Lecture 1 - Physics and Measurement PDF

PH 211. General Physics 1 Introduction Syllabus and teaching strategy Physics Introduction Mathematical review trigonometry vectors  Contact information, Syllabus and teaching strategy Le...

PH 211. General Physics 1 Introduction Syllabus and teaching strategy Physics Introduction Mathematical review trigonometry vectors  Contact information, Syllabus and teaching strategy Lecturer: VU THI HANH THU, Associate Professor. Dr Phone: 094 559 9999 Department Of Applied Of Physics, Faculty Of Physics & Engineering Physics, University Of Sciences Ho Chi Minh City Viet Nam Email: [email protected] Office: Vacuum Laboratory A or F Building, (A07, F14) Grading: Midterm examination: 25%; Final examination: 50% (multi - choice) Homework assignments: 25%; Class participation: bonus + total mark Syllabus: See Syllabus.doc Book: Serway & Jewett, Physics for Scientists and Engineers with Modern Physics, 9th edition, Brooks/Cole, 2014  Contact information, Syllabus and teaching strategy ► Mail: [email protected]; [email protected] ✓ Messenger (Fb: Thu Vu) https://www.facebook.com/thu.vu.96343 ✓ Phone (zalo): 094 55 99999 https://www.facebook.com/thu.vu.96343  Physics: Introduction ►Physics: ▪ The most fundamental physical science ▪ Is concerned with the fundamental principles of the Universe ►The study of physics can be divided into six main areas: 1. Classical mechanics, concerning the motion of objects that are large relative to atoms and move at speeds much slower than the speed of light  2. Relativity, a theory describing objects moving at any speed, even speeds approaching the speed of light 3. Thermodynamics, dealing with heat, work, temperature, and the statistical behavior of systems with large numbers of particles  4. Electromagnetism, concerning electricity, magnetism, and electromagnetic fields 5. Optics, the study of the behavior of light and its interaction with materials 6. Quantum mechanics, a collection of theories connecting the behavior of matter at the submicroscopic level to macroscopic observations CHAPTER 1: PHYSICS AND MEASUREMENT 1.1 Standards of Length, Mass, and time 1.2 Matter and Model Building 1.3 Dimensional analysis 1.4 Conversion of Units 1.5 Estimates and Order-of-Magnitude Calculations 1.6 Significant Figures CHAPTER 1: PHYSICS AND MEASUREMENT Like all other sciences, physics is based on experimental observations and quantitative measurements Objectives: to identify fundamental laws governing natural phenomena and use them to develop theories Tool: language of mathematics (a bridge between theory and experiment) Classical physics: includes the principles of classical mechanics, thermodynamics, optics, and electromagnetism developed before 1900 (Newton mechanics) Modern physics: the major revolution in physics began near the end of the 19th century (theories of relativity and quantum mechanics)  Classical Mechanics ► Classical mechanics deals with the motion of objects ► Classical Mechanics: Theory that predicts qualitatively & quantitatively the results of experiments for objects that are NOT ▪ Too small: atoms and subatomic particles – Quantum Mechanics ▪ Too fast: objects close to the speed of light – Special Relativity ▪ Too dense: black holes, the early Universe – General Relativity ► Classical mechanics concerns the motion of objects that are large relative to atoms and move at speeds much slower than the speed of light (i.e. nearly everything!) Measurement  Measurement ► To be quantitative in Physics requires measurements ► How tall is Ming Yao? How about his weight? ▪ Height: 2.29 m (7 ft 6 in) ▪ Weight: 141 kg (310 lb) ► Number + Unit ▪ “thickness is 10.” has no physical meaning ▪ Both numbers and units necessary for any meaningful physical quantities  Type Quantities ► Many things can be measured: distance, speed, energy, time, force …… ► These are related to one another: speed = distance / time ► Choose three basic quantities (DIMENSIONS): ▪ LENGTH ▪ MASS ▪ TIME ► Define other units in terms of these.  