Physics for Scientists and Engineers I PHY 2048H Dr Beatriz Rold n Cuenya University of Central Florida Physics Department Orlando FL Chapter 1 Introduction I General II International System of Units III Conversion of units IV Dimensional Analysis V Problem Solving Strategies I 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 Relativity 3 Thermodynamics 4 Electromagnetism PHY2049 5 Optics PHY2049 6 Quantum Mechanics II International System of Units QUANTITY UNIT NAME POWER PREFIX ABBREVIATION 1015 peta P 1012 tera T 109 giga G 106 mega M UNIT SYMBOL Length meter m Time second s Mass kilogram kg 103 kilo k Speed m s 102 hecto h Acceleration m s2 101 deka da 10 1 deci D 10 2 centi c 10 3 milli m 10 6 micro 10 9 nano n 10 12 pico p 10 15 femto f Force Newton N Pressure Pascal Pa N m2 Energy Joule J Nm Power Watt W J s Temperature Kelvin K III Conversion of units Chain link conversion method The original data are multiplied successively by conversion factors written as unity Units can be treated like algebraic quantities that can cancel each other out Example 316 feet h m s feet 1 h 1 m 0 027 m s 316 h 3600s 3 28 feet IV Dimensional Analysis Dimension of a quantity indicates the type of quantity it is length L mass M time T Dimensional consistency both sides of the equation must have the same dimensions Example x x0 v0t at2 2 L L 2 L L T 2 T L L L T T 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 entire calculation Check if the values obtained are reasonable order of magnitude and units MECHANICS Kinematics Chapter 2 Motion along a straight line I Position and displacement II Velocity III Acceleration IV Motion in one dimension with constant acceleration V Free fall Particle point like object that has a mass but infinitesimal size I Position and displacement Position 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 Position Time graph shows the motion of the particle car The smooth curve is a guess as to what happened between the data points I Position and displacement Change from position x1 to x2 during a time interval Displacement x x2 x1 2 1 Vector quantity Magnitude absolute value and direction sign Coordinate position Displacement x x x x Coordinate system x1 x2 x2 x1 t x 0 t x 0 Only the initial and final coordinates influence the displacement many different motions between x1and x2 give the same displacement Distance length of a path followed by a particle Scalar quantity Displacement Distance Example round trip house work house distance traveled 10 km displacement 0 Review 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 II Velocity Average velocity Ratio of the displacement x that occurs during a particular time interval t to that interval v avg x x 2 x 1 t t 2 t1 2 2 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 velocity during that time interval Motion along x axis Average speed Total distance covered in a time interval Savg Total distance t 2 3 Savg magnitude Vavg Savg always 0 Scalar quantity Same units as velocity Example A person drives 4 mi at 30 mi h and 4 mi and 50 mi h Is the average speed 40 mi h 40 mi h t1 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 h Instantaneous velocity How fast a particle is moving at a given instant x dx t 0 t dt vx lim 2 4 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 x t The instantaneous velocity is the slope of the line tangent to the x vs t curve at a given instant of time green line t Instantaneous velocity Position Slope of the particle s position time curve at a given instant of time V is tangent to x t when t 0 When 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 quantity Average velocity or average acceleration always refers to an specific time interval Instantaneous velocity acceleration refers to an specific instant of time Time III Acceleration Average acceleration Ratio of a change in velocity v to the time interval t in which the change occurs aavg v2 v1 v t 2 t1 t 2 5 Vector quantity V t Dimensions L T 2 Units m s2 The average acceleration in a v t plot is the slope of a straight line connecting points corresponding to two different times t t Instantaneous acceleration Limit of the average acceleration as t approaches zero Vector quantity v dv d 2 x 2 a lim t 0 t dt dt 2 6 The instantaneous acceleration is the slope of the tangent line v t plot at a particular time green line in B Average acceleration blue line When an object s velocity and acceleration are in the same direction same sign the object is speeding up When an object s …