PHY 111: MECHANICS AND PROPERTIES TOPIC : MEASUREMENT,UNITS AND DIMENSIONAL ANALYSIS CLASS : A LEVEL AND O LEVEL PHY 111: MECHANICS AND PROPERTIES TOPIC : MEASUREMENT,UNITS AND DIMENSIONAL ANALYSIS Measurement is a proces of assigning numbers according to a rule. Thre are various types of measurements they specically include : * Measurements of lenght * Measurements of mass * Measurements of time * Measurements of weight Measurements of lenght Lenght can be defined as the extent of an object from end to end here below are some materials use fo rmeasuring lenght 1 Metre rule: it is used for measuring the lenght of a desk 2 Tape rule : it is used for measuring the lenght of a field 3 Venier calliper : it is used for measuring the internal and external diameter of an object 4 Micrometer Screw guage : it is used for measuring the external diameter only of an object Measurements of mass Mass can be defined as the quantity of matter in which a body contains. Here below are some materials used for measuring mass. 1 Beam balance 2 Triple beam balance 3 Chemical balance pg1 Measurements of time Time can be defined as that in which an event is placed or distingushed in reference to before or after. Here below are some materials used for measuring time. 1 Stop clock 2 Stop watch 3 Water clock 4 pendulum clock. Measurements of weight Weight is a force that tends to pull a body towards the centre of the earth. Here are some materials used for measuring weight . 1 Lever balance 2 Spring balance 3 Dial spring balance With the aid of some instruments PHYSICAL QUANTITIES Physical quantities are quantities that can be measured physically with the aid of some instruments. Physical quantities are divided into two parts they are: 1 Fundamental quantities 2 Derived quantities Fundamental quantities are known as the basic unit of measurements they are basically seven in number they include: QUANTITIES UNITS SYMBOLS * Lenght Metre m * Mass Kilogram kg * Time Seconds s * Current Ampere A * Temperature Kelvin k * Amt of substance mole mol * Light intensity Candela c Pg2 Derived quantities involves two or more fundamental quantities. E.g Velocity =distance m = ms_1 Time s Acceleration = velocity ms_1 = ms_2 Time s Force = mass x acceleration = kgms_2 or N Work = force x distance = Nm Dimensional analysis Dimensional analysis is a process of identifying and proofing a mathematical expression in physics. It basically has four parts which are. 1 Dimensions of fundamental quantities 2 Dimensions of derived quantities 3 Dimensional proof of mathematical expressions 4 Identifying mathematical expression from dimensional Quantities. DIMENSIONS OF FUNDAMENTAL QUANTITIES QUANTITIES UNITS Lenght metre Mass kilogram Time seconds Temperature kelvin Current Ampere Amt of subs mole Light intensity candela SYMBOLS m kg s k A mol c DIMENSIONS L M T 0 I n J N. B : In dimensional analysis numbers do not count they are considered to be 1. Pg3 DIMENSIONS OF DERIVED QUANTITIES Velocity = Distance = L = LT_1 Time T Acceleration = velocity = LT_1 = LT_2 Time T Force = mass x acceleration = MLT_2 Work = force x distance = MLT_2 x L = ML2T_2 DIMENSIONAL PROOF OF A MATHEMATICAL EXPRESSION. 1 v=u+at LT_1= LT_1 + LT_2 T LT_1 = LT_1 + LT_1 2 s= ut + 1/2 at2 L= LT_1T + LT_2 T2 L=L + L 3 s = ut + 3/2 kat3 L = LT-1 T + KLT-2 T3 L= L + KLT (not correct) To make it correct find k K = L-1T-1 L = L + (L-1T-1)LT L = L (CORRECT) IDENTIFYING MATHEMATICAL EXPRESSION FROM THEIR DIMENSIONAL QUANTITIES 1 The period of a pendulum depends on the mass of the bulb, the lenght of the string and the acceleration due to gravity acting on the bulb. Deduce an expression of the period of the pendulum from these quantities T= K M L g T = K M x Ly g z pg4 T = K Mx Ly ( LT-2)z T= K Mx Ly Lz T-2 z T = K Mx Ly+Z T-2 Z X=0 because its not on the other side of the equation -2z = 1 Z = -1/2 y+z = 0 Y = -z Y = 1 /2 T = K M0 L1/2 g-1/2 T = K √L √g T = K √L/g EXERCISE 1 Identify the dimensions of the following derived quantities (a) Specific heat capacity (b) Surface tension (c) Viscosity (d) Gravitational constant (e) Young’s modulus 2 Proof the following equations S= ut + 3/2 ka2t4 V2= u2 + 2ca3s2 3 The wave of an ocean has its density (ρ) and velocity (v) related by the expression V = A g x ρy ƛ z . pg5