EJC Physics H201 Measurement 2023 1. Notes (FULL)

Page 1 of 23 9749(202 3) H2 Physics H201 Measurement – Notes H2 Topic 01 – Measurement Content • Physical quantities and SI units • Scalars and vectors • Errors and uncertainties Learning Outcomes Candidates should be able to: (a) recall the following base quantities and their SI units: mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol) (b) 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 (c) use SI base units to check the homogeneity of physical equations (d) 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) (e) 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) (f) make reasonable estimates of physical quantities included within the syllabus (g) distinguish between scalar and vector quantities, and give examples of each (h) add and subtract coplanar vectors (i) represent a vector as two perpendicular components (j) show an understanding of the distinction between systematic errors (including zero error) and random errors (k) show an understanding of the distinction between precision and accuracy (l) assess the uncertainty in a derived quantity by addition of actual, fractional, percentage uncertainties or by numerical substitution (a rigorous statistical treatment is not required). * Additional requirement for 8867 H1 Physics (2020) subsumed under H208 Temperature and Ideal Gases (e) state that 1 mole of any substance contains 6.02 × 10 23 particles & use the Avogadro number NA = 6.02 × 1023 mol-1

Page 2 of 23 9749(202 3) H2 Physics H201 Measurement – Notes 1.0 Introduction: The Nature of Science Science is a durable body of knowledge de rived from empirical and repeatable observations. Despite this, science knowledge is also tentative: it is neither set in concrete nor perfect. Rather, it is subject to change. A scientific law describes an observed phenomenon while a scientific theory explains it. The tentative nature of science also means that laws and theories may be updated in the light of new evidence or new interpretation of existing evidence. Since science demands and relies on empirical evidence, a system of measurements is important to allow meaningful and objective comparisons between observations. 1.1 Physical Quantities and Units A physical quantity is a property of a material or system that can be quantified by measurement. Each quantity consists of a numerical magnitude and a unit. We adopt SI units. The SI was founded on 7 base quantities, by which all other physical quantities in the SI are defined. The 7 SI base units are related to the base quantities where each is defined without referring to other units. base quantity SI base unit symbol mass kilogram kg length metre m time second s electric current ampere A temperature kelvin K amount of substance mole mol luminous intensity* candela* cd* * Not in syllabus. Other quantities such as force (in newtons) and energy (in joules) are referred to as derived quantities. These can be expressed in terms of the 7 base quantities. When expressing a derived unit in terms of base units, consider the equations that relate to its associated quantity. Metrology is the scientific study of measurement. A common understanding of units is crucial in collaborative human activities. It has roots in the French Revolution's political motivation to stand ardise units in France, when a length standard taken from a natural source was proposed. It has evolved into the Système international (SI) units that we are used to seeing. Systems of measurements are generally inter-convertible. However, conversion from SI to “English” units (pounds/fe et/inches used in the US) can result in mistakes. In 1999, NASA lost the $125 million Mars Climate Orbiter spacecraft after a 286 -day journey to Mars. Thrusters used to nudge spacecraft onto a correct path were fired incorrectly. Lockheed Martin, sent thruster data in pounds to NASA, but NASA's navigation team was expecting metric units (newtons).

Page 3 of 23 9749(202 3) H2 Physics H201 Measurement – Notes Example 1 Express the following derived SI units in terms of base SI units. ( ) ( ) the newton the jouleab ( )( ) ( )( ) 2 2 22 K 2 1 2 uunit tof u onit o ni f unit of unit of f unit of kg m kg m s s E mvF EF mm m a a v − − == = = = = Notes: Present properly the working for such questions asking for units. 1.1.1 Homogeneous Equations and Dimensional Analysis All correct physical equations are homogenous: all the terms on both sides of the equation have the same base units. If a quantity does not have an associated physical unit (dimension) and is purely a number, it is a dimensionless quantity. Dimensional analysis may be used to determine the • unit of a constant in an equation • unit of an unknown quantity (which can be used to deduce possibilities for the unknown quantity) • plausibility of a proposed physical equation When performing dimensional analysis: • addition or subtraction must involve only terms of the same units • any exponent (the “power” by which a quantity is raised to) must be dimensionless Example 2 The Bernoulli’s equation used for fluid flow in a pipe may be expressed in the form 21 2 x Ah Bp ρρ + + = where p is the pressure of the fluid, ρ is the density of the fluid, h is the height of the pipe, A and B are constants, and x is a physical quantity. (a) Determine, in terms of SI base units, the units of A and x. (b) Suggest a possible physical quantity that is represented by x. speed (of the fluid)

Page 4 of 23 9749(202 3) H2 Physics H201 Measurement – Notes 1.1.2 Prefixes Prefixes tell us the multiple or sub-multiple to cater to larger or smaller values respectively. prefix symbol multiplier prefix symbol multiplier tera T 1012 deci d 10 -1 giga G 109 centi c 10 -2 mega M 106 milli m 10 -3 kilo k 103 micro µ 10 -6 nano n 10 -9 pico p 10 -12 Example 3 (a) Singapore’s total land area is about 730 km2. Express this value in m2. (b) Mercury has a density of 431 36 10 kg m. −× . Express this value in g cm-3. Notes: A tip is to u se brackets (parentheses) to keep track of prefixes before applying the power. When the numbers are very large, it is also a good practice to leave the number in standard form. 1.1.3 Estimation of Physical Quantities The order of magnitude of a given quantity is the power of ten exponent of the numerical value when given in scientific notation. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. The order of magnitude is a useful estimate of values. numerical value scientific notation order of magnitude 125 21 025 1. × 2 12 500 × 41 25 10. 4

Page 5 of 23 9749(202 3) H2 Physics H201 Measurement – Notes Example 4 Which estimate is realistic? A The kinetic energy of a bus travelling on an expressway is 30 000 J. B The power of a domestic light is 300 W. C The temperature of a hot oven is 300 K. D The volume of air in a car tyre is 0.03 m3. Notes: SG 2008 A -Level Physics MCQ. E stimates can be made from typical values of other commonly encountered quantities. We should be more aware of our everyday environment and develop a good sense of the quantities. We can, for e.g., read product specifications for power ratings, mass etc. Solution A) Estimate using “5 tonner” and 50 kmph B) From Lazada/Shopee: ty