Lecture 1 BAS 021 Physics Lecture Notes PDF

Physics1 BAS 021 Dr. Mohamed Sobhy [email protected] Office : 430 Text book: Serway, Jewett – Physics for Scientists and Engineers with Modern Physics 9th edition  Course Content:  Properties of Materials * Measurements – units –Dimentional equations-...

Physics1 BAS 021 Dr. Mohamed Sobhy [email protected] Office : 430 Text book: Serway, Jewett – Physics for Scientists and Engineers with Modern Physics 9th edition  Course Content:  Properties of Materials * Measurements – units –Dimentional equations- Dimensional Analysis * Elasticity –Stress- Strain- Elastic properties of solids * Energy – Kinetic energy –Potential energy – Work – Hook’s law * Oscillatory motion – Simple harmonic motion – Simple Pendulum  Electricity  Physics and Measurements Physics Fundamental Science  Concerned with the fundamental principles of the Universe  Foundation of other physical sciences  Has simplicity of fundamental concepts Introduction Physics, cont. Divided into six major areas:  Classical Mechanics  Relativity  Thermodynamics  Electromagnetism  Optics  Quantum Mechanics Introduction Classical Physics Mechanics and electromagnetism are basic to all other branches of classical and modern physics. Classical physics  Developed before 1900  First part of text deals with Classical Mechanics  Also called Newtonian Mechanics or Mechanics Modern physics  From about 1900 to the present Introduction Objectives of Physics To find the limited number of fundamental laws that govern natural phenomena To use these laws to develop theories that can predict the results of future experiments Express the laws in the language of mathematics  Mathematics provides the bridge between theory and experiment. Introduction Classical Physics Overview Classicalphysics includes principles in many branches developed before 1900. Mechanics  Major developments by Newton, and continuing through the 18th century Thermodynamics, optics and electromagnetism  Developed in the latter part of the 19th century  Apparatus for controlled experiments became available Introduction Modern Physics Began near the end of the 19th century Phenomena that could not be explained by classical physics Includes theories of relativity and quantum mechanics Introduction Special Relativity Correctly describes motion of objects moving near the speed of light Modifies the traditional concepts of space, time, and energy Shows the speed of light is the upper limit for the speed of an object Shows mass and energy are related Introduction Quantum Mechanics Formulated to describe physical phenomena at the atomic level Led to the development of many practical devices Introduction Measurements Used to describe natural phenomena Each measurement is associated with a physical quantity Need defined standards Characteristics of standards for measurements  Readily accessible  Possess some property that can be measured reliably  Must yield the same results when used by anyone anywhere  Cannot change with time Section 1.1 Standards of Fundamental Quantities 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 text Section 1.1 Fundamental Quantities and Their Units Quantity SI Unit Length meter Mass kilogram Time second Temperature Kelvin Electric Current Ampere Luminous Intensity Candela Amount of Substance mole Section 1.1 Quantities Used in Mechanics In mechanics, three fundamental quantities are used:  Length  Mass  Time Allother quantities in mechanics can be expressed in terms of the three fundamental quantities. Section 1.1 Length Length is the distance between two points in space. Units  SI – meter, m Defined in terms of a meter – the distance traveled by light in a vacuum during a given time Section 1.1 Mass Units  SI – kilogram, kg Defined in terms of a kilogram, based on a specific cylinder kept at the International Bureau of Standards See Table 1.2 for masses of various objects. Section 1.1 Standard Kilogram Section 1.1 Time Units  seconds, s Defined in terms of the oscillation of radiation from a cesium atom See Table 1.3 for some approximate time intervals. Section 1.1 US Customary System Still used in the US, but text will use SI Quantity Unit Length foot Mass slug Time second Section 1.1 Prefixes Prefixes correspond to powers of 10. Each prefix has a specific name. Each prefix has a specific abbreviation. The prefixes can be used with any basic units. They are multipliers of the basic unit. Examples:  1 mm = 10-3 m  1 mg = 10-3 g Section 1.1 Prefixes, cont. Section 1.1 Fundamental and Derived Units Derived quantities can be expressed as a mathematical combination of fundamental quantities. Examples:  Area  A product of two lengths  Speed  A ratio of a length to a time interval  Density  A ratio of mass to volume Section 1.1 Basic Quantities and Their Dimension Dimension has a specific meaning – it denotes the physical nature of a quantity. Dimensions are often denoted with square brackets.  Length [L]  Mass [M]  Time [T] Section 1.3 Dimensions and Units Each dimension can have many actual units. Table 1.5 for the dimensions and units of some derived quantities Section 1.3 Dimensional Analysis Technique to check the correctness of an equation or to assist in deriving an equation Dimensions (length, mass, time, combinations) can be treated as algebraic quantities.  Add, subtract, multiply, divide Both sides of equation must have the same dimensions. Any relationship can be correct only if the dimensions on both sides of the equation are the same. Cannot give numerical factors: this is its limitation Section 1.3 Dimensional Analysis, example Given the equation: x = ½ at 2 Check dimensions on each side: L L  2  T2  L T The T2’s cancel, leaving L for the dimensions of each side.  The equation is dimensionally correct.  There are no dimensions for the constant. Section 1.3  Show that the following equation is dimensionally correct: 𝑉=𝑉𝑜+𝑎𝑡 where (𝑉𝑜) is velocity and (𝑎) is acceleration  Solution: 𝐷𝑖𝑚[𝐿𝐻𝑆]=[𝐿/𝑇] 𝐷𝑖𝑚[𝑅𝐻𝑆]=[𝐿/𝑇]+[𝐿 / 𝑇2][𝑇]=[𝐿/𝑇]+[𝐿/𝑇] 𝐷𝑖𝑚[𝐿𝐻𝑆]=𝐷𝑖𝑚[𝑅𝐻𝑆]⟹ ∴𝑇ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑖𝑠 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑎𝑙𝑙𝑦 𝑐𝑜𝑟𝑟𝑒𝑐𝑡 (𝑖𝑔𝑛𝑜𝑟𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡𝑠) Newton's second law states that acceleration is proportional to the force acting on an object and is inversely proportional to the object mass. What are the dimensions of force? Solution: 𝑇ℎ𝑒 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑎⟶[𝑎]=[𝐿]/[𝑇]2, 𝑇ℎ𝑒 𝑓𝑜𝑟𝑐𝑒 𝐹⟶[𝐹]?? 𝑇ℎ𝑒 𝑚𝑎𝑠𝑠 𝑚⟶[𝑚]=[𝑀] 𝑎∝𝐹𝑚−1⟹ 𝑎= 𝑘𝐹/𝑚 ∴ 𝐹=𝑚𝑎/𝑘⟹[𝐹]=[𝑚][𝑎]=[𝑀][𝐿][𝑇−2] Dimensional Analysis to Determine a Power Law Determine powers in a proportionality  Example: find the exponents in the expression x  amt n  You must have lengths on both sides.  Acceleration has dimensions of L/T2  Time has dimensions of T.  Analysis gives x  at 2 Section 1.3