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CHAPTER 1: Physical quantities and measurements (3 Hours)

CHAPTER 1 PHYSICAL QUANTITIES AND MEASUREMENTS. CHAPTER 1: Physical quantities and measurements (3 Hours). UNIT FIZIK KOLEJ MATRIKULASI MELAKA. Learning Outcome:. 1.1 Physical Quantities and Units (1 hours). At the end of this chapter, students should be able to:

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CHAPTER 1: Physical quantities and measurements (3 Hours)

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  1. CHAPTER 1 PHYSICAL QUANTITIES AND MEASUREMENTS CHAPTER 1:Physical quantities and measurements(3 Hours) UNIT FIZIK KOLEJ MATRIKULASI MELAKA

  2. Learning Outcome: 1.1 Physical Quantities and Units (1 hours) At the end of this chapter, students should be able to: • State basic quantities and their respective SI units: length (m), time (s), mass (kg), electrical current (A), temperature (K), amount of substance (mol) and luminosity (cd). ( Emphasis on units in calculation) State derived quantities and their respective units and symbols: velocity (m s-1), acceleration (m s-2), work (J), force (N), pressure (Pa), energy (J), power (W) and frequency (Hz). • State and convert units with common SI prefixes.

  3. 1.1 Physical Quantities and Units • Physical quantity is defined as a ………………………………. • It can be categorized into 2 types • Basic (base) quantity • Derived quantity • Basic quantity is defined as ……………………………………………. • ……………………………………………………………………………….. • Table 1.1 shows all the basic (base) quantities. Table 1.1

  4. Derived quantity is defined as a quantity which can be expressed in term of base quantity. • Table 1.2 shows some examples of derived quantity. Table 1.2

  5. 1.1.1 Unit Prefixes • It is used for presenting larger and smaller values. • Table 1.3 shows all the unit prefixes. • Examples: • 5740000 m = 5740 km = 5.74 Mm • 0.00000233 s = 2.33  106 s = 2.33 s Table 1.3

  6. Example 1.1 : Solve the following problems of unit conversion. a. 15 mm2 = ? m2 b. 65 km h1 = ? m s1 c. 450 g cm3 = ? kg m3 Solution : a. 15 mm2 = ? m2 b. 65 km h-1 = ? m s-1 1st method :

  7. 2nd method : c. 450 g cm-3 = ? kg m-3

  8. Follow Up Exercise 1. A hall bulletin board has an area of 250 cm2. What is this area in square meters ( m2 ) ? 2. The density of metal mercury is 13.6 g/cm3. What is this density as expressed in kg/m3 3. A sheet of paper has length 27.95 cm, width 8.5 cm and thickness of 0.10 mm. What is the volume of a sheet of paper in m3 ? • Convert the following into its SI unit: • (a) 80 km h–1 = ? m s–1 • (b) 450 g cm–3 = ? kg m–3 • (c) 15 dm3 = ? m3 • (d) 450 K = ? ° C

  9. Learning Outcome: 1.2 Scalars and Vectors (2 hours) At the end of this chapter, students should be able to: a) Define scalar and vector quantities, b) Perform vector addition and subtraction operations graphically. c) Resolve vector into two perpendicular components (2-D) • Components in the x and y axes. • Components in the unit vectors in Cartesian coordinate.

  10. Learning Outcome: 1.2 Scalars and Vectors At the end of this topic, students should be able to: d) Define and use dot (scalar) product; e) Define and use cross (vector) product; Direction of cross product is determined by corkscrew method or right hand rule.

  11. 1.2 Scalars and Vectors • Scalar quantity is defined as a quantity with magnitude only. • e.g. mass, time, temperature, pressure, electric current, work, energy and etc. • Mathematics operational : ordinary algebra • Vector quantityis defined as a quantity with both magnitude & direction. • e.g. displacement, velocity, acceleration, force, momentum, electric field, magnetic field and etc. • Mathematics operational : vector algebra

  12. 1.2.1 Vectors Vector A Length of an arrow– magnitude of vector A • Table 1.4 shows written form (notation) of vectors. • Notation of magnitude of vectors. Direction of arrow – direction of vector A v (bold) a (bold) s (bold) Table 1.4

  13. Two vectors equal if both magnitude and direction are the same. (shown in figure 1.1) • If vector A is multiplied by a scalar quantity k • Then, vector A is • if k = +ve, the vector is in the same direction as vector A. • if k = -ve, the vector is in the opposite direction of vector A. Figure 1.1

  14. y 50 x 0 1.2.2 Direction of Vectors • Can be represented by using: • Direction of compass, i.e east, west, north, south, north-east, north-west, south-east and south-west • Angle with a reference line e.g. A boy throws a stone at a velocity of 20 m s-1, 50 above horizontal.

  15. y/m 5 x/m 0 1 • Cartesian coordinates • 2-Dimension (2-D)

  16. y/m 3 x/m 4 0 2 z/m • 3-Dimension (3-D)

  17. Unit vectors A unit vector is a vector that has a magnitude of 1 with no units. Are use to specify a given direction in space. i , j & k is used to represent unit vectors pointing in the positive x, y & z directions. | | = | | = | | = 1

  18. 150 + + - - • Polar coordinates • Denotes with + or – signs.

