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# General Physics I w P 250

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This 30 page Class Notes was uploaded by Raymundo Legros on Tuesday October 20, 2015. The Class Notes belongs to P 250 at South Carolina State University taught by Staff in Fall. Since its upload, it has received 29 views. For similar materials see /class/225410/p-250-south-carolina-state-university in Physics 2 at South Carolina State University.

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Vectors 7 Unit 34A 7 Problem 31A 3759 A woman jogs from the front door of her house for 08 miles in a direction 400 south of east then jogs for an additional 12 miles in a direction due east a How far has she jogged b What is the straightiline distance from her front door to the end of her jog c What is the direction of the straightrline trip from her front door to where she stopped jogging 391 Because of the definition of equal vectors frame 323 the vectors A and E can be moved to make the new diagram shown where BZl In general the order of the terms is unimportant in vector addition As mathematicians would say vector addition is commutative Components of a Vector 3760 Vectors 7 Unit 34A 7 Problem 31A A woman jogs from the front door of her house for 08 miles in a direction 400 south of east then jogs for an additional 12 miles in a direction due east a How far has she jogged b What is the straightiline distance from her front door to the end of her jog c What is the direction of the straightrline trip from her front door to where she stopped jogging 392 We will return to equation 311 after discovering its meaning in the vector diagram If the magnitudes of the vectors i and S in the diagram below were known the Pythagorean theorem would allow us to calculate the magnitude of The vectors g and S are called components of the vector 539 Because vector g points downward and to the right y points downward and g points to the right Vector components are always perpendicular to each other with each component pointing along a coordinate axis the x and y axes in this case A vector can always be written as a sum of its components From the diagram write a vector equation relating to its components Vectors 7 Unit 34A 7 Problem 31A 3761 A woman jogs from the front door of her house for 08 miles in a direction 400 south of east then jogs for an additional 12 miles in a direction due east a How far has she jogged b What is the straightiline distance from her front door to the end of her jog c What is the direction of the straightrline trip from her front door to where she stopped jogging 393 Because of the definition for vector addition x w 313 The vector diagram can be used to determine the components i and First redraw the vector A in terms of its components This is called resolving a vector into its components Because vector B points in the xdirection it is already resolved B5B and By 0 By examining the vector diagram below write one equation relating i A and Br and another relating 539 y and Vectors 7 Unit 34A 7 Problem 32A 3763 Robert s friend Keisha lives in a large Victorian house 20 km 12 mi away From where Robert lives the direction of Keisha s house is 700 west of north Keisha decides to move to a smaller house which is 150 south of west from where Robert lives and 38 km 24 mi away a How far and in what direction did Keisha move b If Keisha and Robert both live in a city whose blocks are rectangular and form a grid how far must Robert actually drive to visit Keisha 395 Label the vectors in the diagram with the symbols Iii and g for the displacement vector the vector from Robert s t0 the large house and the vector from Robert s t0 the small house respectively Workbook for Introductory Mechanics Problemisolving Copyright 1996799 by Daniel M Smith Jr Sponsored by FIPSE US Department of Education 3764 Vectors 7 Unit 34A 7 Problem 32A Robert s friend Keisha lives in a large Victorian house 20 km 12 mi away From where Robert lives the direction of Keisha s house is 700 west of north Keisha decides to move to a smaller house which is 150 south of west from where Robert lives and 38 km 24 mi away a How far and in what direction did Keisha move b If Keisha and Robert both live in a city whose blocks are rectangular and form a grid how far must Robert actually drive to visit Keisha 396 397 Write a vector equation for the diagram in the previous frame Vectors 7 Unit 34A 7 Problem 32A 3765 Robert s friend Keisha lives in a large Victorian house 20 km 12 mi away From where Robert lives the direction of Keisha s house is 700 west of north Keisha decides to move to a smaller house which is 150 south of west from where Robert lives and 38 km 24 mi away a How far and in what direction did Keisha move b If Keisha and Robert both live in a city whose blocks are rectangular and form a grid how far must Robert actually drive to visit Keisha 398 Using the familiar headetoetail definition for vector addition we have D wim Did you remember to put arrows above your L D and S If not please correct your error Solve this equation for D just as you would solve an algebraic equation Write out your answer 399 By adding to both sides of the equation we get first E 61D