Physics for Scientists and Engineers IDr. Beatriz Roldán CuenyaUniversity of Central Florida, Physics Department, Orlando, FLPHY 2048HChapter 1 - IntroductionI. GeneralII. International System of UnitsIII. Conversion of unitsIV. Dimensional AnalysisV. Problem Solving StrategiesI. Objectives of Physics- Find the limited number of fundamental laws that govern natural phenomena.- 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 UnitsQUANTITY UNIT NAME UNIT SYMBOLLength meter mTime second sMass kilogram kgSpeed m/sAcceleration m/s2Force Newton NPressure Pascal Pa = N/m2Energy Joule J = NmPower Watt W = J/sTemperature Kelvin KPOWER PREFIX ABBREVIATION1015peta P1012tera T109giga G106mega M103kilo k102hecto h101deka da 10-1deci D10-2centi c10-3milli m10-6micro μ10-9nano n10-12pico p10-15femto fExample: 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 algebraicquantities 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.V. 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 entirecalculation.• Check if the values obtained are reasonable  order of magnitude andunits.Chapter 2 - Motion along a straight lineI. Position and displacementII. VelocityIII. AccelerationIV. Motion in one dimension with constant accelerationV. Free fallMECHANICS  KinematicsParticle: point-like object that has a mass but infinitesimal size.I. Position and displacementPosition: Defined in terms of a frame of reference: x or y axis in 1D.- The object’s position is its location with respect to the frame of reference.The smooth curve is a guess as to what happened between the data points.Position-Time graph: shows the motion of the particle (car).I. Position and displacementDisplacement: Change from position x1to x2  Δx = x2-x1(2.1)during a time interval. - Vector quantity: Magnitude (absolute value) and direction (sign).- Coordinate (position) ≠ Displacement  x ≠∆xtx∆x = 0 x1=x2Only the initial and final coordinates influence the displacement  many different motions between x1and x2 give the same displacement.tx∆x >0x1x2Coordinate systemDistance: length of a path followed by a particle.Displacement ≠ DistanceExample: round trip house-work-house  distance traveled = 10 kmdisplacement = 0- Scalar quantity- Vector quantities need both magnitude (size or numerical value) and direction to completely describe them.- We will use + and – signs to indicate vector directions in 1D motion.- Scalar quantities are completely described by magnitude only.Review:II. Velocity)2.2(ttxxΔtΔxv1212avgAverage velocity: Ratio of the displacement ∆x that occurs during a particular time interval ∆t to that interval.Motion along x-axis-Vector quantity  indicates not just how fast an object is moving but also in which direction it is moving.-SI Units: m/s- Dimensions: Length/Time [L]/[T]- The slope of a straight line connecting 2 points on an x-versus-t plot is equal to the average velocityduring that time interval.Average speed: Total distance covered in a time interval.)3.2(ΔtdistanceTotalSavgExample: A person drives 4 mi at 30 mi/h and 4 mi and 50 mi/h  Is theaverage speed >,<,= 40 mi/h ?<40 mi/ht1= 4 mi/(30 mi/h)=0.13 h ; t2= 4 mi/(50 mi/h)=0.08 h  ttot= 0.213 h  Savg= 8 mi/0.213h = 37.5mi/hSavg≠ magnitude VavgSavgalways >0Scalar quantitySame units as velocityInstantaneous velocity: How fast a particle is moving at a given instant.)4.2(lim0dtdxtxvtx- Vector quantity- The limit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zero.- The instantaneous velocity indicates what is happening at every point of time.- Can be positive, negative, or zero.- The instantaneous velocity is the slope of the line tangent to the x vs. t curve at a given instant of time (green line).x(t)tWhen the velocity is constant, the average velocity over any time interval is equal to the instantaneous velocity at any time.Instantaneous speed: Magnitude of the instantaneous velocity. Example: car speedometer.- Scalar quantityAverage velocity (or average acceleration) always refers to an specifictime interval.Instantaneous velocity (acceleration) refers to an specific instant of time.Slope of the particle’s position-time curve at a given instant of time. V is tangent to x(t) when ∆t0Instantaneous velocity:TimePositionIII. AccelerationVAverage acceleration:Ratio of a change in velocity ∆v to the time interval∆t in which the change occurs.- Vector quantity- Dimensions [L]/[T]2, Units: m/s2- The average acceleration in a “v-t” plot is the slopeof a straight line connecting points corresponding totwo different