Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents frm the previus step keeping directin f the cmpnents in mind. Determine the length f the hyptenuse using Pythagrean Therem. Prvide a scale based n the length f ne blck n the reference grid. K. Write each f the vectr pairs frm the table in step nt an individual card. Mix up rder f the cards and exchange with anther grup. On a piece f graph paper, diagram the mtin f the ther teams ty using vectr skills. Determine the resultant. Cmpare the values with the ther grup. L. Mtin withut a grid - Starting the ladybug frm near the center f a blank dry erase bard, allw it t mve ne single path t the edge f the bard. The lady bug must travel a path that is entirely hrizntal r vertical. Trace the vectr and indicate directin with an arrw. Measure the length in cm f the vectr and determine the angle f the vectr relative t the hrizntal axis. Recrd values in the table belw. making triangle (ie same reference angle) ). This is a standard frm that will allw us all t have the O. Using yur knwledge f SOH CAR TOA determine the angle between the resultant and the hrizntal. Shw yur wrk. Questins 1. Hw d the hyptenuse frm step H and the hyptenuse fr step J cmpare? 2. What cnclusin(s) can yu draw frm this finding? 3. In Step K yu were nt prvided with any rder fr adding vectrs. Did the randm rder have any impact n the magnitude r directin f the resultant vectr? 4. What is the vectr term fr the hyptenuse f triangle that results frm cmbining the hrizntal and vertical vectrs? 5. What type f vectr quantity is represented in tltis activity? Magnitude r length f Vectr (cm) Angle r directin f vectr relative t x axis Cnclusin (Cmplete in tbe space belw): Cmpare the distance traveled t the displacement f the lady bug ty. xplain the difference in prcess fr finding each value. In yur cmparisn, explain the terms vectr and scalar in terms f the cncepts f distance and displacement. M. On the dry erase bard, draw the hrizntal and vertical cmpnents f the vectr indicating apprpriate directin. Measure the length f each vectr and use a + r - t indicate apprpriate directin n either axis. Recrd values in table belw. Magnitude flength f the hrizntal cmpnent (cm) Magnitude r length f the vertical cmpnent (cm) N. Draw a scaled versin f the resultant displacement and the hrizntal and vertical cmpnents in the space prvided belw: [draw hrizntal and then vertical when..:::::::j.-
Intrductin t Vectrs I 23 Intrductin t Vectrs I 24 ~ T investigate and represent the mtin f an bject experiencing tw simultaneus (cncurrent) velcities. mtin f a wind-up ty. Wind-up ladybug 3 Meter Dry erase grid Large dry erase bard Stp watch Prcedure: Vectr additin and vectr reslutin will be used t analyze the A. Mtin f the ty is due t wind up device. Befre all experiments the ty will be fully wund. B. The paper mves alng the hrizntal x axis by pulling it at rughly cnstant speed C. The relative mtin f the bjects is fund by mving bth the paper and the ty between statinary meter Prir t all data cllectin students shuld practice crdinating materials and establish a realistic divisin f labr. See yur instructr Data and Calculatins if yu need assistance with this step 1. Determine the average speed f the ladybug as it mves tward the right acrss a statinary grid. (Take the average f 3 trials). Yu will use this average speed as a reference value thrughut the lab. Ty Data Distance (cm) TIme Speed AVRAG 2. Determine the resultant velcity f the ty and the paper if bth have a rightward velcity. Attempt t mve the paper at a speed similar t the ty. Fill in measurements n the table belw Time f Displacement Displacement Displacement Velcity Velcity Resultant Interval f paper f ladybug fthe fthe fthe velcity relative t relative t ladybug paper ladybug fthe meter stick the grid relative t n the ladybug the meter paper a) Shw yur wrk used t determine the velcity values fr the chart abve b) Cnstruct a vectr diagram that shws hw the displacement f the ty and the displacement f the paper add t the resultant displacement f the ty. (Label each vectr with a magnitude Including units. Des nt have t be drawn t scale but shuld shw relative size.) c) Cnstruct a vectr diagram that shws hw the velcity f the ty and the velcity f the paper add t the resultant velcity f the ty. (Label each vectr with a magnitude including units. Des nt have t be drawn t scale but shuld shw relative size.) d) Since the paper and the lady bug are bth mving in the same directin, hw wuld we define the angle between their mtins?
