What the Puck? an exploration of Two-Dimensional collisions

Transcription

1 Wha he Puck? an exploraion of Two-Dimensional collisions 1) Have you ever played 8-Ball pool and los he game because you scrached while aemping o sink he 8-Ball in a corner pocke? Skech he sho below: Each figure below shows a cue ball hiing an 8-ball a differen impac poins. Rank, from greaes o leas, he angle beween he balls afer collision A B C D E F Greaes Leas Or, all of he angles beween he balls afer collision will be he same. 2) Please carefully explain your reasoning.

2 How sure were you of your ranking? (circle one) Basically Guessed Sure Very Sure ) If you re close o a pool hall, you may wan o convince your insrucor o move he lab here. If no, you can do similar analysis wih a pair of hover pucks. Obain 3 overhead movies of puck collisions ha have one puck iniially saionary, and he colliding puck hiing a differen impac poins on he saionary one. Play each movie muliple imes and esimae he angle of moion beween he pucks afer collision. 4) Explain your observaion: Since his is Physics and we have he ools, we won sop wih esimaes. You will use video analysis o quanify he moion and explore he role ha momenum plays in wo-dimensional collisions. Use one or more of he following analysis approaches: Componen Slopes Componen Calculaed Columns Vecor Each approach is rewarding in is own righ and you have hree movies

3 Wha he Puck? Componen Slopes 1) Open up Logger Pro. Under Inser, go o Movie. Locae he movie file you wan o open and open i. You should have he movie opened in fron of he LoggerPro graph. Click on o open he oolbar for video analysis. Click on and seup your scale for a known objec s dimension on he screen. 2) Click he posiion locaor,, and sar marking one of he pucks before, during and afer collision wih he 2 nd puck. Make sure you have a leas 8-10 poins jus before collision and righ afer collision. 3) Click he add daa se buon,, and mark he 2 nd puck before, during and afer collision. Again, make sure you have a leas 8-10 poins jus before and righ afer collision. 4) To beer view your daa, go under Page and click on Auo Arrange. Now you should have a window wih he movie, daa able, and graph in is own place. 5) If your wo pucks have he same mass, you don really need o creae momena columns. If, however, your masses are no he same, hen you need o creae New Calculaed Columns under he Daa menu for he momena of each puck in he x and y-direcions. 6) On your graphs, find he slope of he x graphs before (iniial) and afer (final) collision. Find he slope of he y graphs before (iniial) and afer (final) collision. Fill in he able below wih your calculaed values. p1x iniial p2x iniial poalx iniial p1x final p2x final poalx final p1y iniial p2y iniial poaly iniial p1y final p2y final poaly final 7. Was momenum conserved in each direcion?

4 8. Also calculae he angles of each puck before and afer collision. Angle puck 1before Angle puck 1 afer Angle puck 2 before Angle puck 2 afer 9. Wha was he angle beween he wo pucks afer collision?

5 Wha he Puck? Componen Calculaed Columns Objecive: To deermine wha happens o he momenum of a sysem as wo fricionfree pucks collide. In his experimen you will analyze he momenum of wo pucks in such a way ha you will be looking a he horizonal and verical componens of each puck s momenum before, during and afer he wo collide. Opion 1: Perform your own collision and gaher video evidence of he collision. Opion 2: Analyze he daa from a movie ha has already been produced. 2A: Analysis from scrach. 2B: Analysis of momenum wih pre-made columns. Experimen: Opion 1 If you are choosing opion one, your firs mission will be o creae a movie waching an overhead view of a collision beween wo Air Pucks. The collision should be one in which a moving puck approaches and collides wih a saionary puck. Once he movie is produced impor i ino LoggerPro o prepare for analysis. Then follow he guide for Opion 2A beginning a he second sep. Opion 2A: 1) Open he LoggerPro File eniled Scrach 2-D Puck Analysis 2) Begin he analysis by racking he posiion of boh pucks. 3) Be sure o include daa from before as well afer he collision. LoggerPro will keep rack of boh he X and Y posiions and velociies. 4) Se an origin a he beginning of he analysis 5) Se a Scale o conver ino meric posiion (widh of puck is 19 cm) 6) Creae a PuckMass parameer, find and ener he acual mass of he puck. 7) Creae Calculaed Columns by selecing New Daa Column in he Daa menu