SI Unit for 3 Basic Quantities ► Many possible choices for units of Length, Mass, Time (e.g. Yao is 2.29 m or 7 ft 6 in) ► In 1960, standards bodies control and define Système Internationale (SI) unit as, ▪ LENGTH: Meter ▪ MASS: Kilogram ▪ TME: Second 1.1. Standards of Length, Mass, and Time ► Basisof testing theories in science ► Need to have consistent systems of units for the measurements ► Uncertainties are inherent ► Need rules for dealing with the uncertainties 1.1. Standards of Length, Mass, and Time ► Standardized systems ▪ agreed upon by some authority, usually a governmental body ► SI -- Systéme International ▪ agreed to in 1960 by an international committee ▪ main system used in this course ▪ also called mks for the first letters in the units of the fundamental quantities  Systems of Measurements ► cgs -- Gaussian system ▪ named for the first letters of the units it uses for fundamental quantities ► US Customary ▪ everyday units (ft, etc.) ▪ often uses weight, in pounds, instead of mass as a fundamental quantity  Length ► The distance between two points in space ► Units ▪ SI: meter, m ▪ cgs: centimeter, cm ▪ US Customary: foot, ft ► Defined in terms of a meter: ▪ 1960: the distance between two lines on a specific platinum–iridium bar stored under controlled conditions in France ▪ 1960s-1970s: 1m = 1 650 763.73 wavelengths of orange-red light emitted from a krypton-86 lamp ▪ October 1983: 1m = the distance traveled by light in a vacuum during a given time (1/299 792 458 s) Table 1.1 Approximate Values of Some Measured Lengths  Mass Why is it hidden under two glass domes? ► Units ▪ SI -- kilogram, kg ▪ cgs -- gram, g ▪ USC -- slug, slug → Avoid vibration by air, dust ► Defined in terms of the kilogram 1987: 1kg = the mass of a specific Pt – Ir alloy cylinder kept at the International Bureau of Weights and Measures at Sèvres, France Table 1.2 Approximate Masses of Various Objects  Time ► Units ▪ seconds, s in all three systems ► Defined in terms of the second ▪ 1967: the oscillation of radiation from a cesium atom (Ce) ▪ 1s = 9 192 631 700 times the period of vibration of radiation from the cesium-133 atom (in an atomic clock) Time Measurements US “Official” Atomic Clock Table 1.3 Approximate Values of Some Time Intervals Fundamental Quantities and SI Units Length meter m Mass kilogram kg Time second s Electric Current ampere A Thermodynamic Temperature kelvin K Luminous Intensity candela cd Amount of Substance mole mol  1.2. Dimensional Analysis ► Dimension denotes the physical nature of a quantity ► Technique to check the correctness of an equation ► Dimensions (length, mass, time, combinations) can be treated as algebraic quantities ▪ add, subtract, multiply, divide ▪ quantities added/subtracted only if have same units ► Both sides of equation must have the same dimensions  1.2. Dimensional Analysis ► Dimensions for commonly used quantities ◼ Example of dimensional analysis distance = velocity · time L = (L/T) · T Example 1 Analysis of an Equation Show that the expression v = at, where v represents speed, a acceleration, and t an instant of time, is dimensionally correct. The dimensions of v The dimensions of a v = at is dimensionally correct (the same dimensions on both sides) Example 1.2 Analysis of a Power Law Suppose we are told that the acceleration a of a particle moving with uniform speed v in a circle of radius r is proportional to some power of r, say rn, and some power of v, say vm. Determine the values of n and m and write the simplest form of an equation for the acceleration An expression for a with a dimensionless constant of proportionality k The dimensions of a, r, and v on uniform circular motion → k = 1 if a consistent set of units is used  1.2. Dimensional Analysis ► Necessary either to derive a math expression, or equation or to check its correctness. ► Quantities can be added/subtracted only if they have the same dimensions. ► The terms of both sides of an equation must have the same dimensions. ▪ a, b, and c have units of meters, s = a, what is [s] ? ▪ a, b, and c have units of meters, s = a + b, what is [s] ? ▪ a, b, and c have units of meters, s = (2a + b)b, what is [s] ? ▪ a, b, and c have units of meters, s = (a + b)3/c, what is [s] ? ▪ a, b, and c have units of meters, s = (3a + 4b)1/2/9c2, what is [s] ?  