Uni 1 - Descripive Models for Linear Moion A workbook and noebook for sudens aking Physics wih Mr. Lonon. Version 3. 212 1
Aciviy 1 - Umm, which way did he go? Designing an invesigaion for our buggy. You are o design wha you would do if given a buggy so ha you could laer answer he quesion, Where will your buggy be afer X seconds? Use he page below o describe his invesigaion and is oucome. Be sure o describe wha daa you would collec and how his daa would enable you o laer make a predicion. 212 2
Discussion Se 1 Deploying our Model The goal of a Discussion Se is no jus o supply an 'answer' o he quesion. We as a class are ineresed in deermining wheher our curren model can handle he problem, and wha assumpions are made in order o use he model. Therefore, your soluion o each siuaion should include a descripion of how you are using our model(s) o deermine your answer. If you encouner somehing ha our model has no been asked o handle ye, please say so. 1. A hamser scurries across a 5 meer long room wih a speed of 45 cm/s, how long would his ake? 2. A vehicle ravels 6 mph for 3 seconds. How far did i ravel during hese 3 seconds? 3. A snail moves a a speed of 3 cm/hr for 1 minues and hen 5 cm/hr for 15 minues. How far did i ravel? Wha single speed could anoher snail have if i waned o arrive a he same place in he same amoun of ime? 4. A ball rolls down a ramp ha is 5 meers long, and i akes 3 seconds o do his. How fas is he ball raveling a he end of he ramp? 5. A fish ravels 13 cm/s forward for 3 seconds, and hen immediaely urns around and ravels 2 cm/s backwards for 1 minue. a) How far did he fish ravel? b) How far away from where he sared is he? c) If you were asked how fas he fish raveled on average, wha would be your response? d) Wha single speed would a seahorse have o ravel in order o arrive a he same spo a he same ime? (Assuming he sared a he same place) 212 3
Uni 1 Discussion Se 2 : Alernae Represenaions In class, Mr. Lonon inroduced he represenaion called a moion map. Now le's see wha issues come up when we ry o use hem. Consider he following moion map: Objec A 2 4 6 8 1 12 14 16 18 2 22 24 26 3 Objec B 1. Do he objecs sar a he same place? 2. Who is raveling faser, and how do you know? 3. Who will be a posiion 12 firs? 4. How many unis of ime will i ake Objec B o make i o posiion 3? How did you deermine his? 5. If asked o deermine he speed of each objec, wha would be your response? 2. Anoher represenaion inroduced was he posiion-ime graph. Try your hand a skeching a posiion-ime graph for he same moions described in problem #1. 212 4
. 3. Consider he posiion vs. ime graph below for cycliss A and B. a. Do he cycliss sar a he same poin? How do you know? If no, which is ahead? X(m ) A B 5 (s) b. Which cyclis is raveling faser a = 3s? How do you know? c. Describe wha is happening a he inersecion of lines A and B. d. Which cyclis raveled a greaer disance during he firs 5 seconds? How do you know? e. Skech a moion map for his moion (ha hing from problem 1). 212 5
4. You already know he answers o Discussion Se 1, bu I'd like o see if you can apply hese new represenaions o he same quesions. So, on his page, please repea Discussion Se 1, bu explicily use moion maps and/or posiion ime-graphs o arrive a he resuls. 212 6
Aciviy 2 - Graph Maching During his aciviy, your group should have engaged in maching he posiion-ime graphs displayed on he compuer screen. Please ake a momen o wrie down below some specific quesions and/or challenges your group had when aemping his aciviy. Also you may wish o use he space for joing down oher group's quesions as I ofen end up using hose when creaing es quesions. 212 7
Uni 1 Discussion Se 3: Velociy versus Speed 1. Craig is biking along a mounain when his posiion a cerain imes is recorded. The following daa is obained: a. Plo he posiion vs. ime graph for Craig. (s). 2. 4. 6. 8. 1. x (m). 6. 12. 12. 8. 4. 12.. b. Wha do you hink is happening during he ime inerval: = 4s o = 6s? The ime inerval =6s o =12 s? How do you know? c. Wha is Craig's speed a =3 secs? Why should we believe you? d. Wha is Craig s average speed from =s o =12s? Please be prepared o explain how you arrived a his answer. e. Wha is Craig s average velociy from =s o =12s? 212 8
