G Physics 1 Ch-1 ENGINEERS- PDF

General physics 1 -ENGINEERS-(A0111201) Faculty of ENGINEERS… Chapter 1 Dr. Talal Haimur The Presentations are based on " University physics with modern physics” H, D...

General physics 1 -ENGINEERS-(A0111201) Faculty of ENGINEERS… Chapter 1 Dr. Talal Haimur The Presentations are based on " University physics with modern physics” H, D. Young and R, A. Freedman 15th edition (person Addison Wesley, 2020) & PHYSICS PRINCIPLES WITH APPLICATIONS 7th edition 2015 DOUGLAS C. G I A N C O L I Talal Haimur  Ch 1: Units, Physical quantities and Vectors. - The Nature of Physics. - Standards and units. - Using and Converting Units. - Vectors and vector addition. - Components of vectors. - Unit vectors. - Products of vectors. Solve Problem. Talal Haimur  1.3 STANDARDS AND UNITS - The measurement of any quantity is made relative to a particular standard or unit, and this unit must be specified along with the numerical value of the quantity. * For example, we can measure length in inches, feet, or yard or miles, or centimeters, meters, or kilometers, or gram, or kilogram, or ton or second, or minibus, or hour or day or………..etc. - a particular standard or unit.: 1) Length. 2) Time. 3) Mass. * Physical quantities can be divided into two categories: base quantities and derived quantities. The corresponding units for these quantities are called base units and derived units. A base quantity must be defined in terms of a standard. The major systems of units: -To distinguish between units- Systems Length Units “Abbreviation” Time Units Mass Units International (I S) or Meter “m” Second “s” Kilogram “kg” MKS system (meter, kilogram, second). British inch “in.”, foot “ft”, mile “mi” Second “s” ton Derived or c g s system Centimeter “cm” Second “s” gram “gm” (centimeter, gram, second) (pound for the force) SI Base Quantities and Units Quantity Unit Unit Abbreviation Length meter m Time second s Mass kilogram kg Electric current ampere A Temperature kelvin K Amount of mole mol substance Luminous candela cd intensity Talal Haimur  The prefix “kilo-,” abbreviated k, always means a unit larger by a factor of 1000; thus 1 kilometer = 1 km = 103 meters = 103 m 1 kilogram = 1 kg = 103 grams = 103g 1 kilowatt = 1 kW = 103 watts = 103 W Talal Haimur  1.4 USING AND CONVERTING UNITS: - Any quantity we measure, such as a length, a speed, or an electric current, consists of a number (value) and a unit. - Often, we are given a quantity in one set of units, but we want it expressed in another set of units. We need conversion factors: 1 cm = 10 mm , 1 m = 100 cm , 1 km = 1000 m 1 cm2 = (mm)2 = m2 = 1 cm3 = (mm)3 = m3 = 1 in. = 2.54 cm = 0.0254 m , 1 ft = = 30.48 cm = 0.3048 m 1 in. 2 = ? (cm)2 = ? (m)2 = ? 1 in.3 = ? (cm)3 = ? (mm)3 = ? 1 mile = 1.609 km = 1609 m , 1 ft = 12 inch 1 ft 2 = ? (inch)2 = ? (cm)2 = ? m2 = 1 in.3 = ? (inch)3 = ? (cm)3 = ? m3 = Note that : 1ml = 1cm3 , 1 liter = 1000 ml or 1000 cm3 or (1000 cc) 1 hr = 60 minutes = 3600 s , 1 kg = 1000 gm Talal Haimur  EX 1: How many centimeters, meters in 21.5 inches? Sol: 21.5 inches = (21.5) x (2.54 cm) = 54.6 cm 21.5 inches = 54.6 cm = 54.6 x (0.01m) =0.546 m EX 2: There are only 14 peaks whose summits are over 8000 m above sea level. They are the tallest peaks in the world and are referred to as “eight-thousands.” What is the elevation, in feet, of an elevation of 8000 m? Sol: We need to convert meters to feet, and we can start with the conversion factor which is: 1 in = 2.54 cm so: 1 ft = (12 in. ) ( 2.54 cm/ in.) = 30.48 cm = 0.3048 m or: 1 m = 1 ft/0.3048 m = 3.28084 ft so: 8000 m = (8000) x (3.28084 ft) = 26.247 ft. Or: 8000.0 m = (8000.0 m) x (100 cm) x (1/2.54 in) x (1/12 ft) = 26,247 ft. EX 3: You have seen a nice apartment whose floor area is 880 square feet. What is its area in square meters? Sol: Since 1 ft = 30.48 cm = 0.3048 m, so 880 ft2 = (880) x (0.3048 m)2 = (880) x (0.0929 m2) = 81.75 m2 ≈ 82 m2. EX 4: Where the posted