then E 61 This is the important equation for solving part a of the problem it is analogous to equation 311 in frame 390 As before we will continue in a hard way using the vector diagram as a method of verifying the vector equations for the x and y components of 15 3766 Vectors 7 Unit 34A 7 Problem 32A Robert s friend Keisha lives in a large Victorian house 20 km 12 mi away From where Robert lives the direction of Keisha s house is 700 west of north Keisha decides to move to a smaller house which is 150 south of west from where Robert lives and 38 km 24 mi away a How far and in what direction did Keisha move b If Keisha and Robert both live in a city whose blocks are rectangular and form a grid how far must Robert actually drive to visit Keisha 3100 Draw the x and ycomponent vectors in the diagram above for all three vectors and give each component an appropriate label As a check be sure that the sum of the vector s components equals that vector 3101 In the diagram below every pair of components satisfies the headitoitail definition of vector addition If the magnitudes of 15 and Dy were known then the Pythagorean theorem could be used to find the magnitude of 15 Use the diagram to write equations for Dr and Q Watch your signs Vectors 7 Unit 34A 7 Problem 32A 3767 Robert s friend Keisha lives in a large Victorian house 20 km 12 mi away From where Robert lives the direction of Keisha s house is 700 west of north Keisha decides to move to a smaller house which is 150 south of west from where Robert lives and 38 km 24 mi away a How far and in what direction did Keisha move b If Keisha and Robert both live in a city whose blocks are rectangular and form a grid how far must Robert actually drive to visit Keisha 3102 If the dotidashed vector L is subtracted from the dot7 dashed vector i we are left with the dashed vector 15 D 3 L 319 Reversing the direction of the dotidashed vector L3 resulting in Ey then adding it to the dotidashed vector 3 gives the vector Dy written as D 3 320 When actually solving problems you will avoid the painstaking work just completed by resolving the vector equation into its components The recipe is simple First write the vector equation 318 D s E 318 then rewrite it twice for the component equations once with x subscripts and again with y subscripts Dx a Dy x O x 1 Lx z y 3768 Vectors 7 Unit 34A 7 Problem 32A Robert s friend Keisha lives in a large Victorian house 20 km 12 mi away From where Robert lives the direction of Keisha s house is 700 west of north Keisha decides to move to a smaller house which is 150 south of west from where Robert lives and 38 km 24 mi away a How far and in what direction did Keisha move b If Keisha and Robert both live in a city whose blocks are rectangular and form a grid how far must Robert actually drive to visit Keisha 3103 Write the vector equations for the three vector diagrams from frame 331 reproduced below whose vectors do not conform to the problem data as given a b C Vectors 7 Unit 34A 7 Problem 32A 3769 Robert s friend Keisha lives in a large Victorian house 20 km 12 mi away From where Robert lives the direction of Keisha s house is 700 west of north Keisha decides to move to a smaller house which is 150 south of west from where Robert lives and 38 km 24 mi away a How far and in what direction did Keisha move b If Keisha and Robert both live in a city whose blocks are rectangular and form a grid how far must Robert actually drive to visit Keisha 3104 By using the headitoitail definition for vector addition we get the following equations a 5GE0 0r GE 0 0r E G0 etc Order of terms is unimportant because vector addition is commutative as discussed in frame 391 b H1 F c1115j Did you remember to place arrows above all of your vector symbols If not please correct this error 3105 Solve each vector equation in the previous frame for the unknown displacement vector then write the two component equations a b C 3770 Vectors 7 Unit 34A 7 Problem 32A Robert s friend Keisha lives in a large Victorian house 20 km 12 mi away From where Robert lives the direction of Keisha s house is 700 west of north Keisha decides to move to a smaller house which is 150 south of west from where Robert lives and 38 km 24 mi away a How far and in what direction did Keisha move b If Keisha and Robert both live in a city whose blocks are rectangular and form a grid how far must Robert actually drive to visit Keisha 3106 Rules for addition and subtraction in vector algebra are like those for ordinary algebra whatever is added to one side of the equation must be added to the other side and whatever is subtracted from one side of the equation must be subtracted from the other side a C E 6 Components CI Ex Cx b R 1 3 no change Components F H 11 y y y c A J 15 Components A j fx y y y Any one of these three sets of equations could be used to solve for the displacement vector but the equations in frame 3102 will be used instead Vectors 7 Unit 34A 7 Problem 33A 3771 Two friends Keith and Jamal who have gone hiking in the woods have become separated Keith has walked for an unknown distance before realizing that his friend is not near Keith then walks 05 km due north to look for Jamal but sends up a are signal when he cannot find him then waits