Reflecion Time Ok, we've accomplished a lo. Bu he odds are you will forge much of i if you don' wrie i down in a place where i can be rerieved. Concenrae on describing he differen ways o represen he model of moion we've been creaing so far. 212 9
Uni I Discussion Se 4: Velociy-ime graphs Skech velociy vs ime graphs corresponding o he following descripions of he moion of an objec. 1. The objec is moving away from he saring posiion a a consan (seady) velociy. 2. The objec is sanding sill. 3. The objec moves oward he origin a a seady velociy for 1s, hen sands sill for 1s. 4. The objec moves away from he origin a a seady velociy for 1s, reverses direcion and moves back oward he origin a he same velociy. 212 1
Draw he velociy vs ime graphs for an objec whose moion produced he posiion vs ime graphs shown below a lef. 5. Posiion (m) 1 2 3 4 5 In he nex wo problems, he wo segmens on each graph represen wo differen moions of he objecs. 6 1 2 3 4 5 Time (s) 7. 212 11
Uni 1 - Pracice Se 1: Using he Consan Velociy Model (For bes resuls, you should pracice using differen models each problem using boh he algebraic and graphical mehods we have described so far.) 1. You drive a a consan speed of 3 mph for 3 minues. Ten, as rafc hins, you pump i up o 45 mph for 2 minues. Wha average velociy would you need in order o reurn back o your saring posiion in 4 minues? 2. I's a sunny Sunday afernoon, abou 65 F, and you are walking around he Lake enjoying he las of he auumn color. Te sidewalk is crowded wih runners and walkers. You noice a runner approaching you wearing a ee-shir wih wriing on i. You read he frs wo lines, bu are unable o read he hird and fnal line before he passes. You wonder, "Hmm, if he coninues around he lake, I be I'll see him again, bu I should anicipae he ime when we'll pass again." You look a your wach and i is 3:7 p.m. You recall he lake is 3.4 miles in circumference. You esimae your walking speed a 3 miles per hour and he runner's speed o be abou 7 miles per hour. A wha ime should you expec o see he runner again? (I helps o hink of he circular pah as a sraigh line.) 3. You are approached by one of hose senseless compeiion programs ha appear on Saurday afernoon when here isn' anyhing else o wach.. Tey propose ha you compee in a 1m dash wih Carl Lewis, bu o make he race more ineresing, you are o ge a 3m head sar. Your bes ime in he 1m is 14.2s and Carl (who is no in op form now) can run i in 1.1s. To simplify he problem, assume ha you and Carl run a consan velociy during he race. Do whaever is necessary o deermine who crosses he fnish line frs. 212 12
4. For he following rows of he able, you will be presened wih one represenaion of moion and you are asked o fll in he oher 3. x vs. Graph v vs. Graph Wrien Descripion Moion Map x Objec moves wih consan posiive velociy for 4 seconds. Then, i sops for 2 seconds and reurns o he iniial posiion in 2 seconds. ANSWERS 1. 45 mph back (negaive) 2. abou 3:27 pm 3. You win! More specifically you cross he line 9.94 seconds afer he sar, whereas we were given ha i will ake Carl 1.1 seconds. Good job. 212 13
Uni 1: Aciviy 3 - Speeding Up and Slowing Down In each of he following problems, a car is placed ono a ramp eiher allowed o roll down he ramp or given a quick push up he ramp. A moion sensor is placed a some locaion on he ramp as shown. Your ramps should have numbers on hem, from o 227 cm. In he diagrams, he posiion is denoed wih a, and he 227 posiion is denoed wih a sign. In each problem, you are asked o observe he moion wihou using he sensor, make some predicions, and hen repea he moion wih he moion deecor acive. Do no erase your predicion if urns ou o be wrong. 1. Speeding up, moving in he posiive direcion a. Observe he moion of he car saring from res and rolling down he incline wihou using he moion deecor. moion deecor b. Predic a moion map. c. Predic he graphs describing he moion. d. Record he graphs as displayed by he moion deecor. posiion posiion velociy velociy 212 14
