Conservation Laws (Collisions) Phys101 Lab - 04

Transcription

1 Conservaton Laws (Collsons) Phys101 Lab Objectves The objectves o ths experment are to expermentally test the valdty o the laws o conservaton o momentum and knetc energy n elastc collsons. 2. Theory 2.1 Conservaton o Lnear Momentum For a system o partcles, the orces that these partcles exert upon each other are termed nternal orces, whle the orces exerted on the system by agents outsde the system are termed external orces. I there are no external orces exerted on the system, the system s called an solated system. Consder an solated system comprsed o just two partcles, or objects, o mass m 1 and m2 that are allowed to collde wth each other. The ree body dagrams o the two partcles are shown here. Accordng to Newton's Thrd Law F 12= F 21, so the net orce on the system s zero. Ths can be combned wth Newton's Second Law. Combnng Newton's Thrd Law wth Newton's Second Law d p =0, where p = p 1 p 2 s the total lnear momentum o the system. leads to: F 12 F 21= dt Thereore, when two partcles collde, wth no net external; orces appled. The total lnear momentum o the partcles s conserved. Or, equvalently stated, the net momentum o the two partcles pror to the collson s equal to the net momentum o the two partcles ater the collson. 2.2 Conservaton o Knetc Energy For all collsons where the net external orces are equal to zero, momentum s conserved. Total Knetc Energy o a system s not necessarly conserved, even the net external orce on the partcles s zero. I the Total Knetc Energy ( the sum o the knetc energy o all the partcles ) o a system s conserved, then we call that system Perectly Elastc. In most realstc stuatons collsons are nether perectly elastc or perectly nelastc. In ths lab, you wll mnmze any losses due to rctonal orces by loatng the pucks over a cushon o ar and attempt to smulate a nearly perectly elastc collson. The success o your attempt can be expermentally vered by measurng the knetc energy o the system beore and ater the collson.

2 Name: Sec./Group Date: Prelab: Y Poston vs X poston y(cm) x(cm) 1.) Consder a 0.52 g puck that moves as shown n the graph above. Consder each pont to be a pcture o the puck and consder that 60 pctures were taken each second. Plot the x poston versus tme and the y poston versus tme and use a lnear trend lne to nd the x component o the velocty and the y component o the velocty. Attach you graphs. a.) What are the x component o the velocty and the y component o the velocty? b.) Wrte the velocty o the puck n and j notaton and n magntude and angle notaton. c.) What s the momentum o the puck? (Wrte t both n I and j notaton and as a magntude and an angle.)

3 Y Poston vs X poston y(cm) x(cm) 2.) Consder the collson o a m1 = 0.52 g puck movng as shown n the graph, whch colldes wth a m2 = 0.32 g puck ntally at rest. Only the track o the m1 = 0.52 g puck, whch s ntally movng, s shown n the graph. Consder each pont to be a pcture o the puck and consder that 60 pctures were taken each second. a.) What s the ntal momentum o the m1 puck? (Wrte n both I and j ormat and as a magntude and an angle.) a.) What s the nal momentum o the m1 puck? (Wrte n both I and j ormat and as a magntude and an angle.) c.) What s the nal momentum o the m2 puck? (Wrte n both I and j ormat and as a magntude and an angle.)

4 Procedure: In ths experment you wll take vdeo o collsons o pucks on a rctonless table. The table s made rctonless much lke an ar hockey table s made rctonless, wth the excepton that nstead o orcng ar up through the table, ar s by pumped down through and under the pucks. You wll use these vdeos to analyze the collsons. Fgure 3.1 The VdeoPont Icons Ths wll nvolve two peces o sotware. As the name suggests, VdeoPont Capture s the sotware or controllng the vdeo camera and capturng the vdeo. VdeoPont Physcs Fundamentals s the sotware that wll be used to analyze the data. The analyss that the sotware provdes s a lst o x and y coordnates as a uncton o tme. Ths poston versus tme data wll be exported to a spreadsheet, where the velocty as a uncton o tme wll be computed. In ths lab, you wll very total lnear momentum and total knetc energy o a system are conserved durng collsons. The collsons you wll observe wll be between two pucks ( masses ) on an ar table. You wll consder two collsons n ths lab. The rst collson wll consst o one puck at rest and a second puck colldes wth a glancng blow ( Fgure 3.2 ). The second collson wll conssts o two pucks, both pucks ntally n moton, colldng together( Fgure 3.3 ). Fgure 3.2 Collson Number One One Puck Intally at Rest.