speed limit is 55 miles per hour (or mph), what is this speed: a) in meters per second and b) in kilometers per hour (km/h). Sol: since 1 mile = 1.609 km = 1609 m. so, a) 55 mi / h = ( 55 ) x (1609 m / 3600 s) = 25 m/s. b) 55 mi / h = ( 55 ) x ( 1.609 km ) /h = 88 km/h. Talal Haimur  EX: EX: * Dimensions and Dimensional Analysis: * Dimensions can be used as a help in working out relationships, a procedure referred to as dimensional analysis. * useful technique is the use of dimensions to check if a relationship is correct or incorrect. * Note that numerical factors, like ( 1, 2, ½ …….), do not affect dimensional checks. * (In numerical calculations, the units must also be the same on both sides of an equation.) * When we speak of the dimensions of a quantity, we are referring to the type of base units or base quantities. * We use brackets [ ] to denote (abbreviate) the dimension.so, Physical quantity (base) Unit (in SI) Dimension Time s [T] Mass kg [M] Length m [L] Talal Haimur  EX 5: Find the dimension of: Remember that: the area of a triangle of base b and height h is: A = ½ bh, whereas the area of a circle of radius r is: A = πr2 1) Area. So, dimension is: [ L 2 ]. Unit is: 2) Speed. So, speed = distance traveled ( x ) / elapse time ( t ) = x/t. so, dimension is [L / T]. Or [L] / [T]. Unit is: Practice. 3) Acceleration. Where acceleration = velocity / travelling time. Sol: Unit is: Practice. 4) Force. where force equal object mass times its acceleration. Sol: Unit is: EX 6: suppose you derived the equation: v = v0 + ½ at2. where v is the speed of an object after a time t, v0 is the object’s initial speed, and the object undergoes an acceleration a. Let’s do a dimensional check to see if this equation could be correct or is surely incorrect. So, [L / T] ≠ [L / T] + [L]. The dimensions are incorrect: on the right side, we have the sum of quantities whose dimensions are not the same. Thus, we conclude that an error was made in the derivation of the original equation. Note that: Talal Haimur  Since the constant (2π) has no dimensions and so can’t be checked using dimensions. Practice : For the formula: v2 = v02 + 2 at2 , show that its incorrect ? Sol: 1.7 VECTORS AND VECTOR ADDITION: Some physical quantities, such as time, temperature, mass, and density, can be described completely by a single number with a unit. But many other important quantities in physics have a direction associated with them and cannot be described by a single number. A simple example is the motion of an airplane: We must say not only how fast the plane is moving but also in what direction. The speed of the airplane combined with its direction of motion constitute a quantity called velocity. Another example is force, which in physics means a push or pull exerted on an object. Giving a complete description of a force means describing both how hard the force pushes or pulls on the object and the direction of the push or pull. When a physical quantity is described by a single number, we call it a scalar quantity. In contrast, a vector quantity has both a magnitude (the “how much” or “how big” part) and a direction in space. Calculations that combine scalar quantities use the operations of ordinary arithmetic. For example, 6 kg + 3 kg = 9 kg, or 4 * 2 s = 8 s. However, combining vectors requires a different set of operations. Talal Haimur  To understand more about vectors and how they combine, we start with the simplest vector quantity, displacement. Displacement is a change in the position of an object. Displacement is a vector quantity because we must state not only how far the object moves but also in what direction. Walking 3 km north from your front door doesn’t get you to the same place as walking 3 km southeast; these two displacements have the same magnitude but different directions. We usually represent a vector quantity such as displacement by a single letter, such as in Fig. 1.8a. In this book we always print vector