Measurement JPJC Notes

1 JURONG PIONEER JUNIOR COLLEGE 9749 H2 PHYSICS /8867 H1 PHYSICS 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 nam ed 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 pub lication 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 ( ), 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 errors) 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).

2 Introduction ▪ Physics aims to understand the natural world around us and to represent the various phenomenon via mathematical relationships. Scientific experiments are then designed to test out the validity of the mathematical relationships. ▪ Such experiments involve the measurements of various physical quantities. The reliability of the measurements is important so as to correctly verify the concepts and theories. The precisions of any experimental results should also be quoted to an appropriate numbers of significant figures to reflect on the order or accuracy. ▪ In this lecture, we will learn to use different physical quantities , their SI units and how to work with the errors and uncertainties incurred when taking measurements. We will also be learning the classification of physical qu antities as scalars or vectors, the addition and subtraction of vectors and the resolving of a vector into its components. 1 SI units (a) Candidates should be able to recall the following base quantities and their units: mass (kg), length (m), time (s) , current (A), temperature (K), amount of substance (mol). 1.1 Physical quantities  Physical quantities are quantities that can be measured.  A physical quantity consists of a numerical value and a unit.  For example, the height of a man is about 1.70 m. In experiments, instruments are used for the measurement and recording of various physical quantities. Some examples are: Physical quantity Instrument Mass, weight Spring balance, lever balance Length Ruler, vernier callipers, micrometer screw gauge Time Stopwatch, clock, cathode ray oscilloscope Temperature Thermometer Angle Protractor Electric current Ammeter Potential difference Voltmeter h = 1.70 m numerical value unit physical quantity

3  In 1960, the international scientific community adopted a number of conventions about physical quantities and their units. The Système Internationale d’Unités (International System of Units) is based on seven base quantities and their corresponding units, called base units. 1.2 Base quantities and base units ▪ Base quantities are physical quantities that are fundamental and are not defined in terms of other physical quantities. *not in syllabus ▪ There are other physical quantities such as velocity and pressure that need to be measured. Such physical quantities are called derived quantities. (b) Candidates should be able to 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. 1.3 Derived quantities and derived units ▪ Derived quantities are physical quantities that are defined in terms of base quantities according to a defining equation. For example, velocity is a d erived qua ntity and it has the defining equation change in displacement time takenv  .. ▪ Units of derived quantities are called derived units and are expressed as products or quotients of base units. ▪ Derived units can be obtained from the defining equation as follows: The defining equation for velocity is change in displacement time takenv  .. Hence, the unit of velocity is m s–1 (metre per second). [Note the space break between the m and s–1]. base quantity usual symbol for base quantity SI base unit symbol for base unit Mass m kilogram kg Length l metre m Time t second s Electric current I ampere A Thermodynamic Temperature T kelvin K Amount of substance n mole mol Luminous intensity* L candela cd

4  In determining derived units, it is important to differentiate between symbols used for the physical quantities and the corresponding symbols for units. A summary of the usual symbols and units for different physical quantities can be found on pages 34 – 35 of the 9749 H2 Physics syllabus document (www.seab.gov.sg). Derived quantity Defining equation Derived unit Usual unit acceleration t uv time velocityinchange 1 2ms mss   - force   t uvm  time momentuminchange 2 1 smkgs smkg    newton (N) pressure A Farea force 21 2 2 smkg m smkg    pascal (Pa) work force  displacement in the direction of the force Fs 22 2 smkg msmkg    joule (J) power t Etime work 32 22 smkg s smkg    watt (W) potential difference Q Echarge work 132 22 Asmkg sA smkg    volt (V) 1.4 Dimensionless quantities and dimensionless constants  Dimensionless quantities are physical quantities that have no units. Some examples are refractive index and relative molecular mass.  All real numbers and some mathematical constants like  have no units. They are called dimensionless constants.  Note: Some physical quantities that are constants have units. Some examples are: o acceleration of free fall, g = 9.81 m s−2, o elementary charge,  191.60 10 Ce

5 (c) Candidates should be able to use SI base units to check the homogeneity of physical equations. 1.5 Homogeneity of equations  An equation is called homogeneous or dimensionally consistent if every term on both sides of the equation has the same units. That is, units on the LHS = units on the RHS.  For example, for a n equation W = X + Y, the units of the physical quantities W, X and Y must be the same.  Base units can be used to check the homogeneity of physical equations.  An equation that is physically correct must be dimensionally consistent or homogeneous.  However, note that an equation that is dimensionally consistent or homogeneous may NOT be physically correct. Example 1 Check whether the following equations are homogeneous and state whether they are physically correct. (a) v = u + at (b) v = u + 2at (c) s = ut +