2. Slowing down, moving in he posiive direcion a. Observe he moion of he car slowing afer an iniial push wihou using he moion deecor. Answer he following quesions for he car while coasing. Sop he car a is highes poin. Give he car an iniial push up he ramp. b. Predic a moion map. d. Record he graphs as displayed by he moion deecor. posiion posiion c. Predic he graphs describing he moion. 212 velociy velociy 15
3. Speeding up, moving in he negaive direcion a. Observe he moion of he car saring from res and rolling down he incline wihou using he moion deecor. b. Predic a moion map. d. Record he graphs as displayed by he moion deecor. posiion posiion c. Predic he graphs describing he moion. 212 velociy velociy 16
4. Slowing down, moving in he negaive direcion a. Observe he moion of he car slowing afer an iniial push wihou using he moion deecor. Answer he following quesions for he car while coasing. Sop he car a is highes poin. moion deecor Give he car an inial push up he ramp b. Draw a moion map. d. Record he graphs as displayed by he moion deecor. posiion posiion c. Predic he graphs describing he moion. 212 velociy velociy 17
5. Up and down he ramp a. Observe he moion of he car afer an iniial push wihou using he moion deecor. Answer he following quesions for he car while coasing. Give he car an iniial push up he ramp. Cach he car jus before i reaches he moion deecor on he way back down. b. Draw a moion map. c. Predic he graphs describing he moion. d. Record he graphs as displayed by he moion deecor. posiion posiion 212 velociy velociy 18
6. Up and down he ramp wih a differen zero posiion Imporan: For his one, you will be changing he posiion ha he deecor hinks is posiion. The way his is done is o have someone hold he car a he place you wan o be posiion, and hen anoher member chooses Experimen->Zero from he drop down menus on Logger Pro. You will hear a series of clicks as he deecor figures ou where he car is, and hen ses ha posiion o be. a. Observe he moion of he car afer an iniial push wihou using he moion deecor. Answer he following quesions for he car while coasing. Give he car an iniial push up he ramp. moion deecor B A Cach he car jus before i reaches he moion deecor on he way back down. posiion posiion b. Predic he graphs describing he c. Record he graphs as displayed by he moion deecor. moion. Label poins A and B on your posiion vs. ime graph. velociy velociy 212 19
Reflecion Time You should use his page o make some noes abou wha you now know abou his ype of moion versus he moion we sudied a he beginning. For insance, consider he quesions: Do all posiion-ime graphs have similar qualiies? If so, wha are hey? Do all velociy-ime graphs have similar qualiies? If so, wha are hey? Does he slope of a velociy-ime graph mean anyhing? 212 2
Uni 1 Discussion Se 5: Wach ou for ha. While cruising along a dark srech of highway wih he cruise conrol se a 25 m/s ( 55 mph), you see, a he fringes of your headlighs, ha a bridge has been washed ou. I akes.5 s from he ime you see he danger o apply he brakes and anoher 3.5 s afer applying he brakes o sop. 1. Consruc a moion map ha represens he moion described above, including posiion, velociy, and acceleraion arrows. Clearly demonsrae how you can deermine he direcion (sign) of he acceleraion from he moion map represenaion. 2. Consruc quaniaively accurae graphical represenaions of he siuaion described above for: a) v vs. b) a vs. 3. Uilizing he v- graph, deermine how far he car wen from he ime he danger was firs observed unil sopping was complee. (Please explain your problem solving mehod.) 4. Did he car, according o your graph, have a consan acceleraion afer he brakes were applied? Please explain how you know. 5. From he v vs graph, deermine he acceleraion of he car once he brakes were applied. 212 21
6. A sun car driver esing he use of air bags drives a car a a consan speed of 25 m/s for 1 m. When a wall appears 5 meers in fron of him, he applies his brake and acceleraes uniformly o a sop jus as he reaches he wall. This shee will lead you sep by sep hrough one possible way of aacking he problem. Noice ha all of he ools we have discussed so far are combined ogeher o form a nice, logical argumen. a. Skech qualiaive posiion vs. ime and velociy vs ime graphs. b. How long does i ake for he car o ravel he firs 1 m? c. Remember ha he area under a velociy vs ime graph equals he displacemen of he car. How long mus he brakes be applied for he car o come o a sop in 5 m? d. Now ha you know he oal ime of ravel, skech a quaniaive velociy vs ime graph. e. Wha acceleraion is provided by he brakes? How do you know? 212 22