  19. 1.2.3 Addition of Vectors • There are two methods involved in addition of vectors graphically i.e. • Parallelogram • Triangle • For example : O O

  20. Triangle of vectors method: • Use a suitable scale to draw vector A. • From the head of vector A draw a line to represent the vector B. • Complete the triangle. Draw a line from the tail of vector A to the head of vector B to represent the vector A + B. Commutative Rule O

  21. If there are more than 2 vectors therefore • Use vector polygon and associative rule. E.g. Associative Rule

  22. Distributive Rule : a. b. • For example : Proof of case a:let  = 2 O

  23. O

  24. Proof of case b:let  = 2 and  = 1

  25. 1.2.4 Subtraction of Vectors • For example : O O

  26. Vectors subtraction can be used • to determine the velocity of one object relative to another object i.e. to determine the relative velocity. • to determine the change in velocity of a moving object. • Vector A has a magnitude of 8.00 units and 45 above the positive x axis. Vector B also has a magnitude of 8.00 units and is directed along the negative x axis. Using graphical methods and suitable scale to determine a) b) c) d) (Hint : use 1 cm = 2.00 units) Exercise 1 :

  27. y y    x x 0 0 1.2.5 Resolving a Vector • 2nd method : • 1st method :

  28. The magnitude of vector R : • Direction of vectorR : • Vector R in terms of unit vectors written as or

  29. N 30 60 W E S Example 1.2 : A car moves at a velocity of 50 m s-1 in a direction north 30 east. Calculate the component of the velocity a) due north. b) due east. Solution : or a) b)

  30. 150 x S y 150 30 x S Example 1.3 : A particle S experienced a force of 100 N as shown in figure above. Determine the x-component and the y-component of the force. Solution : or or

  31. y x O 30o 30o Example 1.4 : The figure above shows three forces F1, F2and F3 acted on a particle O. Calculate the magnitude and direction of the resultant force on particle O.

  32. y 30o 60o x 30o O Solution :

  33. Solution : Vector sum

  34. y 18 x O Solution : The magnitude of the resultant force is and Its direction is 162 from positive x-axis OR 18 above negative x-axis.

  35. y 37.0 x 0 Figure 1.2 Exercise 2 : • Vector has components Ax = 1.30 cm, Ay = 2.25 cm; vector has components Bx = 4.10 cm, By = -3.75 cm. Determine • the components of the vector sum , • the magnitude and direction of , • the components of the vector , • the magnitude and direction of . (Young & freedman,pg.35,no.1.42) ANS. : 5.40 cm, -1.50 cm; 5.60 cm, 345; 2.80 cm, -6.00 cm; 6.62 cm, 295 • For the vectors and in Figure 1.2, use the method of vector resolution to determine the magnitude and direction of • the vector sum , • the vector sum , • the vector difference , • the vector difference . (Young & freedman,pg.35,no.1.39) ANS. : 11.1 m s-1, 77.6; U think; 28.5 m s-1, 202; 28.5 m s-1, 22.2

  36. y 50 x 0 Figure 1.3 Exercise 2 : Vector points in the negative x direction. Vector points at an angle of 30 above the positive x axis. Vector has a magnitude of 15 m and points in a direction 40 below the positive x axis. Given that , determine the magnitudes of and . (Walker,pg.78,no. 65) ANS. : 28 m; 19 m Given three vectors P,Q and R as shown in Figure 1.3. Calculate the resultant vector of P,Q and R. ANS. : 49.4 m s2; 70.1 above + x-axis

  37. 1.2.6 Unit Vectors • notations – • E.g. unit vector a – a vector with a magnitude of 1 unit in the direction of vector A. • Unit vectors are dimensionless. • Unit vector for 3 dimension axes :

  38. y x z • Vector can be written in term of unit vectors as : • Magnitude of vector,

  39. y/m x/m 0 z/m • E.g. :

  40. Example 1.5 : Two vectors are given as: Calculate the vector and its magnitude, the vector and its magnitude, the vector and its magnitude. Solution : a) The magnitude,

  41. b) The magnitude, c) The magnitude,

  42. 1.2.7 Multiplication of Vectors Scalar (dot) product • The physical meaning of the scalar productcan be explained by considering two vectors and as shown in Figure 1.4a. • Figure 1.4b shows the projection of vector onto the direction of vector . • Figure 1.4c shows the projection of vector onto the direction of vector . Figure 1.4a Figure 1.4b Figure 1.4c

  43. From the Figure 1.4b, the scalar product can be defined as meanwhile from the Figure 1.4c, where • The scalar product is a scalar quantity. • The angle  ranges from 0 to 180 . • When • The scalar product obeys the commutative law of multiplication i.e. scalar product is positive scalar product is negative scalar product is zero

  44. y x z • Example of scalar product is work done by a constant force where the expression is given by • The scalar product of the unit vectors are shown below :

  45. Example 1.6 : Calculate the and the angle  between vectors and for the following problems. a) b) Solution : a) The magnitude of the vectors: The angle  , ANS.:3; 99.4

  46. y 25 x 19 0 Figure 1.5 Example 1.7 : Referring to the vectors in Figure 1.5, a) determine the scalar product between them. b) express the resultant vector of C and D in unit vector. Solution : a) The angle between vectors C and D is Therefore

  47. b) Vectors C and D in unit vector are and Hence

  48. RIGHT-HAND RULE Vector (cross) product • Consider two vectors : • In general, the vector product is defined as and its magnitude is given by where • The angle  ranges from 0 to 180  so the vector product always positive value. • Vector product is a vector quantity. • The direction of vector is determined by

  49. For example: • How to use right hand rule : • Point the 4 fingers to the direction of the 1st vector. • Swept the 4 fingers from the 1st vector towards the 2nd vector. • The thumb shows the direction of the vector product. • Direction of the vector product always perpendicular to the plane containing the vectors and . but

  50. y x z • The vector product of the unit vectors are shown below : • Example of vector product is a magnetic force on the straight conductor carrying current places in magnetic field where the expression is given by

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