Meanwhile Jamal has walked 13 km at 350 south of west but after seeing the are he walks 16 km 150 east of north to meet Keith How far and in what direction did Keith wander when he and Jamal first became separated 3107 Label the two legs of Keith s hike K1 and K2 and the two legs of Jamal s hike J1 and J2 Workbook for Introductory Mechanics Problemisolving Copyright 1996799 by Daniel M Smith Jr Sponsored by FIPSE US Department of Education 3772 Vectors 7 Unit 34A 7 Problem 33A Two friends Keith and Jamal who have gone hiking in the woods have become separated Keith has walked for an unknown distance before realizing that his friend is not near Keith then walks 05 km due north to look for Jamal but sends up a are signal when he cannot find him then waits Meanwhile Jamal has walked 13 km at 350 south of west but after seeing the are he walks 16 km 150 east of north to meet Keith How far and in what direction did Keith wander when he and Jamal first became separated 3108 3109 Write a vector equation for the diagram in the previous frame Workbook for Introductory Mechanics ProblemSolving Daniel M Smith Jr South Carolina State University To the Student The Workbook should help you to learn how to think about physics problems before you try using equations The format is designed to carefully build each level of your problemesolving ability before moving you to the next level So instead of working one problem at a time you will work several problems at once Here is advice on how to use this Workbook After printing place these materials in a binder before beginning work If possible use doubleesided or duplex printing EV Attempt to answer every question by drawing or writing before looking at the answer OJ Warning Simply reading the questions the answers and the discussion without doing the work is a complete waste of time Copyright 1996799 by Daniel M Smith Jr All rights reserved Sponsored by FIPSE US Department of Education Acknowledgments Students have provided invaluable assistance in word processing and in creating graphics for this workbook Thanks go to Andrick Anderson Kyle Herbert Tyesia Pompey Tarryn Reeves and Keilah Spann Professors Theodore Hodapp and Dave Maloney are thanked for their criticism and suggestions Clip art is taken from the Art Explosion collection published by the Nova Development Corporation Calabasas CA I have had the pleasure of teaching and tutoring at South Carolina State University and Northeastern University and in the process I have learned much from students about their difficulties in solving physics problems Those who wish to further my enlightenment may send comments to dsmithscsuedu Copyright 1996799 by Daniel M Smith Jr All rights reserved Students using College Physics 4th edition by Jerry Wilson and Anthony Buffa may print out one copy of the Workbook material for their own use but may not otherwise copy or distribute the material in part or in whole by any means whatsoever electronic or otherwise without express written permission from the author and Prentice Hall Inc Chapter 3 A VECTORS WilsonBuffa Chapter 3 Motion in Two Dimensions Section 32 Unit 1 Establish definitions draw vector diagrams Unit 2 Estimate answers Unit 3 Trigonometry review Unit 4 Vector equations and component equations Unit 5 Completion of problem solutions Copyright 1996799 by Daniel M Smith Jr All rights reserved Students using College Physics 4th edition by Jerry Wilson and Anthony Buffa may print out one copy of the Workbook material for their own use but may not otherwise copy or distribute the material in part or in whole by any means whatsoever electronic or otherwise without express written permission from the author and PrenticeeHall lnc Pictorial Definition of a Vector Vectors 7 Unit 31A 7 Problem 31A 375 A woman jogs from the front door of her house for 08 miles in a direction 400 south of east then jogs for an additional 12 miles in a direction due east a How far has she jogged b What is the straightiline distance from her front door to the end of her jog c What is the direction of the straightrline trip from her front door to where she stopped jogging 34 Scale 3 cm 1 mile but any can be used The arrows are called vectors Does every vector in your drawing have an arrowhead at one end like the vectors above CI Yes CI No If quotNoquot then correct your diagram In your drawing does the arrowhead or head of one vector connect to the tail of the other in the way shown above CI Yes CI No If quotNoquot then correct your diagram A correctly drawn vector should have both a and a 35 A correctly drawn vector should have both a head and a tail Restating this a bit more formally a correctly drawn vector should have both a magnitude or lengch and a direction indicated by an arrowheadZ This extremely important pictorial definition of a vector is used in all of physics although it is not the only way to define a vector 3710 Vectors 7 Unit 3lA 7 Problem 3lA A woman jogs from the front door of her house for 08 miles in a direction 400 south of east then jogs for an additional 12 miles in a direction due east a How far has she jogged b What is the straightiline distance from her front door to the end of her jog c What is the direction of the straightrline trip from