UNIT I: Discussion Se 6 1. 25 x (m) a. 5 (s) Describe in words he moion of he objec from - 6. s. b. Consruc a qualiaive moion map o describe he moion of he objec depiced in he graph above. c. d. Wha is he insananeous velociy of he objec a he following imes? i. = 1. s ii. = 3. s Wha is he simple average of hese wo velociies? Wha is he average velociy for he enire inerval? Why are hese wo values differen? Which is bes o describe he moion of he objec? 212 23
e. Graphically represen he relaionship beween velociy and ime for he objec described above. v (m/s) f. (s) 5 From your velociy vs. ime graph deermine he oal displacemen of he objec. 2. The graph below represens he moion of an objec. x B A C D E G F a. A wha poin(s) on he graph above is he objec moving mos slowly? (How do you know?) b. Over wha inervals on he graph above is he objec speeding up? (How do you know?) 212 24
c. Over wha inervals on he graph above is he objec slowing down? (How do you know?) d. A wha poin(s) on he graph above is he objec changing direcion? (How do you know?) 212 25
1.A poorly uned Yugo can accelerae from res o a speed of 28 m/s in 2 s. a) Wha is he average acceleraion of he car? b) Wha disance does i ravel in his ime? v (m/s) UNIT I: Discussion Se 7 (s) 3. A car whose iniial speed is 3 m/s slows uniformly o 1 m/s in 5 seconds. a) Deermine he acceleraion of he car. b)deermine he disance i ravels in he 3rd second ( = 2s o = 3s). v (m/s) v (m/s) 2. A = a car has a speed of 3 m/s. A = 6 s, is speed is 14 m/s. Wha is is average acceleraion during his ime inerval? (s) (s) v (m/s) 4. A bus moving a 2 m/s ( = ) slows a a rae of 4 m/s each second. a) How long does i ake he bus o sop? b) How far does i ravel while braking? 212 26 (s)
7.A mounain goa sars a rock slide and he rocks crash down he slope 1 m. If he rocks reach he boom in 5 s, wha is heir acceleraion? v (m/s) 6.A dog runs down his driveway wih an iniial speed of 5 m/s for 8 s, hen uniformly increases his speed o 1 m/s in 5 s. a)wha was his acceleraion during he 2nd par of he moion? b) How long is he driveway? v (m/s) v (m/s) 5.A physics suden skis down a hill, acceleraing a a consan 2. m/s2. If i akes her 15 s o reach he boom, wha is he lengh of he slope? (s) (s) (s) 8. A bear spies some honey and akes off from res, acceleraing a a rae of 2. m/s2. If he honey is 16 m away, how fas will his snou be going a he momen of ecsasy? 212 27 v (m/s) BONUS: (s)
a. Deermine he average velociy of he objec. b. Wrie a mahemaical model o describe he moion of he objec. -5-4 -3-2 -1 1. Consider he posiion vs ime graph a righ. 1 2 3 4 5 Uni I Review Pracice 2. Shown a righ is a velociy vs ime graph for an objec. a. Describe he moion of he objec. b. Draw he corresponding posiion vs ime graph. Number he x - axis. c. How far did he objec ravel in he inerval =1s o =2s? d. Wha is he oal displacemen? Explain how you go he answer. 212 28
3. Johnny drives o Wisconsin (192 miles) in 32 hours. He reurns o Arizona by he same roue in he same amoun of ime. a. Deermine his average speed. b. Deermine his average velociy. c. Compare hese wo values and explain any differences. 5. A race car ravels a a speed of 95 m/s. How far does i ravel in 12.5 s? Use he appropriae mahemaical model and show how unis cancel. (Keep he proper number of sf's.) Use he graph below o answer quesions #6-9 ha follow: 6. Give a wrien descripion o describe he moion of his objec. 7. Draw he moion map for he objec. Include velociy and acceleraion vecors. 212 29
8. If you had o guess, how would you esimae he insananeous velociy of he objec a = 2 s. 9. Using measuremens obainable from he graph, deermine he acceleraion of he objec. 1. For each of he posiion vs ime graphs shown below, draw he corresponding v vs, a vs, and moion map. 212 3