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# Note for PH 101 at UA-General Physics I (3)

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This 26 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Alabama - Tuscaloosa taught by a professor in Fall. Since its upload, it has received 20 views.

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Date Created: 02/06/15

GIANCOLI Lecture PowerPoints Chapter 3 Physics Principles with Applications 6 edition Giancoli Chapter 3 Kinematics in Two Dimensions Vectors Units of Chapter 3 Vectors and Scalars Addition of Vectors Graphical Methods Subtraction of Vectors and Multiplication of a Vector by a Scalar Adding Vectors by Components Projectile Motion Solving Problems Involving Projectile Motion Projectile Motion ls Parabolic Relative Velocity 31 Vectors and Scalars A vector has magnitude as well as direction Some vector quantities displacement velocity force momentum Scale for velocity A scalar has only a magnitude 10111290 kmh Some scalar quantities mass time temperature Copyright 2005 Pearson Prentice Hall Inc 32 Addition of Vectors Graphical Methods For vectors in one x km dimenSIon Simple East addItIon and subtraction are all that is needed Resultant 14 km east You do need to be careful about the signs as the figure indicates Resultant 2 km east 6 km x km East 8km b Copyright 2005 Pearson Prentice Hall Inc 32 Addition of Vectors Graphical Methods If the motion is in two dimensions the situation is somewhat more complicated Here the actual travel paths are at right angles to one another we can find the displacement by y km using the Pythagorean Theorem North amp 6 DR xDi D West 32 Addition of Vectors Graphical Methods Adding the vectors in the opposite order gives the gt same result V1 72 v 71 West South Copyright 2005 Pearson Prentice Hall Inc 32 Addition of Vectors Graphical Methods Even if the vectors are not at right angles they can be added graphically by using the tailtotip method Copyright 2005 Pearson Prentice Hall inc 32 Addition of Vectors Graphical Methods The parallelogram method may also be used here again the vectors must be tailtotip a Tail totip b Parallelogram Copyright 2005 Pearson Prentice Hall Inc 33 Subtraction of Vectors and Multiplication of a Vector by a Scalar In order to subtract vectors we 7 7 define the negative of a vector which has the same magnitude but points ggggggg in the opposite direction Then we add the negative vector V V 7 V a c gt1 2 4 1 Vz Vl v2 Copyright 2005 Pearson Prentice Hall Inc 33 Subtraction of Vectors and Multiplication of a Vector by a Scalar A vector V can be multiplied by a scalar c the result is a vector cV that has the same direction but a magnitude cV If c is negative the resultant vector points in the opposite direction Copyright 2005 Pearson Prentice Hall Inc 34 Adding Vectors by Components Any vector can be expressed as the sum of two other vectors which are called its components Usually the other vectors are chosen so that they are perpendicular to each other I I I I I I x B East 0 Copyright 2005 Pearson Prentice Hall Inc 34 Adding Vectors by Components V 39 3 sm 9 7 If the components are COS 9 Z 5 perpendicular they can be found V using trigonometric functions V tan 9 y VX W Copyright 2005 Pearson Prentice Hall Inc 34 Adding Vectors by Components The components are effectively onedimensional so they can be added arithmetically y Copyright 2005 Pearson Prentice Hall Inc 34 Adding Vectors by Components Adding vectors Draw a diagram add the vectors graphically Choose X and y axes Resolve each vector into X and y components Calculate each component using sines and cosines Add the components in each direction QWPPNT To find the length and direction of the vector use 3E5 rjcg rt t cgmr projectile ES gm b t mm mg rm Mm mgr rgmr rg wriner 1mg mfl rremg 373 Ear hg gravity HE S path g 51 parabolau Copyright 2005 Pearson Prentice HaH Inc 35 Projectile Motion y m It can be understood by k l g analyzing the horizontal and vertical motions separately IgtVx I Projectile I V motion y gt I I l Vertical fall Copyright 2005 Pearson Prentice Hall Inc 3E5 Prejeettte Metteh The speed h the emetheetteh te eeheteht Eh the y ettteet eh the eh eet mewee with eeheteht acceleration Qt Tte phetegreph ehewe the he te that etert te felt at the eeme time Te ehe eat the rtght hee eh th t e speed h the X el reetteh Ht eeh e eeeh thet vett eet eeett ehe et the the hette ere tetehtteet et deht eet tthmee wh te the hertzehtet heettteh et the yettew hetl theteeeee ttheetty Copyright 2005 Pearson Prentice Hall Inc 35 Projectile Motion If an object is launched at an initial angle of 00 with the horizontal the analysis is similar except that the initial velocity has a vertical component Vy O at this point Copyright 2005 Pearson Prentice Hall Inc 36 Solving Problems Involving Projectile Motion Projectile motion is motion with constant acceleration in two dimensions where the acceleration is g and is down TABLE 3 2 Kinematic Equations for Projectile Motion y positive upward ax 0 ay g 980 msz Horizontal Motion V ertical MotionT ax 0 vx constant ay g constant vx vxo Eq211a vy vyo gt x x0 vxot Eq2 11b y yo vyot gt2 Eq2 11c vy v30 2gy yo T If y is taken positive downward the minus signs in front of g become signs Copyright 2005 Pearson Prentice Hall Inc 36 Solving Problems Involving Projectile Motion 1 Read the problem carefully and choose the objects you are going to analyze 2 Draw a diagram 3 Choose an origin and a coordinate system 4 Decide on the time interval this is the same in both directions and includes only the time the object is moving with constant acceleration g 5 Examine the X and y motions separately 36 Solving Problems Involving Projectile Motion 6 List known and unknown quantities Remember that VX never changes and that vy 0 at the highest point 7 Plan how you will proceed Use the appropriate equations you may have to combine some of them 397 mjmit m MQE m H113 Pambm rm QTCEQQB m dcamm gitmig tha pm m t g mam g parabolicg Wg waged m WWW yag a fumtmm f X Wham W W W f md that M hag mg wsz y Ax 8x2 Th g g mdaedthe equation fmquot a para m au 38 Relative Velocity We already considered relative speed in one dimension it is similar in two dimensions except that we must add and subtract velocities as vectors Each velocity is labeled first with the object and second with the reference frame in which it has this velocity Therefore vWS is the velocity of the water in the shore frame vBS is the velocity of the boat in the shore frame and vBW is the velocity of the boat in the water frame 38 Relative Velocity In this case the relationship between the three velocities is N River current sz VBS VBW sz 3396 Copyright 2005 Pearson Prentice Hall Inc Summary of Chapter 3 A quantity with magnitude and direction is a vector A quantity with magnitude but no direction is a scalar Vector addition can be done either graphically or using components The sum is called the resultant vector Projectile motion is the motion of an object near the Earth s surface under the influence of gravity

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