NUN Physics 101 Lecture Notes - General Physics I, Lecture 1 PDF

PHY 101: General Physics I Lecture 1 NUN Physics Department  Introduction  PHY101 – Course Information  Brief Introduction to Physics  Chapter 1 – Measurements Measuring things Three basic units: Length, Mass, Time SI units U...

PHY 101: General Physics I Lecture 1 NUN Physics Department  Introduction  PHY101 – Course Information  Brief Introduction to Physics  Chapter 1 – Measurements Measuring things Three basic units: Length, Mass, Time SI units Unit conversion Dimension  Chapter 2 – Vectors Vectors and scalars Describe vectors geometrically Components of vectors Unit vectors Vectors addition and subtraction January 22-25, 2013 Course Information: Instuctor  Instructor: Dr Sharafadeen ADENIJI  Office: Room B111 Block (Volta)  Office hours: 2-4 pm (Monday)  Telephone: 08055667505  Email: [email protected] January 22-25, 2013  Course Information: Materials  Lecture Slides and University Physics Textbook by Sears and Zemansky (Pearson Education) have been uploaded on team.  Lab Material: “Physics Laboratory Manual ” January 22-25, 2013 Course Information: Grading  Final Exam (60%)  Midterm Exam (40%)  Final Letter Grade A 70-100 B 60-69 C 50-59 D 45-49 E 40-44 F 0-39 January 22-25, 2013  Physics and Mechanics  Physics deals with the nature and properties of matter and energy. Common language is mathematics. Physics is based on experimental observations and quantitative measurements.  The study of physics can be divided into six main areas: Classical mechanics Electromagnetism Optics – Physics III Relativity Thermodynamics Quantum mechanics  Classical mechanics deals with the motion and equilibrium of material bodies and the action of forces. January 22-25, 2013  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!) January 22-25, 2013  Lesson 1 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 January 22-25, 2013  Type of Quantities  Many things can be measured: distance, speed, energy, time, force ……  These are related to one another: speed = distance / time  List the three basic quantities (DIMENSIONS): LENGTH MASS TIME  Define other units in terms of these. January 22-25, 2013 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 TIME: Second January 22-25, 2013 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 January 22-25, 2013  SI Length Unit: Meter  French Revolution Definition, 1792  1 Meter = XY/10,000,000  1 Meter = about 3.28 ft  1 km = 1000 m, 1 cm = 1/100 m, 1 mm = 1/1000 m  Current Definition of 1 Meter: the distance traveled by light in vacuum during a time of 1/299,792,458 second. January 22-25, 2013  SI Time Unit: Second  1 Second is defined in terms of an “atomic clock”– time taken for 9,192,631,770 oscillations of the light emitted by a 133Cs atom.  Defining units precisely is a science (important, for example, for GPS): This clock will neither gain nor lose a second in 20 million years. January 22-25, 2013  SI Mass Unit: Kilogram  1 Kilogram – the mass of a specific platinum-iridium alloy kept at International Bureau of Weights and Measures near Paris. (Seeking more accurate measure: http://www.economist.com/news/leaders/21569417-k ilogram-it-seems-no-longer-kilogram-paris-worth-mas s )  Copies are kept in many other countries.  Yao Ming is 141 kg, equivalent to weight of 141 pieces of the alloy cylinder. January 22-25, 2013 Length, Mass, Time January 22-25, 2013  Prefixes for SI Units  3,000 m = 3 x 1,000 m 10x Symb = 3 x 103 m = 3 km Prefix ol  1,000,000,000 = 109 = x=1 exa E 1G 8  1,000,000 = 106 = 1M 15 peta P  1,000 = 103 = 1k 12 tera T 9 giga G  141 kg = ? g  6 M 1 GB = ? Byte = ? MB If you are rusty with scientific notation, mega see appendix B.1 of the text 3 kilo k January 22-25, 2013 h 2 hecto  Prefixes for SI Units 10x Symb  0.003 s = 3 x 0.001 s Prefix ol = 3 x 10-3 s = 3 ms  0.01 = 10-2 = centi x=- deci d 1  0.001 = 10-3 = milli -2  0.000 001 = 10-6 = micro centi c  0.000 000 001 = 10-9 = -3 milli m nano -6 µ  0.000 000 000 001 = 10-12 micro = pico = p -9 nano n  1 nm = ? m = ? cm -12  3 cm = ? m = ? mm pico p f January 22-25, 2013 -15  Derived Quantities and Units  Multiply and divide units just like numbers  Derived quantities: area, speed, volume, density …… Area = Length x Length SI unit for area = m2 Volume = Length x Length x Length SI unit for volume = m3 Speed = Length / time SI unit for speed = m/s Density = Mass / Volume SI unit for density = kg/m3  In 2008 Olympic Game, Usain Bolt sets world record 100 m 100 m at 9.69speed  s in Men’s  m Final. 100 10.32 is  What m/shis average speed ? 9.69 s 9.69 s January 22-25, 2013  Other Unit System  U.S. customary system: foot, slug, second  Cgs system: cm, gram, second  We will use SI units in this course, but it is useful to know conversions between systems. 