1Physics for Scientists and Engineers IDr. Beatriz Roldán CuenyaUniversity of Central Florida, Physics Department, Orlando, FLPHY 2048, Section 4Chapter 0 - IntroductionI. GeneralII. International System of UnitsIII. Conversion of unitsIV. Dimensional AnalysisV. Problem Solving Strategies2I. Objectives of Physics- Find the limited number of fundamental laws that govern naturalphenomena.- Use these laws to develop theories that can predict the results of future experiments.-Express the laws in the language of mathematics.- Physics is divided into six major areas:1. Classical Mechanics (PHY2048)2. Relativity3. Thermodynamics4. Electromagnetism (PHY2049)5. Optics (PHY2049)6. Quantum MechanicsII. International System of UnitsKKelvinTemperatureW = J/sWattPowerJ = NmJouleEnergyPa = N/m2PascalPressureNNewtonForcem/s2Accelerationm/sSpeedkgkilogramMassssecondTimemmeterLengthUNIT SYMBOLUNIT NAMEQUANTITYffemto10-15ppico10-12nnano10-9µmicro10-6mmilli10-3ccenti10-2Ddeci10-1dadeka101hhecto102kkilo103Mmega106Ggiga109Ttera1012Ppeta1015ABBREVIATIONPREFIXPOWER3Example: 316 feet/h  m/sIII. Conversion of unitsChain-link conversion method: The original data are multiplied successivelyby conversion factors written as unity. Units can be treated like algebraic quantities that can cancel each other out.IV. Dimensional AnalysisDimension of a quantity: indicates the type of quantity it is; length [L],mass [M], time [T]Example: x=x0+v0t+at2/2smfeetmshhfeet/027.028.3136001316 =⋅⋅[ ] [ ][][ ][ ][][ ][][ ] [ ] [ ]LLLTTLTTLLL ++=++=22Dimensional consistency: both sides of the equation must have the samedimensions.Note: There are no dimensions for the constant (1/2)Significant figure  one that is reliably known.Zeros may or may not be significant:- Those used to position the decimal point are not significant.- To remove ambiguity, use scientific notation.Ex:2.56 m/s has 3 significant figures, 2 decimal places.0.000256 m/s has 3 significant figures and 6 decimal places. 10.0 m has 3 significant figures.1500 m is ambiguous  1.5 x 103 (2 figures), 1.50 x 103(3 fig.),1.500 x 103(4 figs.)Order of magnitude  the power of 10 that applies.4V. Problem solving tactics• Explain the problem with your own words.• Make a good picture describing the problem.• Write down the given data with their units. Convert all data into S.I. system.• Identify the unknowns.• Find the connections between the unknowns and the data.• Write the physical equations that can be applied to the problem.• Solve those equations. • Always include units for every quantity. Carry the units through the entire calculation.• Check if the values obtained are reasonable  order of magnitude and units.Chapter 1 - VectorsI. DefinitionII. Arithmetic operations involving vectorsA) Addition and subtraction - Graphical method- Analytical method  Vector componentsB) Multiplication5Review of angle reference systemOrigin of angle reference systemθ10º<θ1<90º90º<θ2<180ºθ2180º<θ3<270ºθ3θ4270º<θ4<360º90º180º270º0ºΘ4=300º=-60ºAngle originI. DefinitionVector quantity: quantity with a magnitude and a direction. It can be represented by a vector.Examples: displacement, velocity, acceleration.Same displacementDisplacement  does not describe the object’s path.Scalar quantity: quantity with magnitude, no direction.Examples: temperature, pressure6Rules:)1.3()( lawecommutativabba+=+)2.3()()()( laweassociativcbacba++=++II. Arithmetic operations involving vectors- Geometrical methodabbas+=Vector addition:bas+=Vector subtraction:)3.3()( babad−+=−=Vector component: projection of the vector on an axis.θθsin)4.3(cosaaaayx==xyyxaaaaa=+=θtan)5.3(22Vector magnitudeVector directionaofcomponentsScalar7Unit vector: Vector with magnitude 1.No dimensions, no units.axeszyxofdirectionpositiveinvectorsunitkji ,,ˆ,ˆ,ˆ→)6.3(ˆˆjaiaayx+=Vector component- Analytical method: adding vectors by components.Vector addition:)7.3(ˆ)(ˆ)( jbaibabaryyxx+++=+=Vectors & Physics:-The relationships among vectors do not depend on the location of the origin of the coordinate system or on the orientation of the axes.- The laws of physics are independent of the choice of coordinate system.φθθ+=+=+=')8.3(''2222yxyxaaaaaMultiplying vectors:- Vector by a scalar:- Vector by a vector:Scalar product = scalar quantityasf⋅=)9.3(coszzyyxxbababaabba ++==⋅φ(dot product)8)90(0cos0)0(1cos==←=⋅==←=⋅φφφφbaabbaRule:)10.3(abba⋅=⋅090cos1110cos11=⋅⋅=⋅=⋅=⋅=⋅=⋅=⋅=⋅⋅=⋅=⋅=⋅jkkjikkiijjikkjjiiMultiplying vectors:- Vector by a vectorVector product = vectorφsinˆ)(ˆ)(ˆ)(abckabbajbaabiabbacbayxyxxzxzzyzy=−+−−−==×(cross product)MagnitudeAngle between two vectors:baba⋅⋅=ϕcos)12.3()( baab×−=×Rule:)90(1sin)0(0sin0==←=×==←=×φφφφabbabaDirection  right hand rulebacontainingplanetolarperpendicuc,1) Place a and b tail to tail without altering their orientations.2) c will be along a line perpendicular to the plane that contains a and b where they meet.3) Sweep a into b through the smallest angle between them.Vector product9Right-handed coordinate systemxyzijkLeft-handed coordinate systemyxzijk00sin11 =⋅⋅=×=×=×kkjjiijkiikijkkjkijjikkjjii=×−=×=×−=×=×−=×=×=×=×)()()(010P1: If B is added to C = 3i + 4j, the result is a vector in the positive direction of the y axis, with a magnitude equal to that of C. What is the magnitude of B?ˆ ˆ2.319ˆˆ3ˆ5)ˆ4ˆ3(543ˆ)ˆ4ˆ3(22=+=→+−=→=++=+====++=+BjiBjjiBDCjDDjiBCBMethod 1Method 22.32sin22/2sin9.36)4/3(tan==→==→=θθθθDBDBDCBB/2θIsosceles triangleP2: A fire ant goes through three displacements along level ground: d1for 0.4m SW, d2 0.5m E, d3=0.6m at 60º North of East. Let the positive x direction be East and the positive y direction be North. (a) What are thex and y components of d1, d2and d3? (b) What are the x and the y components, the magnitude and the directionof the ant’s net displacement? (c)