ࡱ> ? $jbjb )J}}NS^lTTTT8L{ X \ ( QsQsQs8::::::, VfQs_pQsQsQsf!uTT OX !u!u!uQsTP  8!u(6^6TTTTQs8!u!u{Ȓp4 $ gsĕ,{{,!u!uIn the tutorial about velocity and acceleration graphs last week, most of you didnt finish the last set of questions about a cart going up and down a ramp. The first two pages below cover that same tutorial material. If you didnt complete all of the tutorial questions do them below, working with a group, if possible. DO NOT hand in these first two (tutorial) pages with this homework . Up and down a ramp In all these questions, just think about the carts motion after you stop pushing it up the ramp but before you catch it on the way down. Velocity graph review. This graph shows the carts velocity vs. time. On those same axes, graph the carts speed vs. time. Speed is how fast something is moving, independent of direction. What would you guess is a common mistake students make on the velocity vs. time graph for this and similar situations? Explain. Acceleration on the way down Consider the cart as it rolls down the ramp after reaching its peak. Give a reason why a smart student might think the carts acceleration during that segment of the motion is positive. Briefly summarize the reasoning. Now give a reason why a smart student might think the carts acceleration during that segment of the motion is negative. Briefly summarize the reasoning. Below, sketch two different predictions for the carts acceleration vs. time. On "Prediction graph1," assume the carts acceleration as it rolls down the ramp is positive (argument 1 above). On "Prediction graph 2," assume the acceleration is negative during that segment (argument 2). When performed with good equipment, the acceleration graph comes out as shown here. Two students disagree about what they should do next to continue learning about acceleration. VENUS: Look, now we know which argument to believe about whether the acceleration is positive or negative when the cart rolls down the ramp. Physics is an experimental science! Since we know the right answer and the reasoning behind it, were ready to move on. SERENA: But we also came up with a sensible argument that the acceleration would be positive, not negative. To understand acceleration, I think we also need to understand whats wrong with that argument. Which student do you agree with more in this case? Explain. How to decide? Consider the contradictory arguments from part B about whether the carts acceleration is positive or negative as it rolls down the ramp. Was it possible to decide for sure, without doing the experiment, which argument was correct? Explain. Lets see if the president-for-life of mistake-avoidance strategies can help us here. Look at the velocity graph on the previous page.. By checking for coherence between your velocity graph predictions and your acceleration graph, could you decide whether the acceleration is positive or negative as the cart rolls down the ramp? Explain. (If your above answers addressed this issue, skip this question.) We just saw that checking for coherence can help you decide between sensible competing arguments. Can that game also help you understand why the other argument is wrong? See if you can use the connection between velocity and acceleration graphs to explain, in a common sense way, why the carts acceleration is negative even though its gaining speed (as it rolls down the ramp)? Hint: Is the carts velocity (not speed) trending up or down? Rolling ball A ball, released from rest, rolls down ramp A, then along the floor, then