6 Creae X-Momenum columns for boh pucks 1 and 2 Creae a Toal X Momenum Column by adding he wo above. Creae Y-Momenum columns for boh pucks 1 and 2 Creae a Toal Y Momenum Column by adding he wo above. Opion 2B: 1) Open Suden Analysis 2-D Puck LoggerPro Lab 2) Begin he analysis by racking he posiion of boh pucks. 3) Be sure o include daa from before as well afer he collision. LoggerPro will keep rack of boh he X and Y posiions and velociies. 4) LoggerPro will also keep rack of he X, Y and Toal Momenums of he pucks 5) This informaion will be ploed and displayed on he wo graphs Daa Analysis: Opion 1 and 2A: (The nex sep has already been done for Opion 2B) Creae and Display wo graphs each one displaying hree lines The firs graph should display he X momenum of puck 1, puck 2, and oal. The second graph should display he Y momenum of puck 1, puck 2, and oal. Inerpreaion: Wha does your daa sugges is happening o he Horizonal (X) momenum? Wha does your daa sugges is happening o he Verical (Y) momenum? Wha do you suppose his suggess abou he oal momenum of he sysem hroughou he video?

7 Follow-up Quesions 1) I has been said ha in an elasic collision like he one we performed, he angle made beween he pahs of he pucks afer he collision should be 90. The picure o he righ represens a collision similar o he one you sudied. Does i suppor or refue he saemen above? (Carefully measure o suppor your answer) 2) Now use he X and Y componens of he pos collision vecors from your daa o deermine he angle of deflecion from he original pah for each puck. Then calculae he angle beween he wo pahs. How well does his daa agree wih he saemen made in number 1? 3) In he pool rick shown in he picure a he righ he cue ball is inended o push he yellow ball direcly ino he side pocke and hen ravel down o hi he yellow sriped ball in he corner pocke. Discuss he physical possibiliy of successful compleion of his rick based on he physics displayed in his lab.

8 Wha he Puck? Vecor In his exploraion you are going o cause a collision beween wo air pucks, wih one siing sill and one moving ha his he firs. You wan o have hem hi so ha i is no a head on collision. 1) Deermine how you are going o ake he daa. You will need o clean off your able and use i o ake he daa as he floor will no work well. You will need o ake a video of he collision making sure you have daa before and afer he collision. 2) You will likely need o sand on he able o hold he camera above he moion o ge a good video. You will need o use good video pracices when aking you video. You can use he pucks as your scale. 3) Once you have your video in logger pro, analyze he video, remembering you will need o rack wo objecs. Once you have done he analysis, you will need o creae a calculaed column for he magniude of he oal velociy of he puck for each ime. 4) Once you have he velociy daa, use his and he mass o creae a vecor riangle showing he momenum before and afer he collision. Does he riangle close if drawn o scale? To find ou, measure he angles he pucks are moving afer he collision and draw a scale riangle and see if he iniial momenum of he moving puck is he equal o he vecor sum of he wo puck afer. Make your drawing on a whieboard. 5) If you riangle did no fully close, describe one or more possible reasons since we know momenum should have been conserved. 6) Wha is he angle beween he velociy vecors afer collision? Wha should hey be? Explain any differences.