1.3. Conversion of units ► When units are not consistent, you may need to convert to appropriate ones ► Units can be treated like algebraic quantities that can cancel each other out 1 mile = 1609 m = 1.609 km 1 ft = 0.3048 m = 30.48 cm 1m = 39.37 in = 3.281 ft 1 in = 0.0254 m = 2.54 cm  Example Scotch tape: Example Trip to Canada: Legal freeway speed limit in Canada is 100 km/h. What is it in miles/h? km km 1 mile miles 100 = 100   62 h h 1.609 km h Example 1.3 Is He Speeding? On an interstate highway in a rural region of Wyoming, a car is traveling at a speed of 38.0 m/s. Is the driver exceeding the speed limit of 75.0 mi/h? What if the driver were from outside the United States and is familiar with speeds measured in kilometers per hour? What is the speed of the car in km/h? 36km/h = ? m/s 200mi/h = ? m/s  Prefixes ► Prefixescorrespond to powers of 10 ► Each prefix has a specific name/abbreviation Power Prefix Abbrev. 1015 peta P 109 giga G Distance from Earth to nearest star 40 Pm 106 mega M Mean radius of Earth 6 Mm 103 kilo k Length of a housefly 5 mm 10-2 centi c Size of living cells 10 m 10-3 milli m Size of an atom 0.1 nm 10-6 micro  10-9 nano n Table 1.4 Prefixes for Powers of Ten 1.5. Estimates and Order-of-Magnitude Calculations Order of magnitude, which is a power of ten determined as follows: 1. Express the number in scientific notation, with the multiplier of the power of ten between 1 and 10 and a unit. 2. If the multiplier is less than 3.162 (the square root of 10), the order of magnitude of the number is the power of 10 in the scientific notation. If the multiplier is greater than 3.162, the order of magnitude is one larger than the power of 10 in the scientific notation Example 1.4 Breaths in a Lifetime Estimate the number of breaths taken during an average human lifetime Guessing that the typical human lifetime is about 70 years, average number of breaths that a person takes in 1 min (This number varies depending on whether the person is exercising, sleeping, angry, serene, and so forth) To the nearest order of magnitude, we shall choose 10 breaths per minute as our estimate. (This estimate is certainly closer to the true average value than an estimate of 1 breath per minute or 100 breaths per minute) The approximate number of minutes in a year: The approximate number of minutes in a 70-year lifetime The approximate number of breaths in a lifetime  1.4. Uncertainty in Measurements ► There is uncertainty in every measurement, this uncertainty carries over through the calculations ▪ need a technique to account for this uncertainty ► We will use rules for significant figures to approximate the uncertainty in results of calculations  1.5 Significant Figures ► A significant figure is one that is reliably known ► It is the number of numerical digits used to express the measurement ► All non-zero digits are significant ► Zeros are significant when ▪ between other non-zero digits ▪ after the decimal point and another significant figure ▪ can be clarified by using scientific notation 17400 = 1.74 10 4 3 significant figures 17400. = 1.7400 10 4 5 significant figures 17400.0 = 1.74000 10 4 6 significant figures Operations with Significant Figures ► Accuracy -- number of significant figures Example: meter stick:  0.1cm ► When multiplying or dividing, round the result to the same accuracy as the least accurate measurement 2 significant figures Example: rectangular plate: 4.5 cm by 7.3 cm area: 32.85 cm2 33 cm2 ► When adding or subtracting, round the result to the smallest number of decimal places of any term in the sum Example: 135 m + 6.213 m = 141 m Example 1.5 Installing a Carpet A carpet is to be installed in a rectangular room whose length is measured to be 12.71 m and whose width is measured to be 3.46 m. Find the area of the room The area of the room: A = 12.71 x 3.46 = 43.976 6 m2. The lowest number of significant figures is three in 3.46 m, Final answer as 44.0 m2  Order of magnitude ► Approximation based on a number of assumptions ▪ may need to modify assumptions if more precise results are needed Question: McDonald’s sells about 250 million packages of fries every year. Placed back-to-back, how far would the fries reach? Solution: There are approximately 30 fries/package, thus: (30 fries/package)(250. 106 packages)(3 in./fry) ~ 2. 1010 in ~ 5. 108 m, which is greater then Earth-Moon distance (4. 