up ramp B, as drawn here. Rounded segments at the bottoms of the ramps allow the ball to roll smoothly from a ramp to the floor and vice versa. Air resistance is negligible. Sketch the balls velocity vs. time and acceleration vs. time, from the moment its released until the moment it reaches its peak on the second ramp. Label your graphs in such a way that we can tell when the ball is on ramp A, when its on the floor, and when its on ramp B. Remember to end your graphs at the moment the ball reaches its highest point on ramp B.  Now sketch distance vs. time. (Distance here means the distance the ball has rolled along the track from its starting place.) Explain your reasoning in words. Bill got his position and acceleration graphs right but drew the incorrect velocity vs. time graph shown here. Why do you think Bill make this mistake? What advice would you give him to help him avoid that mistake in the future?  After drawing his velocity graph, how could Bill have realized that its wrong? (If you already answered this in question 1, just say so.)  Velocity graph Consider the velocity vs. time graph shown here, focusing on the issue of whether the object turns around (reverses direction). Why might a smart student say the object reverses direction? Why might a smart student say the object doesnt reverse direction? Does the object reverse direction? As part of your explanation, explain why the other argument is incorrect, and give advice to someone who made that mistake that can help them understand why they made the mistake and how they can avoid it in the future. Sketch a graph of the objects position vs. time. Bouncing ball A hard rubber ball is dropped from rest. It falls to the concrete floor and bounces back up almost to its initial height. A motion detector is mounted on the ceiling directly above the ball, facing down. So, in this example, the positive directionthe away-from-the-detector directionis downward. On these graphs, sketch the balls position, velocity and acceleration vs. time. Treat the bounce as a sudden event that happens in a single instant of time. (Below, youll think about whats going on during the bounce.) Because youre dealing with all three kinds of graphs at once, think carefully and use the strategies youve learned for avoiding and catching mistakes. Two students discuss the acceleration during the bounce, i.e., during the brief time the ball is in contact with the floor. SMITHA: The balls acceleration must be large during the bounce, larger than when its just falling or rising. Because during the bounce, the balls velocity changes a lot, very suddenly, a big change in velocity over a very small time. So, the acceleration the rate of change of velocity is big. AJITA: But look...because the ball is very bouncy, it hardly loses any velocity during the bounce. Thats why it rebounds almost to its initial height. For instance, if it reached the floor going down at 8.0 meters per second, then maybe it bounces back up at 7.9 meters per second or even 7.95 meters per second. So, during the bounce, the velocity changes by a tiny amount. Even though this change happens over a small time, the change in velocity per change in time isnt too big, probably smaller than when its just rising or falling. Which student do you agree with? Explain. During the bounce, is the acceleration positive or negative? Explain. Tutorial 2 Homework Name Catching mistakes: Motion graphs Tutorial section University of Maryland Physics Education Research Group, Fall 2004. HW2- PAGE 5 Tutorial 2 Homework Name Catching mistakes: Motion graphs Tutorial section University of Maryland Physics Education Research Group, Fall 2004. HW2- PAGE 1 time velocity bounce bounce time Acceleration time Velocity time bounce Position time peak acceleration time peak acceleration time peak acceleration Prediction graph 2 Prediction graph 1 time peak 3 6 9 velocity detector velocity time distance time acceleration time velocity time B A  ()>BCm ; C  + , ,4hixijSTDZ`AF N!a!g!h!i!j!