symbols in boldface italic type with an arrow above them. We always draw a vector as a line with an arrowhead at its tip. The length of the line shows the vector’s magnitude, If two vectors have the same direction, they are parallel. If they have the same magnitude and the same direction, they are equal, no matter where thy located in space. Talal Haimur  Vector B in Fig. 1.9, however, is not equal to A because its direction is opposite that of A. We define the negative of a vector as a vector having the same magnitude as the original vector but the opposite direction. The negative of vector quantity A is denoted as -A A = -B or B = -A we say that they are antiparallel. When a physical quantity is described by a single number, we call it a scalar quantity. In contrast, a vector quantity has both a magnitude and direction. Addition of Vectors + Graphical Methods ( 1- tail-to-tip method of adding vectors ) (2- A second way to add two vectors is the parallelogram method Or tail-to-tail ) Talal Haimur Talal Haimur Talal Haimur  EX: ??? EX: A cross-country skier skis 1.00 km north and then 2.00 km east on a horizontal snowfield. How far and in what direction is she from the starting point? The problem involves combining two displacements at right angles to each other. This vector addition amounts to solving a right triangle, so we can use the Pythagorean theorem and trigonometry. Figure is a scale diagram of the two displacements and the resultant net displacement. Talal Haimur  We denote the direction from the starting point by the angle f (the Greek letter phi). The displacement appears to be a bit more than 2 km. Measuring the angle is about 63°. + Subtraction of Vectors, and Multiplication of a Vector by a Scalar EX: Talal Haimur  EX: EX: EX: Talal Haimur  1.8 COMPONENTS OF VECTORS Adding vectors graphically using a ruler and protractor is often not sufficiently accurate and is not useful for vectors in three dimensions. We discuss now a more powerful and precise method for adding vectors. The components are usually chosen to be along two perpendicular directions, such as the x and y axes. Components of a vector The components of a vector (Ax, Ay, and Az) along the x, y, and z directions are called the rectangular (or Cartesian) components. Components are not vectors the components Ax and Ay of a vector A are numbers; they are not vectors themselves. θ measured from the +x-axis, rotating toward the +y-axis2 Talal Haimur  EX: Talal Haimur  Using Components to Do Vector Calculations EX : Talal Haimur Talal Haimur  EX *: (Practice for you) 1- Find the magnitude and direction of the vector represented by the following pairs of components: (a) Ax = -8.60 cm, Ay = 5.20 cm; (b) Ax = -9.70 m, Ay = -2.45 m; (c) Ax = 7.75 km, Ay = -2.70 km. EX**: (Practice for you) (a) Write each vector in Fig. in terms of the unit vectors i and j. (b) Use unit vectors to express vector C , where C =3.00 A - 4.00 B. (c) Find the magnitude and direction of C? EX***: (Practice for you) Vector A is in the direction 34.0 clockwise from the –y-axis. The x-component of A is Ax = -16.0 m. (a) What is the y-component of A? (b) What is the magnitude of A? Talal Haimur  1.10 PRODUCTS OF VECTORS: We saw how vector addition develops naturally from the problem of combining displacements. It will prove useful for calculations with many other vector quantities. We can also express many physical relationships by using products of vectors. Vectors are not ordinary numbers, so we can’t directly apply ordinary multiplication to vectors. We’ll define two different kinds of products of vectors. The first, called the scalar product, yields a result that is a scalar quantity. The second, the vector product, yields another vector. The scalar product is a scalar quantity, not a vector, and it may be positive, negative, or zero. Talal Haimur Talal Haimur Talal Haimur Talal Haimur Talal Haimur Talal Haimur Talal Haimur  Sol: Sol: Talal Haimur