PHYSICAL QUANTITIES AND UNITS


 Russell Walker
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1 1 PHYSICAL QUANTITIES AND UNITS Introduction Physics is the study of matter, its motion and the interaction between matter. Physics involves analysis of physical quantities, the interaction between them and the formulation of principles to explain natural phenomena. A physical quantity is made up of a numerical magnitude and a unit. Making measurement is important in physics. A measurement has uncertainty or errors. Many physical quantities are vectors. Knowing basic operations such as addition and products of vector are fundamental skills required in the study of physics. International Prototype Metre standard bar made of platinumiridium. This was the standard until 1960, when the new SI system used a kryptonspectrum measurement as the base. Concept Map Physical Quantities and Units Base Quantities and SI Units SI units Base quantities and units Derived quantities and units Dimensions Dimensions of base quantities Dimensional analysis check homogeneity construct equations Scalars and Vectors Sum, scalar and vector products of vectors Resolving a vector to two components Errors Calculate uncertainty in a derived quantity Significant figures
2 2 ACE AHEAD Physics First Term LEARNING OUTCOMES (a) List base quantities as mass (kg), length (m), time (s), current (A), temperature (K), and quantity of matter (mol) (b) Deduce units for derived quantities 1.1 Base Quantities and SI Units 1 A physical quantity is a property that can be measured. 2 Examples of physical quantities are: length, mass, time, speed, energy, temperature and current. 3 A physical quantity is described by a numerical value and a unit. Example: the height of a person is 2 m. The numerical value is 2 and the unit is metre (m). 4 The unit of a physical quantity is the standard size used to compare different sizes of the physical quantity. In the above example, the height of the person is two times the standard length which is the metre (m). 5 In the International System of Units (SI), seven physical quantities are chosen as fundamental or base quantities. Definition of the base units for the base quantities are given in Table 1.1. PHYSICS FILE In 1790 the metre was fixed as the length of the pendulum with a halfperiod of one second. Base quantity Length Base unit metre (m) Definition of base unit Distance travelled by light in vacuum during the time interval of 1/( ) second. Mass of a platinumiridium cylinder kept at the International Bureau of Weights and Measures in Sevres, France. The time interval for the light emitted from the cesium133 atom to complete oscillations. One kelvin (1 K) = 1/ of the temperature of the triple point of water. The constant current which, if maintained in two straight parallel conductors of infinite length, negligible circular crosssectional area and placed one metre apart in vacuum, would produce between these conductors a force of newton per metre of length. The amount of substance of a system which contains as many elementary entities as there are atoms in kg of carbon12. The candela (cd) is the luminous intensity, in a given direction of a source that emits monochromatic radiation of frequency Hz and that has a radiant intensity in that direction of 1/683 watt per steradian. Mass kilogram (kg) Time second (s) Temperature kelvin (K) ampere (A) Current Amount of substance mole (mol) Luminous intensity candela (cd) Table 1.1 Base quantities in SI
3 1 Physical Quantities and Units 21 2 The diameter of a metal sphere is ( ) cm, and its mass is (235 5) g. (a) Calculate the percentage uncertainty in the determination of the density of the metal. (b) Calculate the density of the metal and state its absolute uncertainty. 3 The time for 40 oscillations of a simple pendulum recorded using a stopwatch is 48.6 s. Calculate the period of the simple pendulum to the correct number of significant figures. 4 A rectangular plot of land is ( ) m long and ( ) m wide. Calculate (a) the perimeter and (b) the area of the plot. Give the uncertainty for each of the answers. COMPANION WEBSITE Online Test Summary 1 A physical quantity is a property that can be measured. 2 The unit of a physical quantity is the standard size used to compare different sizes of the physical quantity. 3 The dimension of the derived quantity is the relationship between a derived quantity and the base quantities. 4 The dimension of a physical equation is homogeneous if all the terms in the equation have the same dimension. 5 Dimensional analysis enables us to construct an equation that relates a physical quantity to the variables that are observed in experiments. 6 A scalar is a physical quantity that has only magnitude. 7 A vector has both magnitude and direction. 8 The addition of two vectors P and Q is a new vector R, (P + Q) = R which is known as the resultant vector. 9 A vector R can be resolved into two components R x and R y that are mutually perpendicular R x = R cos q and R y = R sin q tan q = R y R = R R 2 + x R2 y x where q is the angle between the component R x and the vector R. 10 The scalar product of two vectors a.b = a b cos q where q is the angle between the two vectors. 11 The vector product of two vectors a b is a vector whose magnitude is given by a b = a b sin q The direction of a b is such that the vectors a, b and a b form a righthand system.