>*5CJOJQJ6CJOJQJ CJOJQJCJ656 jUmH5>*5O(Bk l m g h i     +   & Fh^h Y^`Y h(Bk l m g h i     + ´}olgb\YVSPM uCKL_   _f   fcde   "#     ~>   >  b  b  [hcwxyz{|}h & F h[hcwxyz{|}hiklmŷ~{xug[XURO     WXYZ[\       `   `efg          hiklmOPQRSb h & FmOPQRSb踲蕒~{xpk_QNKK   K            1   1 3p  p   b   b !!!!!N!j!!!!! !$$dN !$&dP d !B$h`h K^`Kh^h Y^`Y !!!!!N!j!!!!!"""""""""""""""""""""""""""#$M   M12RS+j!!!!!!!!!!!! """""5"F"G"J""""""""""""""""""""""""""""""""""""## # # #### #$#%#&#+#,#9#:#>#?#@#E#5CJCJCJB*CJOJQJphCJ5CJOJQJ 0JCJmH0JCJj0JCJUCJ>* CJOJQJK!!"H"I"J""""""""""""""""""" !$$dN !$&dP d !B$"""""""""""""""## # #### #%#&#+#,#9#:#?#?#@#E#F#G#H#I#J#W#X#k#l###################E#J#W#X#k#l#############################################$ 56CJCJB*CJOJQJph5CJ2################################$' 0&P1h/ =!"#$%f i(@( NormalCJmH H@H Heading 1$ & F<@&5KH OJQJT@T Heading 2+ & F 8hxx@&^h`CJZ@Z Heading 31 & F dxx@&^`CJZ@Z Heading 41$ & F @ 88xx@&^8`CJB@B Heading 5 & F<@& 56CJ@@@ Heading 6 & F<@&5CJ8@8 Heading 7 & F<@&<@< Heading 8 & F<@&6D @D Heading 9 & F<@& CJOJQJ<A@< Default Paragraph Font,@, Header  !, @, Footer  !&)@& Page Number.B@". Body TextxCJO!2 Text.B. text3x^CJ&O1R& text2 h^h*b* text4 ^CJ&OQr& text1 ^DCD Body Text Indent^`<T< Block Textx]^4P4 Body Text 2 dx2Q2 Body Text 3xCJLM@!L Body Text First Indent `CJXNX Body Text First Indent 2hx^h`JRJ Body Text Indent 2hdx^hHSH Body Text Indent 3hx^hCJ2"2 Caption xx5CJ*?* Closing !^0"0  Comment Text"CJL Date#FYBF  Document Map$-D M OJQJ4[R4 E-mail Signature%0+b0  Endnote Text&CJ\$r\ Envelope Address!'@ &+D/^@ OJQJ>%> Envelope Return( CJOJQJ22  Footnote Text)CJ0`0 HTML Address*6BeB HTML Preformatted+ CJOJQJ2 2 Index 1,^`2 2 Index 2-^`2 2 Index 3.^`2 2 Index 4/^`22 Index 50^`22 Index 61^`22 Index 72^`22 Index 83^`22 Index 94p^p`:!:  Index Heading5 5OJQJ,/b, List6h^h`02r0 List 27^`030 List 388^8`040 List 49^`050 List 5:^`202 List Bullet ; & F666 List Bullet 2 < & F676 List Bullet 3 = & F686 List Bullet 4 > & F696 List Bullet 5 ? & F :D: List Continue@hx^h>E> List Continue 2Ax^>F"> List Continue 3B8x^8>G2> List Continue 4Cx^>HB> List Continue 5Dx^21R2 List Number E & F!6:b6 List Number 2 F & F"6;r6 List Number 3 G & F#6<6 List Number 4 H & F$6=6 List Number 5 I & F%T-T  Macro Text"J  ` @  OJQJmH I Message HeadergK8$d%d&d'd-DM NOPQ^8`OJQJ,^, Normal (Web)L66 Normal Indent M^,O, Note HeadingN4Z4 Plain TextO CJOJQJ(K( SalutationP.@. Signature Q^:J": SubtitleR$<@&a$OJQJL,L Table of AuthoritiesS^`D#D Table of FiguresT ^` D>RD TitleU$<@&a$5CJ KHOJQJ:.:  TOA HeadingVx 5OJQJ TOC 1W&& TOC 2 X^&& TOC 3 Y^&& TOC 4 Z^&& TOC 5 [^&& TOC 6 \^&& TOC 7 ]^&& TOC 8 ^^&& TOC 9 _^6'@6 Comment ReferenceCJ@@ sgcentera$ h'#a$OJQJP"P sh1/b  8d]^8`OJQJD2D sn2$c 88d]^8OJQJPBP p graph (center)d$ h'#a$OJQJFRF quote&e#x5$7$8$9DH$^#`CJ #)*+-;ACMS[ekq"(6<FLORSTUVWXYZ[\]:ji#" <   234%FEONbaYX<;2 3 4 5 6 789; #)*+-;ACMS[ekq"(6<FLORSTUVWXYZ[\]`    !"#$%&'()*+,-./0123456789:;<J!z!z z z z+h SSRUj!E#$"hb!"?###$ !#$m$FMOU!!`lst,2$J<>x; @ZOsPN(  b |.)7  #" T  # '|./ 'T  # #V"6$7 #j`  : # /!6BB      tBCDE F5%K@ :W ~t 0( # #" 2<):3BB B  B!