Cambridge IGCSE™ Physics 4th edition

Book Preface

FOCUS POINTS

★ Describe how to measure length, volume and time intervals using simple devices.
★ Know how to determine the average value for a small distance and a short time interval.

★ Understand the difference between scalar and vector quantities, and give examples of each.
★ Calculate or determine graphically the resultant of two perpendicular vectors.

This topic introduces the concept of describing space and time in terms of numbers together with some of the basic units used in physics. You will learn how to use simple devices to measure or calculate the quantities of length, area and volume. Accurate measurements of time will be needed frequently in the practical work in later topics and you will discover how to choose the appropriate clock or timer for the measurement of a time interval. Any single measurement will not be entirely accurate and will have an error associated with it. Taking the average of several measurements, or measuring multiples, reduces the size of the error.

Many physical quantities, such as force and velocity, have both magnitude and direction; they are termed vectors. When combining two vectors to find their resultant, as well as their size, you need to take into account any difference in their directions.

Units and basic quantities
Before a measurement can be made, a standard or unit must be chosen. The size of the quantity to be measured is then found with an instrument having a scale marked in the unit.
Three basic quantities we measure in physics are length, mass and time. Units for other quantities are based on them. The SI (Système International d’Unités) system is a set of metric units now used in many countries. It is a decimal system in which units are divided or multiplied by 10 to give smaller or larger units.
Measuring instruments on the flight deck of a passenger jet provide the crew with information about the performance of the aircraft (see Figure 1.1.1).

The small figures 1, 2, 3, etc. are called powers of ten. The power shows how many times the number has to be multiplied by 10 if the power is greater than 0 or divided by 10 if the power is less than 0. Note that 1 is written as 100.
This way of writing numbers is called standard notation.

To obtain an average value for a small distance, multiples can be measured. For example, in ripple tank experiments (Topic 3.1), measure the distance occupied by five waves, then divide by 5 to obtain the average wavelength.
Significant figures
Every measurement of a quantity is an attempt
to find its true value and is subject to errors arising from limitations of the apparatus and
the experimenter. The number of figures, called significant figures, given for a measurement indicates how accurate we think it is and more figures should not be given than are justified.
For example, a value of 4.5 for a measurement has two significant figures; 0.0385 has three significant figures, 3 being the most significant and 5 the least, i.e. it is the one we are least sure about since it might be 4 or it might be 6. Perhaps it had to be estimated by the experimenter because the reading was between two marks on a scale.
When doing a calculation your answer should have the same number of significant figures as the measurements used in the calculation. For example, if your calculator gave an answer of 3.4185062, this would be written as 3.4 if the measurements had two significant figures. It would be written as 3.42 for three significant figures. Note that in deciding the least significant figure you look at the next figure to the right. If it is less than 5, you leave the least significant figure as it is (hence 3.41 becomes 3.4), but if it equals or is greater than 5 you increase the least significant figure by 1 (round it up) (hence 3.418 becomes 3.42).
If a number is expressed in standard notation, the number of significant figures is the number of digits before the power of ten. For example,
2.73 × 103 has three significant figures.