108 m)! ► Order of magnitude is the power of 10 that applies Example: John has 3 apples, Jane has 5 apples. Their numbers of apples are “of the same order of magnitude”  Vector vs. Scalar Review A library is located 0.5 mi from you. Can you point where exactly it is? You also need to know the direction in which you should walk to the library! ► All physical quantities encountered in this text will be either a scalar or a vector ► A vector quantity has both magnitude (value + unit) and direction ► A scalar is completely specified by only a magnitude (value + unit)  Vector and Scalar Quantities ❑ Vectors ❑ Scalars: ◼ Displacement ◼ Distance ◼ Velocity (magnitude and ◼ Speed (magnitude of direction!) velocity) ◼ Acceleration ◼ Temperature ◼ Force ◼ Mass ◼ Momentum ◼ Energy ◼ Time To describe a vector we need more information than to describe a scalar! Therefore vectors are more complex!  Important Notation ❑ To describe vectors we will use: ◼ The bold font: Vector A is A  ◼ Or an arrow above the vector: A ◼ In the pictures, we will always show vectors as arrows ◼ Arrows point the direction ◼ To describe the magnitude of a vector we  will use absolute value sign: A or just A, ◼ Magnitude is always positive, the magnitude of a vector is equal to the length of a vector.  Properties of Vectors ► Equality of Two Vectors ▪ Two vectors are equal if they have the same magnitude and the same direction ► Movement of vectors in a diagram ▪ Any vector can be moved parallel to itself without being affected ❑ Negative Vectors ◼ Two vectors are negative if they have the same magnitude but are 180° apart (opposite directions)  ( ) A = −B; A + − A = 0 A  B  Adding Vectors ► When adding vectors, their directions must be taken into account ► Units must be the same ► Geometric Methods ▪ Use scale drawings ► Algebraic Methods ▪ More convenient  Adding Vectors Geometrically (Triangle Method)  ► Draw the first vector A with the appropriate length and in the   direction specified, with respect to a A+ B  coordinate system  B ► Draw the next vector B with the appropriate length and in the direction specified, with respect to a  coordinate system A  whose origin is the end of vector A and parallel  to the coordinate system used for A : “tip- to-tail”. ► The resultant is drawn from the origin   of A to the end of the last vector B  Adding Vectors Graphically ► When you have many vectors, just keep   A+ B repeating the process until all are included    A+ B+C ► The resultant is still drawn from the origin   A+ B of the first vector to the end of the last vector  Adding Vectors Geometrically (Polygon Method)    ► Draw the first vector A with A+ B  the appropriate length and in B the direction specified, with respect to a coordinate system  ► Draw the next vector B with the appropriate length and in the direction specified, with respect to the same coordinate  system A ► Draw a parallelogram ► The resultant is drawn as a diagonal from the origin     A+ B = B+ A  Vector Subtraction  ► Special case of vector B addition ▪ Add the negative of the subtracted vector  A ( ) A − B = A + −B ► Continue with standard   vector addition procedure A−B  −B  Describing Vectors Algebraically Vectors: Described by the number, units and direction! Vectors: Can be described by their magnitude and direction. For example: Your displacement is 1.5 m at an angle of 250. Can be described by components? For example: your displacement is 1.36 m in the positive x direction and 0.634 m in the positive y direction.  Components of a Vector ► A component is a part ► It is useful to use rectangular components These are the projections of the vector along the x- a cos(90 −  ) −  and y-axes = a sin  a cos  Components of a Vector ► The x-component of a vector is the projection along the x-axis Ax cos  = Ax = A cos  A ► The y-component of a vector is the projection along the y-axis Ay sin  = Ay = A sin  A  ► Then, A = Ax + Ay  Components of a Vector ► The previous equations are valid only if θ is measured with respect to the x-axis ► The components can be positive or negative and will have the same units as the original vector θ=0, Ax=A>0, Ay=0 Ax < 0 Ax > 0 θ=45°, Ax=A cos 45°>0, Ay=A sin 45°>0 Ay > 0 Ay > 0 θ=90°, Ax=0, Ay=A>0 θ θ=135°, Ax=A cos 135°0 θ=180°, Ax=−A 0 θ=225°, Ax=A cos 225°