PHYSICS LAB Experiment 7 Fall 2004 CONSERVATION OF MOMENTUM & COLLISIONS

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1 PHYSICS 83 - LAB Experiment 7 Fall 004 CONSERVATION OF MOMENTUM & COLLISIONS In this experiment we will study how the total vector momentum of an isolated system is conserved (remains constant) in collisions. If the total kinetic energy is also conserved in the collision, the collision is called elastic. Otherwise, it is called an inelastic collision. You will study both elastic collisions (kinetic energy is conserved) and perfectly inelastic collisions (where objects stick together after the collision). THE THEORY Momentum is a vector quantity, defined as p = Mv (or ), where v is the velocity vector of the mass, M. We will be dealing with two gliders, of mass M and M which will collide on a frictionless air track. i The initial velocity of glider will be written as v (the initial velocity of M will always f = 0, i.e. M starts out at rest). The final velocities of the two masses will be written as v and v f. Perfect inelastic collisions: Because the two masses stick together after the collision, v f =v f =v f. If we now equate the momenta before and after the collision, we have () We can also look at the initial and final kinetic energies. ()

2 PHYSICS 83 - LAB Experiment 7 Fall 004 Elastic collisions: Here, the two masses have different vector velocities (M may stop, or even change direction). Both the total momentum and total kinetic energy after the collision are equal to their values before the collision. We then have: (3) (4) From (3) and (4) we get: (5) and (6) DATA SETUP A separation of about 50 to 80 cm between the two photogates is convenient. Use a glider car to check that the segment of the air track between the photogates is approximately level. If not, call an instructor or carefully adjust the height of the end of the track supported by a single long screw. (Later, if you suspect that there are systematic errors due to the track being non-level, you can reverse the positions of the gliders to distinguish between effects due to the gliders and those due to the track but be sure to enter new mass values into the computer program). The masses of the gliders and the lengths of the flags have been predetermined. The value of the mass of each glider is marked on the glider. The flags are 5cm = 0.05m long.

3 PHYSICS 83 - LAB Experiment 7 Fall 004 DATA COLLECTION Part : Inelastic collisions: You will investigate perfectly inelastic collisions, where the gliders stick together after the collision, and kinetic energy is not conserved. In this case, glider is initially at rest between the two timers and should NOT have a timer flag in place.. Orient the gliders so the ends with Velcro face each other.. Your computer should be set up with Data Studio loaded. If not, contact the instructor. 3. Load the correct file: File Open 83Exp7_inel 4. If data sheet is not blank, then Experiment Delete All Data Runs 5. Save the file with your initials: File Save Activity As 83E7_your initials (no spaces or periods) 6. Enter the values of the masses (M and M) in Kgrams into the program: I) Click on Calculate (on the tool bar) to open the calculator window ii) Click on Experimental Constants iii) Click on to see the possible choices iv) Click on Mass (to enter the value of Mass ) v) Enter the correct value in the Value box (use kg units) vi) Click Accept (Make sure you click the correct Accept box accepting the experimental constant) vii) Repeat steps iii) vi) with Mass 7. Turn on the air to the air track. Note: Glider # should go through photogate # (the photogate connected to digital channel # on the black interface box). 8. Set glider # near the second photogate in the proper orientation (Velcro facing glider #). 9. Click on Start 0. Data taking has now started. Collide glider # with glider #, which should be at rest before the collision. Catch the gliders before they go back through the second photogate. 3

4 PHYSICS 83 - LAB Experiment 7 Fall 004. Repeat the above step until you have between 5 and 0 or so measurements, spanning a reasonable range of initial momenta (there should be at least a factor of two difference between the lowest and highest recorded momenta, and try for a factor of 4 or 5).. Click on } Stop and turn off the air track. 3. This ends the data run. To save the data, click on File Save Activity. It will be saved with the name you gave it in Step 5. above. 4. Make sure the data window is the active window (ask your instructor if you are not sure). Then print out a copy (File Print). 5. The program has also produced graphs of the difference between the final momentum and the initial momentum as a function of the initial momentum (i.e.p P vs. P ). Make this plot the active window and print it as in Step 4. Do the same with the plot of K / K vs. P. If you don t see the plots, click Window Tile then click the G, maximize icon in the upper right hand part of the graph window. 6. The points on the graph will appear either as symbols or dots. If two symbols would be closer than a certain distance, the program shows one or both of them as dots. If you would like to have only the dots on the data points, click on the graph settings menu at the extreme right end of the toolbar above the graph and click on (to turn off the check mark) the Data Symbols item. All data points should now appear as dots, with different runs appearing in different colors, instead of different symbols. Part : Elastic collisions of nearly equal masses: In this part of the experiment, you will investigate elastic collisions, where the masses are approximately equal (M M). In this case, kinetic energy is conserved. As in the study of inelastic collisions, glider # is initially at rest between the two timers. However, the timing flag should now be INSERTED into the holder atop glider #.. Orient the gliders so the ends with the bumper ends facing each other.. Load the correct file: File Open 83Exp7_el_part 3. If data sheet is not blank, then Experiment Delete All Data Runs 4

