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

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Graphical methods in Graphical methods in physicsphysics

• Graph plottingGraph plotting

• Different types of graphsDifferent types of graphs


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



Graph plotting

Dependent variable – y-axisIndependent variable – x-axise.g. variation of temperature with time

Dependent

variableIndependent

variable



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



1. Straight line graphs

y = mx + cm – slope, c – y-intercept

Different types of graphs



2. Log graphsy = kxn

log y = log k + n log xn – slope, log k – y-intercept

Different types of graphs



Units and dimensionsUnits 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).




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, 106) are attached to a unit.

6. The order of magnitude is the approximation of the value in the power of 10.




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. L2 (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.



Measurements and errorsMeasurements 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.




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.




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 – yError in U:δU = ±(δx + δy)




(b) Product

U = xyz

(c) Quotient

⎢

][zz

yy

xx

UU

yxU

][yy

xx

UU




(d) Constant power

U = x p

(e) General case

where c, p, q and r are positive constants. ⎢

xxp

UU

r

qp

z

ycxU

][zzr

yy

qxxp

UU



Graphical methods in physicsGraphical 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⎢




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