5 Fgure 3.3 Collson Number Two Both Pucks Intally n Moton. (a) (b) (c) (d) (e) Fgure 3.4 Ar Table, Compressor Pump, and Pucks. To elmnate rcton an ar table s used. The ar table, ar compressor, and pucks are shown n Fgure 3.4. The table must be level, and ths s accomplshed by adjustng the heght o the legs shown n Fgure 3.4e. The ar compressor shown n Fgure 3.4b pumps ar through tubes and through the center o the pucks ( Fgure 3.4c and 3.4d ). The pucks have two derent masses. Your TA wll tell you the masses or they wll be wrtten on the pucks. The masses are probably 0.21 kg and 0.52 kg. The compressor s turned on by pluggng t n. Do not turn on the compressor untl you are ready to take data.

6 Part One: Two Puck Collsson, One Puck Intally at Rest Capturng the Vdeo Clp: 1. Open the VdeoPont Capture Sotware by clckng on the con on the desktop. The cons are shown n Fgure 3.1. The openng screen should resemble Fgure 3.5. Fgure 3.5 VdeoPont Capture Openng Screen 2. Next, turn on the camera. 3. Clck on the Capture Button. Ths should brng up a screen whch resembles Fgure 3.6. You should the vdeo nput rom the camera. I you do not see any vdeo nput but nstead see a black screen, clck on the settngs button. A pop-up wndow wll appear ( Fgure 3.7 ) wth a drop down menu wll appear whch lsts the cameras attached to the computer along wth other camera settngs. Choose the proper camera and press the OK button. ( I you stll do not see any vdeo, make sure the camera s on and press record, then press stop, and then press the back arrow. ) Fgure 3.6 VdeoPont Capture Normal Operaton Fgure 3.7 Selectng the camera and settngs.

7 4. Data can now be collected by capturng a vdeo. The camera s mounted over the table. Recordng the data s started by httng the Record button. When recordng, the Record button s grayed out. Keep the large mass at rest and re the smaller mass to provde a glancng blow ( Fgure 3.8 and Fgure 3.9 ). The lm may now be edted wth the VdeoPont Capture Sotware. Fgure 3.8 Beore the Collson. Collson o two masses where one mass s ntally at rest. Fgure 3.9 Ater the collson. Collson o two masses where one mass s ntally at rest.

8 Fgure 3.10 VdeoPont Capture collectng data. Notce that the Record button s grayed out. 5. Once the Stop button s pressed, edtng may begn. Save the vdeo clp as a.mov move le usng the Fle drop down menu at the top o the screen. Edtng the Vdeo Clp: 6. Data analyss wll be easer the length o the vdeo s cropped to nclude only the rames o nterest. Ater the stop button, the edtng screen wll appear. The edtng screen contans a set o controls much lke the set o controls on any dvd player. There are buttons or play, ast orward, ast rewnd, step orward, and step backward. When the play button s pressed, the vdeo wll begn to play, and the button s transormed nto a stop button. These controls are shown n Fgure 3.8. There s also a sldebar wth a black damond on the top. Sldng ths black damond along the slde bar advances/recedes the vdeo clp. Use these controls to revew the lm clp to decde where to crop the vdeo clp. There are also two whte trangles. These trangles are to mark the start and end o the rames that are to be analyzed.

9 Black Damond Whte Trangle Start Fgure 3.11 VdeoPont Capture Edtng Screen Whte Trangle Fnsh 7. Ater revewng the vdeo clp, use the whte trangles to mark the start and nsh o the rames that wll be analyzed. Make sure that the start s marked ater the puck has cleared the hand o the person shootng the puck. Deletng approxmately ve rames ater the puck s released s recommended. Once you have chosen the start and nsh, clp on the Conrm Edt button. Ths wll crop the vdeo clp to the chosen length. ( See Fgure 3.12 ) 8. Ater checkng that the lm clp has the needed rames, save the lm clp. Fgure 3.12 VdeoPont Capture Edtng Screen