5 PHYSICS 83 - LAB Experiment 7 Fall Save the file with your initials: File Save Activity As 83E7_ your initials (no spaces or periods). Be careful to use the _ instead of the _ used for the inelastic collisions. 5. Enter the values of the masses (M and M) into the program: See step 6. in Part of the experiment (inelastic collisions). 6. Turn on the air to the air track 7. Set glider # near the second photogate in the proper orientation (bumper end facing the bumper end of glider #). 8. Click on Start 9. Data taking has now started. Collide glider # with glider #, which should be at rest before the collision. Catch the gliders before they go back through the photogates. 0. Repeat the above step until you have between 5 and 0 or so measurements, spanning a reasonable range of initial momenta (there should be at least a factor of two difference between the lowest and highest recorded momenta, and try for a factor of 4 or 5).. Click on } Stop and turn off the air to the air track.. This ends the data run. To save the data, click File Save Activity. It will be saved with the name you gave it in Step 4. above. 3. Follow steps of Part (inelastic collisions). Part 3: Elastic collisions of unequal masses: In this part of the experiment, you will investigate elastic collisions, where the masses are unequal (M >> M). Kinetic energy is still conserved, but Mass will not be stationary after the collision [see equation (5)], so its final momentum and kinetic energy must also be taken into account. As before, glider is initially at rest between the two timers, with its timing flag in place.. Attach two 50 gram weights to glider # with masking tape, so that M M + 0.kg. 5

6 PHYSICS 83 - LAB Experiment 7 Fall 004. Load the correct file: File Open 83Exp7_el_part3 3. If data sheet is not blank, then Experiment Delete All Data Runs 4. Save the file with your initials: File Save Activity As 83E7_3 your initials (no spaces or periods). Be careful to use the _3 instead of the _ used for the previous part. 5. Enter the values of the masses (M and M) into the program: See step 6. in Part of the experiment (inelastic collisions). 6. Turn on the air to the air track 7. Set glider # near the second photogate in the proper orientation (bumper end facing the bumper end of glider #). 8. Click on Start 9. Data taking has now started. Collide glider # with glider #, which should be at rest before the collision. Catch glider # AFTER it goes back through the first photogate, and glider # before it goes back through the second photogate. 0. Because you will record the passage of glider # back through the first photogate, you have to end the run after each trial. Click on } Stop to end the run.. For each run, record on the worksheet: V, Mom (glider # approaching glider #), V, Mom (glider # continuing in the original direction of glider #), V f, Momf (glider # going back through the first photogate this will be on the second row of the first two columns of the data sheet). Repeat the steps 8.. until you have between 5 and 0 or so measurements, spanning a reasonable range of initial momenta (there should be at least a factor of two difference between the lowest and highest recorded momenta, and try for a factor of 4 or 5). 3. Turn off the air. If you missed taking (or want to check) the data from one of the runs, do the following for each column in the data table: i) Click on the column to make it the active column (it will be surrounded by a black rectangle) ii) Click the Data button iii) Click the run # you want to see. The run # should appear under the column title with the data below that. 6

7 PHYSICS 83 - LAB Experiment 7 Fall This ends the data taking for this part of the experiment. To save the data click on File Save Activity. Your data will be saved with the file name you gave it in Step 4. above. 7

8 PHYSICS 83 - LAB Expt 7 Worksheet and Data Analysis Fall 004 CONSERVATION OF MOMENTUM & COLLISIONS STUDENT NAME DATE PARTNER S NAME LAB SECT Mass of the glider #, M = kg Mass of glider #, M= kg Table : Elastic collisions, M << M Ru n # V Mom K.E. V Mom K.E. Vf Momf K.E.f Data Analysis: For each of the three sets of collisions do the following:. Plot the momentum balance delmom = (p f p) i vs. p i for each collision.. Determine the average value of delmom and its standard deviation. 3. Plot the kinetic energy ratio KErat = K f / K i vs. pi 4. Determine the average value of KErat and its standard deviation.

9 PHYSICS 83 - LAB Expt 7 Worksheet and Data Analysis Fall 004 QUESTIONS. Based on your calculation of the average momentum balance, <delmom>, in each of the 3 different types of collision, is momentum conserved in each of the types of collision? i.e. is the value of <delmom> consistent with zero within standard deviations? If not, within how many standard deviations?. (a) Is the momentum imbalance systematically biased in a particular direction? (b) What are two potential sources of systematic bias? Be specific and explain how the measurements and the momentum imbalance might be affected. 3. (a) Calculate the expected value of the ratio of final to initial kinetic energy for each type of collision. (b) Do the data agree with your prediction? i.e. within how many standard deviations of the prediction is the data in each case? c) For the inelastic case, the kinetic energy is not expected to be conserved. Where does the kinetic energy in this case go?

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