9 Wha he Puck? using simulaions o check your knowledge 1) A nify EJS simulaion will allow you o explore he collision of virual pucks in he absence of all ha messy realiy (fricion, roaion, ec.). When you run he simulaion (linked below), you will see his: 2) You will wan o se V2 = 0 m/s, and adjus he posiion of puck 1 upward:

10 3) Click he sar buon and hi pause immediaely afer he collision: Look a he angle beween he wo momenum arrows. Measure wih a proracor for grins and giggles. To se up for anoher es, click he rese buon, rese V2 = 0 m/s, and posiion puck 1 o anoher verical locaion. 4) Use his simulaion o check your answers o he ranking ask exercise you compleed earlier: Each figure below shows a cue ball hiing an 8-ball a differen impac poins. Rank, from greaes o leas, he angle beween he balls afer collision A B C D E F Greaes Leas You can also mess around wih uneven masses, boh wih iniial velociies, ec. Have fun!

11 Wha he Puck? TIPERs for 2D Momenum Collisions 1) Below are bird s-eye views of six auomobile crashes an insan before hey occur. The auomobiles have differen masses and velociies. All auomobiles will remain joined ogeher afer he impac and skid o res. Rank hese auomobile crashes on he basis of he angle a which he wreckage skids. Le 0 0 be he angle oriened direcly oward he righ and measure angles counerclockwise from 0 0. Larges Smalles The ranking can no be deermined based on he informaion provided. 2) Explain he reason for your ranking:

12 3) Below are bird s-eye views of six auomobile crashes an insan before hey occur. The auomobiles have differen masses and velociies. All auomobiles will remain joined ogeher afer he impac and skid o res a he same angle, as measured from a line oriened direcly oward he righ. Rank hese scenarios on he basis of he iniial velociy of he auo raveling oward he op of he page. A 10 m/s 1000 kg 1000 kg Larges Smalles The ranking can no be deermined based on he informaion provided. 4) Explain he reason for your ranking:

13 5) For each of he collisions illusraed below, skech a graph of he momenum of aseroid A, he momenum of aseroid B, and he oal momenum in he sysem of he wo aseroids. Skech he horizonal and verical momenum separaely. Begin your graph before he collision akes place and coninue i afer he collision is over. Use a consisen scale on all graphs. a. The wo aseroids remain joined ogeher afer he collision. Px Py b. The wo aseroids remain joined ogeher afer he collision. 70 m/s A 100 m/s 700 kg B Px 1000 kg Py

14 6) For each of he collisions illusraed below, skech a graph of he momenum of aseroid A, he momenum of aseroid B, and he oal momenum in he sysem of he wo aseroids. Skech he horizonal and verical momenum separaely. Begin your graph before he collision akes place and coninue i afer he collision is over. The aseroids iniial velociies are boh oriened a he same angle from horizonal. Use a consisen scale on all graphs. a. The wo aseroids remain joined ogeher afer he collision. Px Py b. The wo aseroids remain joined ogeher afer he collision. 100 m/s 70 m/s A B 700 kg Px 1000 kg Py

15 7) For each of he collisions illusraed below, skech a graph of he momenum of aseroid A, he momenum of aseroid B, and he oal momenum in he sysem of he wo aseroids. Skech he horizonal and verical momenum separaely. Begin your graph before he collision akes place and coninue i afer he collision is over. a. The wo aseroids remain joined ogeher afer he collision and move direcly oward he op of he page. 100 m/s A vb 700 kg B Px 1000 kg Py b. The wo aseroids remain joined ogeher afer he collision and move direcly oward he righ. The aseroids iniial velociies are boh oriened a he same angle from horizonal. A 70 m/s 700 kg vb B 1000 kg Px Py

16 8) For each of he explosions illusraed below, skech a graph of he momenum of fragmen A, B, and C, and he oal momenum in he sysem of he hree aseroids. Skech he horizonal and verical momenum separaely. Begin your graph before he explosion akes place and coninue i as he fragmens move apar. The exploding egg is iniially a res. a. Fragmen A moves horizonally and fragmens B and C move a he same angle from horizonal afer he explosion. A 20 kg Px B C 10 kg 10 kg Py b. Fragmen B moves verically and fragmens A and C move a he same angle from verical afer he explosion. B A 10 kg Px 10 kg C 10 kg Py