her front door to where she stopped jogging 319 Use the last definition to draw two diagrams each showing that the answer less than 90quot is correct for the previous question In diagram a the dashed vector is a duplicate of the 08 mi vector along the same line as the original vector According to the definition above the shifted duplicate is equal to the original A dotidashed duplicate of the 12 mi vector has been shifted upward in diagram b After shifting either one of the vectors so that the tails of both vectors meet it is clear that the angle between the two vectors is 40quot Negative of a Vector 3712 Vectors 7 Unit 31A 7 Problem 31A A woman jogs from the front door of her house for 08 miles in a direction 400 south of east then jogs for an additional 12 miles in a direction due east a How far has she jogged b What is the straighteline distance from her front door to the end of her jog c What is the direction of the straightrline trip from her front door to where she stopped jogging 322 Clearly the woman needs only to reverse her trip to return home In diagram a the two vectors describing her return are the negatives of the vectors in frame 34 In diagram b the dotedashed vector representing a direct trip home is just the negative of the dashed vector in frame 311 In general the negative of a vector is formed by drawing a new vector Whose magnitude is the same as that of the original vector but Which is oppositely directed Does every vector in your drawing have an arrowhead at one end like the vectors above CI Yes If quotNoquot then correct your diagram EINo If you made a drawing like the one on the left does the head of one vector connect to the tail of the other in the way shown above CI Yes CI No If quotNoquot then correct your diagram Vectors 7 Unit 31A 7 Problem 32A 3715 Robert s friend Keisha lives in a large Victorian house 20 km 12 mi away From where Robert lives the direction of Keisha s house is 700 west of north Keisha decides to move to a smaller house which is 150 south of west from where Robert lives and 38 km 24 mi away a How far and in what direction did Keisha move b If Keisha and Robert both live in a city whose blocks are rectangular and form a grid how far must Robert actually drive to visit Keisha 325 Draw a compass label its directions then indicate on your compass the general directions quotwest of north and south of westquot 326 WofN orN ofW W E SofW orWofS S Workbook for Introductory Mechanics Problemisolving Copyright 1996799 by Daniel M Smith Jr Sponsored by FIPSE US Department of Education 3716 Vectors 7 Unit 31A 7 Problem 32A Robert s friend Keisha lives in a large Victorian house 20 km 12 mi away From where Robert lives the direction of Keisha s house is 700 west of north Keisha decides to move to a smaller house which is 150 south of west from where Robert lives and 38 km 24 mi away a How far and in what direction did Keisha move b If Keisha and Robert both live in a city whose blocks are rectangular and form a grid how far must Robert actually drive to visit Keisha 327 Using a ruler or some other scale draw a vector diagram of the problem Estimate the angles but draw the distances to scale 1 cm for each 05 km may be convenient Be sure to draw a vector to represent the answer to part a Attention Vectors 7 Unit 31A 7 Problem 32A 3717 Robert s friend Keisha lives in a large Victorian house 20 km 12 mi away From where Robert lives the direction of Keisha s house is 700 west of north Keisha decides to move to a smaller house which is 150 south of west from where Robert lives and 38 km 24 mi away a How far and in what direction did Keisha move b If Keisha and Robert both live in a city whose blocks are rectangular and form a grid how far must Robert actually drive to visit Keisha 328 Lar o e house Robert s house Small house Scale 1cm 05 km but any can be used Even if your diagram does not look exactly like the one above do not change it except as directed below Although this means that you have not used the problem data just as it was given your diagram may still allow you to solve the problem Have you positioned Keisha s old and new address as well as Robert s address correctly in your diagram Yes CI No If No then reread the problem before correcting your diagram Does every vector in your drawing have an arrowhead at one end like the vectors above CI Yes CI No If quotNoquot then draw an arrowhead on each vector Do you have in your diagram a vector pointing away from Keisha s old address and towards her new one as above CI Yes CI No If quotNoquot reread the question in part a of the problem before correcting that vector only 3718 Vectors 7 Unit 31A 7 Problem 32A Robert s friend Keisha lives in a large Victorian house 20 km 12 mi away From where Robert lives the direction of Keisha s house is 700 west of north Keisha decides to move to a smaller house which is 150 south of west from where Robert lives and 38 km 24 mi away a How far and in what direction did Keisha move b If Keisha and Robert both live in a city whose blocks are rectangular and form a grid how far must Robert actually drive to visit Keisha 329 Which two of the three vectors above can be added without rearrangement of the diagram DEandR Uganda DRandC Write out a justification