Intrductin t Vectrs I 25 Intrductin t vectrs! 26 3. Mve the paper t the left at a similar cnstant speed t that f the rightward mving lady bug fr several secnds. As a grup recrd the fllwing. Nte the directin f mtin with a psitive r negative sign. Time f Displacement Displacement Displacement Velcity Velcity Resultant experiment f paper f ladybug lthe f the f the velcity relative t relative t ladybug paper ladybug f the meter stick the grid relative t n the ladybug the meter paper Time f Hrizntal Vertical Displacement Velcity Velcity Resultant experiment Displacement Displacement lthe fthe f the velcity f f paper f ladybug ladybug paper ladybug the relative t relative t relative t nthe ladybug meter stick the grid the meter paper. a) Cnstruct a labeled displacement diagram 'if I't b) Cnstruct a labeled velcity diagram..., 1*'1 cr c) What is the difference in directin (angle) between the papers velcity and the ladybugs velcity? 4. Vectr Rule: The maximum resultant ccurs when the vectrs are arranged at an angle f r similar directin. The minimum resultant ccurs when the vectrs are arranged at an angle f r ppsite directin. Hw culd yu get a different resultant withut changing the magnitude (size) f the cmpnent velcity vectrs? Cnstruct displacement and velcity vectr diagrams shwing cmpnents and resultants. 6. Predict what wuld happen t the angle f mtin if yu pull the paper at twice the speed t the right while the lady bug mves upward. Rughly draw the vectrs (Hint: think f the paper as the x vectr and the ty as the y vectr) 7. Cmplete the scenari presented in the previus questin. (ie lady bug upward and paper 2X velcity right) Time f Hrizntal Vertical Displacement Velcity Velcity Resultant experiment Displacement Displacement f the f the f the velcity f f paper f ladybug ladybug paper ladybug the relative t relative t relative t nthe ladybug meter stick the grid the meter paper S. With the ty starting at the bttm left crner f the paper and pinted upward, pull the paper t the right at a pace clse t that f the ty. Let it run until the ty reaches a pint at the tp. On the dry erase bard, draw a line that cnnects the start and end pint (ie, the resultant displacement) Fill in data n the chart belw
)r~ 1-,.J7 ~ a. Draw a labeled vectr diagram f the resultant displacement and hrizntal and vertical cmpnents. b. Determine the resultant velcity (magnitude and directin). Shw wrk 8. Predict what wuld happen t the angle f mtin if the velcity f the paper were mving t the right at a velcity abut half that f the lady bug. Draw the predicted vectr diagram. Cmplete this scenari with the materials. Des the actual mtin rv r match)l'61lredictin? 9. Draw the bserved resultant path (and cmpnents) fr the lady bug mving upward ~aper mving t the left (use similar speeds fr bth the paper and the ~ Labe.!.!becprnp~ with the apprpriate sign (+ r -I. Intrductin t Vectrs I 27 Intrductin t Vectrs I 28 ing rightward. (Uk C, 1fI...-f;,,,~ 'mpnents) fr the lady bug starting frm the / while the paper is mving leftward a/t 12. a) Determine the hrizntal cmpnent f the mtin f the paper if t~ travelled with a resultant speed f 14.2 m/s and a vertical speed f 8 m~ur wrk. Hint: V= Vy= Fy J, 13. When an bject is launched at an angle, the initial r start velcity can be brken dwn int tw cmpnents, velcity directed hrizntally and velcity directed vertically. What is the launch velcity f an bject with a hrizntal cmpnent f 40 m/s and a vertical cmpnent f 30 m/s? 14. What are the initial hrizntal and vertical cmpnents f an bject's velcity if it is launched at 35 m/s at an angle f 60 degrees? Cnclusins; (t be cmpleted n a separate paper and attached) xplain hw the additin f vectr quantities is different frm additin f scalar quantities. Differentiate between the terms speed and velcity. xplain why vectrs are an imprtant cncept in mtin and hw they can be useful in ther aspects f physics (Think abut real life scenaris in which this applies). Summarize the methds f cmbining hrizntal mtin and vertical mtin t determine a resultant and the methds fr finding the hrizntal and vertical cmpnents f a resultant vectr. xplain hw the angle between the vectrs influences the magnitude f the resultant vectr. Be sure t define terms used in yur explanatins. b) What was the angle f the resultant fr the previus prblem if the lady bug was mving upward and the paper was mving left? (shw wrk with equatin and substitutin) c) What will be the resultant displacement f the lady bug after 4 secnds? Shw wrk (include magnitude and directins)
V) ~_ >- 0 <1/ Zua:: I--- :!l Iii '" >-.. " '" Za::w x r-- c u Q) i..r:; ;... '+- Q)..0... u > U x Z LLJ «... c «