1© Manhattan Press (H.K.) Ltd. Graphical methods in physics Graph plotting Different types of graphs

2 © Manhattan Press (H.K.) Ltd. Graphical methods in physics (SB p. 29) (a) select a suitable set of data; (b) draw the x-axis and y-axis with suitable labels and units; (c) choose the suitable scales for the axes; (d) plot all the points on the graph; and (e) draw a line (or curve) to pass through all the points. Graph plotting

3 © Manhattan Press (H.K.) Ltd. Graphical methods in physics (SB p. 30) Graph plotting Dependent variable – y-axis Independent variable – x-axis e.g. variation of temperature with time   Dependent variable Independent variable

4 © Manhattan Press (H.K.) Ltd. Graphical methods in physics (SB p. 30) Due to errors, a straight line cannot pass through all the plotted points plot a best-fit line Graph plotting Check 3 physical quantities relationship, plot a 3-dimensional graph or keep the third quantity constant

5 © Manhattan Press (H.K.) Ltd. Graphical methods in physics (SB p. 30) 1. Straight line graphs y = mx + c m – slope, c – y-intercept Different types of graphs

6 © Manhattan Press (H.K.) Ltd. Graphical methods in physics (SB p. 31) 2. Log graphs y = kx n log y = log k + n log x n – slope, log k – y-intercept Different types of graphs

7 © Manhattan Press (H.K.) Ltd. Graphical methods in physics (SB p. 32) Units and dimensions 1. Unit of a physical quantity is the standard size of that quantity. 2. SI is a common system of units. 3. Base units are the units for the basic physical quantities, e.g. metre (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance) and candela (luminous intensity).

8 © Manhattan Press (H.K.) Ltd. Graphical methods in physics (SB p. 32) Units and dimensions 4. Derived units are the units for the derived quantities, e.g. cubic metre (volume), kilogram per cubic metre (density) and newton (force). 5. When dealing with very large or very small numbers, prefixes (e.g. 10 –3, 10 6 ) are attached to a unit. 6. The order of magnitude is the approximation of the value in the power of 10.

9 © Manhattan Press (H.K.) Ltd. Graphical methods in physics (SB p. 32) Units and dimensions 7. The dimensions of a physical quantity, e.g. L (length), M (mass) and T (time), can be written as a combination of the dimensions of base quantities, e.g. L 2 (area) and L T –2 (acceleration). 8. The dimension of an equation is said to be homogeneous if all the terms in it have the same dimensions or units.

10 © Manhattan Press (H.K.) Ltd. Graphical methods in physics (SB p. 32) Measurements and errors 9. A reading is a single determination of the value of an unknown quantity while a measurement is the final result of the analysis of a series of readings. 10. A measurement is said to be accurate if it is close to the actual value. 11. The number of significant figures required to express a measurement must be consistent with the accuracy of the measurement.

11 © Manhattan Press (H.K.) Ltd. Graphical methods in physics (SB p. 32) Measurements and errors 12. Vernier caliper and micrometre screw gauge are always used to measure accurately the length of an object. 13. Systematic errors are errors in the measurement of physical quantities due to instruments, faults in the surrounding conditions or mistakes made by the observer. Examples are zero errors, personal errors of the observer, errors due to instruments and errors due to wrong assumption.

12 © Manhattan Press (H.K.) Ltd. Graphical methods in physics (SB p. 32) Measurements and errors 14. Random errors are errors in a measurement made by the observer or person who takes the measurement. Examples are errors due to parallax and changes in temperature during an experiment. 15. Combination of errors: (a) Addition or subtraction U = x + y or U = x – y Error in U:δU = ±(δx + δy)

13 © Manhattan Press (H.K.) Ltd. Graphical methods in physics (SB p. 32) Measurements and errors (b) Product U = xyz (c) Quotient

14 © Manhattan Press (H.K.) Ltd. Graphical methods in physics (SB p. 32) Measurements and errors (d) Constant power U = x p (e) General case where c, p, q and r are positive constants.

15 © Manhattan Press (H.K.) Ltd. Graphical methods in physics (SB p. 33) Graphical methods in physics 16. In a graph, the dependent variable is always put in y-axis while the independent variable is always put in x-axis. 17. Different types of graphs: (a) Straight line graphs y = mx + c (b) Log graphs y = kx n log y = log k + n log x

16 © Manhattan Press (H.K.) Ltd. Graphical methods in physics (SB p. 33)

17 © Manhattan Press (H.K.) Ltd. End