1 mile = 1609 m = 1.609 km 1 ft = 0.3048 m = 30.48 cm 1 m = 39.37 in. = 3.281 ft 1 in. = 0.0254 m = 2.54 cm 1 lb = 0.465 kg 1 oz = 28.35 g 1 slug = 14.59 kg 1 day = 24 hours = 24 * 60 minutes = 24 * 60 * 60 seconds January 22-25, 2013  Unit Conversion  Example: Is he speeding ? On the garden state parkway of New Jersey, a car is traveling at a speed of 38.0 m/s. Is the driver exceeding the speed limit? Since the speed limit is in miles/hour (mph), we need to convert the units of m/s to mph. Take it in two steps. Step 1: Convert m to miles. Since 1 mile = 1609 m, we have two possible conversion factors, 1 mile/1609 m = 6.215x104 mile/m, or 1609 m/1 mile = 1609 m/mile. What are the units of these conversion factors? Since we want to convert m to mile, we want the m units to cancel => multiply by first m   1mile  38.0 mile 38.0 factor:     2.36 10 2 mile/s  s   1609 m  1609 s Step 2: Convert s to hours. Since 1 hr = 3600 s, again we could have 1 hr/3600 s = 2.778x104 hr/s, or 3600 s/hr. Since we want to convert s to hr, we want the s units to cancel =>  2 mile 3600 s 38.0 m/s 2.36 10  85.0 mile/hr = 85.0 mph s hr  Dimensions, Units and Equations  Quantities have dimensions: Length – L, Mass – M, and Time - T  Quantities have units: Length – m, Mass – kg, Time – s  To refer to the dimension of a quantity, use square brackets, e.g. [F] means dimensions of force. Quantity Area Volume Speed Acceleration Dimension [A] = L2 [V] = L3 [v] = L/T [a] = L/T2 SI Units m2 m3 m/s m/s2 January 22-25, 2013  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] ? January 22-25, 2013  Summary  The three fundamental physical dimensions of mechanics are length, mass and time, which in the SI system have the units meter (m), kilogram (kg), and second (s), respectively  The method of dimensional analysis is very powerful in solving physics problems.  Units in physics equations must always be consistent. Converting units is a matter of multiplying the given quantity by a fraction, with one unit in the numerator and its equivalent in the other units in the denominator, arranged so the unwanted units in the given quantity are cancelled out in favor of the desired units. January 22-25, 2013  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) January 22-25, 2013  Vector and Scalar Quantities  Vectors  Scalars: Displacement Distance Velocity (magnitude Speed (magnitude of velocity) and direction!) Temperature Acceleration Mass Force Energy Momentum Time To describe a vector we need more information than to describe a scalar! Therefore vectors are more complex! January 22-25, 2013  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 Asign: or just A, Magnitude is always positive, the magnitude of a vector is equal to the length of a vector. January 22-25, 2013  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 itselfVectors  Negative without being affected Two vectors are negative if they have the same magnitude but are 180° apart (opposite directions)   A   A   B; A   A  0  B January 22-25, 2013  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 January 22-25, 2013  Adding Vectors Geometrically (Triangle  Method)  Draw the first vectorA with the appropriate length and in the direction specified, with   respect to a coordinate  system AB   Draw the next vectorB with B the appropriate length and in the direction specified, with respect to a coordinate system whose origin is the end of vector  and parallel toAthe  coordinateA system used for : A “tip-to-tail”.   The resultant is drawn from the A origin of to the end of the last vector B January 22-25, 2013  Adding Vectors Graphically  When you have many vectors, just   keep repeating the AB process until all are    included ABC  The resultant is still   drawn from the AB origin of the first vector to the end of the last vector January 22-25, 2013  Adding Vectors Geometrically (Polygon  Method)    Draw the first vector A AB with the appropriate length and in the direction specified, with respect  to a coordinate system B   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   is drawn  The resultant  as a A  Bfrom diagonal  B the  Aorigin January 22-25, 2013  Vector Subtraction  Special case of vector addition  Add the negative of B the subtracted vector    A  B A   B   A  Continue with standard    B vector addition A B procedure January 22-25, 2013 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. January 22-25, 2013  Components of a Vector  A component is a part  It is useful to use rectangular components These are the projections of the a cos(90   )  vector along the x- a sin   and y-axes a cos  January 22-25, 2013  Components of a Vector  The x-component of a vector is the projection along theAx-axis cos   x Ax  A cos  A  The y-component of a vector is Athe y projection sin   Ay  A sin  along theAy-axis      A  AxThen,  Ay A  Ax  Ay January 22-25, 2013  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 θ=45°, Ax=A cos 45°>0, Ay=A sin 45°>0 Ax < 0 Ax > 0 θ=90°, Ax=0, Ay=A>0 Ay > 0 Ay > θ 0 θ=135°, Ax=A cos 135°0 Ax < 0 Ax > 0 θ=180°, Ax=A