m s-1 Density Density = mass / volume ρ = m / V [] = [m] / [V] = kg / m3 = kg m-3 kg m-3 kg m-3 Force Force = mass x acceleration F = ma [F] = [m] x [a] = kg x m s-2 = kg m s-2 N (newton) or kg m s-2 kg m s-2 Work Work = force x displacement moved in the direction of force W = F x d [W] = [F] x [d] = [ma] x [d] = kg x m s-2 x m = kg m2 s-2 J (joule) or kg m2 s-2 kg m2 s-2 Electric charge Charge = current x time Q = I x t [Q] = [I] x [t] = A x s = A s C(coulomb) or A s A s Power J s-1 or W (watt) or kg m2 s-3 kg m2 s-3 Note: ‘newton’, ‘joule’, ‘coulomb’ , ‘joule per second’, ‘watt’ are SI units but not SI base units.

CJC H1 PHYSICS LECTURE NOTES JC1 2022 1(6) 1.1.5 Decimal multiples & submultiples of SI base and derived units Prefix Multiple Symbol tera 1012 T giga 109 G mega 106 M kilo 103 k Prefix Submultiple Symbol deci 10-1 d c