Tiêu đề 1. Measurement.pdf ✅

1 Measurement Measurement Introduction Being an experimental science, Physics needs to relate the theoretical description of nature with experimental observations. Before an explanation of nature can be attempted, accurate observations must be made. The relationship between theory and experimental observation is made through quantitative measurements of various physical quantities. Measurement entails assigning numbers to events or observations. In this chapter, you will learn about the differences between fundamental and derived physical quantities, methods of dimensional analysis, and the relationship between physical quantities. You will also learn about types and sources of errors, ways of determining errors from a graph, and distinguishing between accuracy and precision. 1.1 Physical quantities Physical quantities can be divided into two types, namely, fundamental and derived quantities. A fundamental physical quantity is not defined in terms of any other quantity whereas the quantities which are defined in terms of other quantities are called derived physical quantities. The measurement of physical quantities involves their comparison with the chosen standard of the same kind of units. The measure of any physical quantity is merely a number and any idea about its magnitude that can be stated in the unit. The standard units for fundamental quantities are called fundamental units. On the other hand, the standard units for derived quantities are called derived units. For example, units for mass, length and time are chosen as fundamental units while units of area, volume, velocity and energy are derived units. In this section, you will study the interactions existing between the two types of physical quantities. The focus will be on the difference between fundamental and derived physical quantities, the method of dimensional analysis, use of dimensional analysis and the limitations of using the method of dimensional analysis. 1.1.1 Fundamental and derived quantities Physical quantities which cannot be derived or obtained from any other physical quantities are known as fundamental physical quantities. For example, the Chapter One Physics Form V.indd 1 23/07/2020 09:16 FOR ONLINE USE ONLI GOVERNMENT PROPERTY FOR ONLINE USE ONLY

3 Measurement Example 1.2 Example 1.1 the three fundamental basic quantities (length, mass and time). Any physically meaningful equation will have the same dimensions on the left and right sides. Therefore, dimensional analysis is important for checking correctness of formula and establishing the relationship among physical quantities. Table 1.3 shows units and dimensions of some common physical quantities. Table 1.3 Dimensions of some physical quantities Quantity Unit Dimensions Mass kg M Length m L Time s T Velocity ms–1 LT−1 Acceleration ms–2 LT−2 Force kgms–2 MLT−2 Density kgm−3 ML−3 Find the dimensional formula for kinetic energy. Solution Kinetic energy is given by the expression 1 2 mv 2 where m is the mass and v is the velocity. Dimensions of kinetic energy = [mass ]×[velocity]2 , but [mass ] M= and [velocity] = LT−1 . Since 1 2 is dimensionless, then, 1 2 mv2 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ = ML2 T−2 . The dimensions of kinetic energy are ML2 T−2 . where M, L and T are the dimensions of the fundamental quantities mass, length and time, respectively. Therefore, the dimensional formula for kinetic energy is ML2 T−2 . 1.1.3 Uses of dimensional analysis Dimensional analysis is useful in checking correctness of a formula, assigning units of physical quantities and deriving formula. (a) To check the correctness of formula Checking correctness of a given equation using dimensional analysis is based on the principle of dimensional homogeneity. The principle works by comparing the dimensions of each term on either side of an equation. It states that, “An equation is dimensionally correct if the dimensions of the fundamental quantities (mass, length, and time) are the same in each term on either side of the equation”. Only quantities of the same dimensions can be added, subtracted or equated. Consider the physical equation v = u+ at where v and u are final and initial velocities of a body respectively, a is an acceleration, and t is time. Using methods of dimensional analysis, check whether the equation is dimensionally homogeneous. Solution From the principle of dimensional homogeneity, the equation is Physics Form V.indd 3 23/07/2020 09:16 FOR ONLINE USE ONLI GOVERNMENT PROPERTY FOR ONLINE USE ONLY