4 22 ACE AHEAD Physics First Term Focus on Exam 1 OBJECTIVE QUESTIONS 1 The dimension of angular velocity is A T 1 B L T 1 C L T 2 D L 2 T 1 STPM 2005/P1/Q1 2 The tensile strength of a wire is the maximum stress on the wire just before it breaks. What is the dimension of tensile strength? A M L 1 T 1 B M L 1 T 2 C M L T 1 D M L T 2 STPM 2007/P1/Q1 3 The unit for power is watt (W). In terms of the base SI units, W is given by A kg m s 2 B kg m 2 s 1 C kg m 2 s 2 D kg m 2 s 3 4 Newton s law of gravitation states that the gravitational force F between two point masses m and M separated by a distance r is given by F = G mm 2. What is the SI unit r for G? A m s 2 B N m 2 s 2 C m 2 kg 2 D kg 1 m 3 s 2 5 Which of the following equations is dimensionally homogeneous? A Force = mass displacement B Work = mass velocity C Power = force velocity D Impulse = force displacement 6 The possible factors that affect the speed v of waves in the sea are r the density of sea water, h the depth of the sea, l the wavelength and g the acceleration due to gravity. If k is a dimensionless constant, in which equation the dimension is consistent? A v = k gl B v = k ghr C v = k g l D v = k gl r 7 The momentum of a body of mass m is p. Which quantity has the same unit as p2 m? A Force B Energy C Power D Pressure 8 Which pair contains a scalar quantity and a vector quantity? A Work and weight B Power and energy C Impulse and momentum D Potential energy and distance 9 Forces of 10 N and 6 N act on a point. Which of the following cannot be a possible magnitude of the resultant force? A 3 N B 6 N C 10 N D 12 N 10 The resultant of three vectors P, Q and R is X. Which vector diagram correctly shows X = P + Q + R? A R P X Q
5 Model Exam (Paper 1) PHYSICS PAPER 1 Time: 1 hr 45 min Section A (15 marks) Answer all questions in this section. 1 Which of the following is the dimension for pressure? A M L 1 T 2 C M L 2 T 2 B M L T 2 D M L 1 T 1 2 The length of a strip of paper is 20.2 cm and its width is cm. The perimeter of the strip to the correct significant figure is A 42 cm C cm B 42.3 cm D cm 3 A car and a bus pass a point P in the same direction along a road at time t = 0. The speedtime graphs of the vehicles are as shown in the figure. Speed (m s 1 ) Bus Car Time (s) The bus overtakes the car after A 5 s C 15 s B 10 s D 20 s 4 A ball is kicked from a point P and moves off with a speed v at an angle of 45 to the ground. It passes over the horizontal bar of a goal post which is at a height h. What is the speed v of the ball? (g is the acceleration due to gravity.) A 1 gh 2 C 2gh B 1 2 gh D 2 gh 5 A particle P moving with a velocity 4.0 m s 1 collides elastically into another particle Q of the same mass moving with a velocity of 1.6 m s 1 in the same direction. What are the velocities of P and Q after collision? Velocity of P Velocity of Q A 1.6 m s m s 1 B 2.8 m s m s 1 C 3.0 m s m s 1 D 3.8 m s m s 1
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