10 Analyzng the Vdeo Clp: 9. Open the VdeoPont Physcs Fundamentals Sotware. Usng the Fle drop down menu, load the vdeo clp move le saved n step 8. Fgure 3.13 VdeoPont Physcs Fundamentals Prevew Screen 10. The rst screen can be used to vew the vdeo clp. Ths screen s labeled as the Prevew Screen n the tabs whch run along the top o the screen. These tabs may be used to navgate through the program. As each screen progresses, a hnt wll appear n a pop up wndow. These hnts can be closed usng the X button n the upper, rght hand corner o the pop up wndow. Once the clp has been vewed, advance to the next screen usng the orward arrow button. 11. Ths screen s the calbrate screen. Here a yellow calbraton tool can be ound. Move one end o the calbraton tool to meet wth one end o the meter street ( or some other known standard ) and move the other end o the yellow calbraton tool to meet wth the other end o the meter stck. Enter the length o the object between the jaws o the calbraton tool, one meter the meter stck s used. Advance to the next screen. Fgure 3.14 VdeoPont Physcs Fundamentals Calbraton Screen

11 12. Ths s the Set Up Analyss rame. Set the orgn usng Move Orgn x and y poston boxes. The axs may also be rotated and the t = 0.0 seconds rame may also be set. Go to the next rame. Fgure 3.15 VdeoPont Physcs Fundamentals Set Up Analyss Screen 13. Ths s the Collect Data screen. Here the mouse can be used to select data ponts on the screen whle n the Data Collecton Mode. As the data pont s selected, the vdeo clp advances to the next rame. The set o data ponts may be completely deleted by selectng the data set name ( ex. Ponts S1 ) and pressng the Delete button. A new set may be started wth the Add New Ponts drop down menu and httng the OK button. Pont locatons may be moved whle n the Pont Edtng Mode. When n the Pont Edtng Mode, the mouse can grab the pont and drag t to a new poston. Once the ponts have been collected or the one puck a wndow wll appear that allows you to set up a second set o ponts ( Fgure 3.17 ). Select Track another pont ( New Seres ) and select OK.

12 Pont Edtng Mode Data Collecton Mode Fgure 3.16 VdeoPont Physcs Fundamentals Collect Data Screen 14. Export the data set nto a spreadsheet usng the le drop down menu. Fgure 3.17 VdeoPont Physcs Fundamentals Collect Data Screen

13 Fgure 3.18 VdeoPont Physcs Fundamentals Collect Data Screen Fgure 3.19 VdeoPont Physcs Fundamentals Export Data Menu

14 Analyzng the Data Collected: 15. Open the spreadsheet contanng the data collected. 16. Plot the y poston versus the x poston. 17. Calculate the x and y components o the ntal and nal veloctes o each o the pucks by usng the lnear trendlnes o poston versus tme plots. Part One: Two Puck Collsson, Both Pucks Intally n Moton 18. Repeat steps 1 through 17, ths tme colldng two pucks ntally n moton. Fgure 3.20 Collsons o Two Puck, Both Pucks Intally n Moton. Fgure 3.21 Collsons o Two Puck, Both Pucks Intally n Moton.

15 Data Analyss: Part One: Two Puck Collson, One Puck Intally at Rest m1= kg m2= kg v 1x = m/ s v 1y = m/ s v1x = m/ s v1y = m/ s v 2x = m/ s v 2y = m/ s p1x = kg m/ s p1y = kg m/ s p 1x = kg m/ s p 1y = kg m/ s p 2x = kg m/ s p 2y = kg m/ s p x = kg m/ s p y = kg m / s p x = kg m/ s p y = kg m/ s K = J K = J a.) Was momentum conserved? b.) Fnd the percent derence between the ntal momentum and the nal momentum. p y p y 100 % p x p x 100 % % d = % d x = y, ( Note: I the y component o the ntal py px momentum s equal to zero, use the nal value o the y component momentum or the puck ntally n moton.) c.) Was knetc energy conserved? d.) Fnd the percent derence between the ntal knetc energy and the nal knetc energy.

16 Part Two: Two Puck Collson, Two Pucks Intally n Moton m1= kg m2= kg v 1x = m/ s v 1y = m/ s v 2x = m / s v 2y = m/ s v1x = m/ s v1y = m/ s v 2x = m/ s v 2y = m/ s p1x = kg m/ s p1y = kg m/ s p2x = kg m/ s p2y = kg m/ s p 1x = kg m/ s p 1y = kg m/ s p 2x = kg m/ s p 2y = kg m/ s p x = kg m/ s p y = kg m / s p x = kg m/ s p y = kg m/ s K = J K = J a.) Was momentum conserved? b.) Fnd the percent derence between the ntal momentum and the nal momentum. p y p y 100 % p x p x 100 % % d x =, % d y = px py c.) Was knetc energy conserved? d.) Fnd the percent derence between the ntal knetc energy and the nal knetc energy.