(C  tBCDE F5%K@'0(  <"'13)N4 "`B  c $D#/#`6 b  2):  #" :n *A3  #"  21:Z  3 * , Z  3 P2z3 ~t  : # #"  Y+8 a2BB      tBCDE F5%K@ :W ~t 0( # #" x .z/BB B  B!(C  tBCDE F5%K@'0(  <pq/A0 `B  c $D+2:n *A3  #" 2):Z  3 * , Z  3 P2z3 ~t  : # #"  Y+8 a2BB      tBCDE F5%K@ :W ~t 0( # #" x .z/BB B  B!(C  tBCDE F5%K@'0(  <pq/A0 `B  c $D+2NB  S DjJH  # ! !H  #   b ((  #" :n *A3  #" ((Z  3 * , Z  3 P2z3 ~t  : # #"  Y+8 a2BB      tBCDE F5%K@ :W ~t 0( # #" x .z/BB B  B!(C  tBCDE F5%K@'0(  <pq/A0 `B  c $D+2ZB  S DjJ$&$JN HA+!  (n L q(j5  #" HA+!&Z L q(#  L q(#Z  3 L B Z  3  "$# ~t  : # #" h"BB      tBCDE F5%K@ :W ~t 0( # #" 'BB B  B!(C   tBCDE F5%K@'0(   < &q(  `B   c $D8"8"":n *A3   #" L#q(,Z   3  * , Z  3 P2z3 ~t  : # #"  Y+8 a2BB      tBCDE F5%K@ :W ~t 0( # #" x .z/BB B  B!(C  tBCDE F5%K@'0(  < pq/A0  `B  c $D+2:n *A3  #" Lx,q(j5Z  3  * ,  Z  3  P2z3  ~t  : # #"  Y+8 a2BB      tBCDE F5%K@ :W ~t 0( # #" x .z/BB B  B!(C  tBCDE F5%K@'0(   < pq/A0 `B ! c $D+2Z " 3 "n#?B' Z # 3 #n#B'q! ^b !}'7-i* $ #" Z % 3 (%(#(7-c) (Z !}')i* & !}')i*4b ' !}')i*8n q$'%( ( #" &('i)B )  u$'%P(42 * q$($o(42 + $@(^%(B ,  )))E*ZB - S Df&'<((NB . S DNB / S DNB 0 S DNB 1 S D` 2 c $$ $` 3 c $% %` 4 c $& &b , xv  5 #" 4b 6 2 v TB 7 C D r Hr 4b 8B LF xv  9 lBC5DEF9#T,o544@  #"  @ 4 u  : lBCDEF>Xr@  #"  T p l ; c $2$ <  2l < c $1$ <  1N2 = 3 333, ` D& BD%Q), >c æ0e0e`xK xGx+/\ +/x9x`T`T9JL|4R(3Q--H/+$GGK x#" j`  : ?# %H,BB @    A tBCDE F5%K@ :W ~t 0( B# #" +)()BB CB  B!(C D tBCDE F5%K@'0( E <*E')Q)* * F B)FBD%i& )lb H ( G #"  j`  : H#  HBB I    J tBCDE F5%K@ :W j` 0( K# >(BB LB  B!(C M tBCDE F5%K@'0( N <,N&( , O B+OH Im  + b 2 (1 P #" J, BD%Q), QS æ0e0e`xK xGx+/\ +/x9x`T`T9JL|4R(3Q--H/+$GGK x#" 2 A1j`  : R# %H,BB S    T tBCDE F5%K@ :W ~t 0( U# #" +)()BB VB  B!(C W tBCDE F5%K@'0( X <0X')Q)* 0 Y B/YBD%i& /J, BD%Q), ZS æ0e0e`xK xGx+/\ +/x9x`T`T9JL|4R(3Q--H/+$GGK x#"  (,j`  : [# %H,BB \    ] tBCDE F5%K@ :W ~t 0( ^# #" +)()BB _B  B!(C ` tBCDE F5%K@'0( a <.a')Q)* . b B-bBD%i& -NB c S DjJ NB d S DjJ NB e S DjJNB f S DjJ NB g S DjJ N  #,y,0 h Z i 3 i #,'.  j <j*/y,10 ht ` ,+3 k# #" % -+0|f  : l3 { , !3HB m #   n zBCDE F5%K@ :W z 0( o3 #" ` 0+0HB pB # B!(C q zBCDE F5%K@'0(`B r c $DjJ p.`%P0`B s c $DjJ`%p.(`0B S  ?(B +h iS$cm&YT0y% T,$tmlt<m"tq# 4% T5R@$TPZ}$4Gl%Tgt" tftdtct>#aTet4 t3t2t1]o]Kt07o7Kt/oKt.oKthJ&[T|%+T N~)? sN   $&*,8:>@DJV:::::::::::::::::::::::::::::::::::rescherr[C:\Documents and Settings\rescherr\Desktop\121 HW\Cleaned up 121 HW\01 Motion graphs HW.docrescherr8O:\COMMON\_Projects\CCLI\Homework\HW01 Motion graphs.docrescherr8O:\COMMON\_Projects\CCLI\Homework\HW01 Motion graphs.docrescherr8O:\COMMON\_Projects\CCLI\Homework\HW01 Motion graphs.docrescherr8O:\COMMON\_Projects\CCLI\Homework\HW01 Motion graphs.docrescherr*O:\COMMON\_Projects\CCLI\Homework\HW02.docrescherr*O:\COMMON\_Projects\CCLI\Homework\HW02.doc Rachel ScherrIPowerBook HD:Desktop Folder:Rachel:CCLI work:Cleaned up versions:HW02.doc Rachel ScherrRPowerBook HD:Desktop Folder:Rachel:CCLI work:Homework:Cleaned up versions:HW02.doc Rachel ScherrRPowerBook HD:Desktop Folder:Rachel:CCLI work:Homework:Cleaned up versions:HW02.doc|"(I}j:~H~"~~GxFBr?>z=N֙<2ItE@Ÿh;^[ҞGtH]_"&k+ D,3*U3!K0d%N3qHIrescherr Rachel Scherr Oh+'0  4 @ L Xdlt|'Iss rescherrt escescNormalrRachel Scherro7chMicrosoft Word 9.0d@^в@ư%@@ޫ@<$ ՜.+,0 hp  'University of Marylanda0  I Title  !"#$%'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrsuvwxyz{}~Root Entry F/1Table&WordDocument)JSummaryInformation(tDocumentSummaryInformation8|CompObjX FMicrosoft Word DocumentNB6WWord.Document.8