for your choice 330 Only vectorsg and 6 can be added without rearranging the diagram because this is the only choice allowed by the head7 toitail definition of vector addition frame 323 Vectors 7 Unit 31A 7 Problem 32A 3719 Robert s friend Keisha lives in a large Victorian house 20 km 12 mi away From where Robert lives the direction of Keisha s house is 700 west of north Keisha decides to move to a smaller house which is 150 south of west from where Robert lives and 38 km 24 mi away a How far and in what direction did Keisha move b If Keisha and Robert both live in a city whose blocks are rectangular and form a grid how far must Robert actually drive to visit Keisha 331 Although they do not represent the data as they were presented in the problem three other vector diagrams could be drawn for this problem Does your diagram look like any one of them or the diagram in frame 328 CI Yes CI No If No then reread the problem before correcting your diagram 3720 Vectors 7 Unit 31A 7 Problem 32A Robert s friend Keisha lives in a large Victorian house 20 km 12 mi away From where Robert lives the direction of Keisha s house is 700 west of north Keisha decides to move to a smaller house which is 150 south of west from where Robert lives and 38 km 24 mi away a How far and in what direction did Keisha move b If Keisha and Robert both live in a city whose blocks are rectangular and form a grid how far must Robert actually drive to visit Keisha 70 I I Although it is not obvious any one of these diagrams could be used to solve the problem as will be shown later Consider the vectors above labeled 15 E H jM 15 Which two vectors are equal to each other From the same list select all possible pairs of vectors with each member of a pair the negative of the other member Vectors 7 Unit 31A 7 Problem 32A 3721 Robert s friend Keisha lives in a large Victorian house 20 km 12 mi away From where Robert lives the direction of Keisha s house is 700 west of north Keisha decides to move to a smaller house which is 150 south of west from where Robert lives and 38 km 24 mi away a How far and in what direction did Keisha move b If Keisha and Robert both live in a city whose blocks are rectangular and form a grid how far must Robert actually drive to visit Keisha 333 All of the questions are answered by referring to your summary of vector properties in frame 323 Vectors 15 and I are equal to each other Vector E is the negative of vector H and vector j is the negative of vector A71 Vector i has a direction 200 south of east and vector R has a direction 150 north of east 334 From each diagram above select the pair of vectors which can be added without rearrangement of the diagram a b C 3722 Vectors 7 Unit 31A 7 Problem 32A Robert s friend Keisha lives in a large Victorian house 20 km 12 mi away From where Robert lives the direction of Keisha s house is 700 west of north Keisha decides to move to a smaller house which is 150 south of west from where Robert lives and 38 km 24 mi away a How far and in what direction did Keisha move b If Keisha and Robert both live in a city whose blocks are rectangular and form a grid how far must Robert actually drive to visit Keisha 335 Once again we refer to the frame 323 definitions to justify our answers a R and E also E and D or D and R b H and j c I and A71 Vectors 7 Unit 31A 7 Problem 33A 3727 Two friends Keith and Jamal who have gone hiking in the woods have become separated Keith has walked for an unknown distance before realizing that his friend is not near Keith then walks 05 km due north to look for Jamal but sends up a are signal when he cannot find him then waits Meanwhile Jamal has walked 13 km at 350 south of west but after seeing the are he walks 16 km 150 east of north to meet Keith How far and in what direction did Keith wander when he and Jamal first became separated 340 a Keith s b Jamal s c Combined diagrams finish i e Scale 3 cm 1 km though yours may differ Does every vector in your drawing have an arrowhead at one end like the vectors above CI Yes CI No If quotNoquot then draw an arrowhead on each vector Are the directions of your vectors identical to the directions of the vectors above CI Yes CI No If quotNoquot then carefully reread the problem along with frame 339 before correcting your diagram Keeping in mind that Keith and Jamal started from the same point draw in the unknown vector either on your diagram or on the diagram above 3728 Vectors 7 Unit 31A 7 Problem 33A Two friends Keith and Jamal who have gone hiking in the woods have become separated Keith has walked for an unknown distance before realizing that his friend is not near Keith then walks 05 km due north to look for Jamal but sends up a are signal when he cannot find him then waits Meanwhile Jamal has walked 13 km at 350 south of west but after seeing the are he walks 16 km 150 east of north to meet Keith How far and in what direction did Keith wander when he and Jamal first became separated 341 Unknown Have you placed an arrowhead 0n the unknown vector pointing correctly CI Yes CI No If quotNoquot then notice that this vector represents Keith s walk away from the point where he and Jamal parted company Correct your diagram

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