Conservation of Momentum Experiment

Independent Study Project

Daniel Dickinson and Rick Martin

Purpose

To verify that momentum is conserved, using a variety of situations.
i) explosions - one dimensional
ii) collisions - one dimensional
iii) couplings - one dimensional
iv) angular

Hypothesis

We expect that our experiments will show that momentum is conserved.

Materials

air track			2 sets of photogates	
2 air track gliders		SuperCHAMP system
variety of masses		2 velcro couplers
springs				electronic balance
5cm x 5cm paper cards		masking tape and string
rotating disc			2 discs of different sizes
metal bar               	4 retort stands

Procedure

Linear Motion

  1. Set up air track with two sets of photogates a set distance apart.
  2. Equalize masses of gliders with 5 cm cards on top.
  3. Load Superchamp program experiment on collisions.
  4. Push gliders at similar speeds towards each other from either end of air track so that the two gliders collide between the two sets of photogates.
  5. Repeat five times.
  6. Add 20 gram mass to glider one and record total mass.
  7. Repeat steps four and five.
  8. Add 50 gram mass to glider one and record total mass.
  9. Repeat steps four and five.
  10. Place one glider between photogates.
  11. Push other glider towards the stopped glider.
  12. Repeat five times.
  13. Add 50 gram mass to the moving glider. Record mass.
  14. Repeat steps ten to twelve.
  15. Remove the 50 gram mass and place it on the stationary glider. Record mass.
  16. Repeat steps ten to twelve.
  17. Attach velcro strips to ends of gliders.
  18. Push gliders towards each other from either sides of the photogates.
  19. Repeat five times.
  20. Remove velcro strips.
  21. Tie the gliders together compressing the springs on each end of the gliders.
  22. Place in the middle of the sets of photogates.
  23. Cut the string between the gliders.
  24. Repeat three times.
  25. Add 50 gram mass to glider one.
  26. Repeat steps 21 to 24

Angular Momentum

Calculations

Linear Momentum

Momentum before = Mass * Velocity before
Momentum after  = Mass * Velocity after
Total momentum before = momentum of glider 1 before + 	
			momentum of glider 2 before
Total momentum after  = momentum of glider 1 after + 	
			momentum of glider 2 after

Absolute difference = | momentum before - momentum after |
Percent error  = Absolute Difference / momentum before * 100 


 	Table 1
                      
    A     = Trial
    B     = Mass of glider 1 in kg
    C     = Velocity of glider 1 before collision, coupling, or 
	    explosion in m/s
    D     = Velocity of glider 1 after collision, coupling, or 
	    explosion in m/s
    E     = Momentum of glider 1 before in kg.m/s
    F     = Momentum of glider 2 after in kg.m/s

 A       B            C            D            E           F  
=============================================================== 
Collisions, both moving
 1      0.23295     0.7474     -0.4044     0.174107    -0.094205
 2      0.23295     0.6720     -0.5456     0.156542    -0.127098
 3      0.23295     0.6702     -0.4735     0.156123    -0.110302
 4      0.23295     0.6083     -0.4854     0.141703    -0.113074
 5      0.23295     0.7102     -0.3520     0.165441    -0.081998

 1      0.25317     0.7547     -0.3266     0.191067    -0.082685
 2      0.25317     0.6333     -0.2459     0.160333    -0.062255
 3      0.25317     0.559      -0.3851     0.141750    -0.097496
 4      0.25317     0.5869     -0.2931     0.148585    -0.074204
 5      0.25317     0.5485     -0.2665     0.138864    -0.067470

 1      0.28322     0.7559      0.3407     0.214086     0.096493
 2      0.28322     0.5653      0.3962     0.096493     0.112212
 3      0.28322     0.6812      0.2023     0.160104     0.057295
 4      0.28322     0.6414      0.2068     0.112212     0.058570
 5      0.28322     0.5787      0.1390     0.192929     0.039300

	Table 2

    A     = Trial Number
    B     = Mass of glider 2 in kg
    C     = Velocity of glider 2 before collision, coupling, or
            explosion in m/s
    D     = Velocity of glider 2 after collision, coupling, or
            explosion in m/s
    E     = Momentum of glider 2 before in kg.m/s
    F     = Momentum of glider 2 after in kg.m/s

 A       B            C            D            E           F    
=================================================================
Collisions, both moving
 1      0.23295    -0.4958      0.6028     -0.11550     0.140422
 2      0.23295    -0.6321      0.5181     -0.14725     0.120691
 3      0.23295    -0.5747      0.5155     -0.13388     0.120086
 4      0.23295    -0.5734      0.4850     -0.13357     0.112981
 5      0.23295    -0.4223      0.5834     -0.09837     0.135903

 1      0.23295    -0.4699      0.6680     -0.10946     0.155611
 2      0.23295    -0.3775      0.5757     -0.08794     0.134109
 3      0.23295    -0.5181      0.4801     -0.12069     0.111839
 4      0.23295    -0.4290      0.5211     -0.09994     0.121390
 5      0.23295    -0.3934      0.4936     -0.09164     0.114984

 1      0.23295     0.6169      0.7491      0.14371     0.174503
 2      0.23295     0.6435      0.5727      0.17450     0.133410
 3      0.23295     0.5238      0.6689      0.14990     0.155820
 4      0.23295     0.5038      0.6333      0.13341     0.147527
 5      0.23295     0.4452      0.5631      0.12202     0.131174

	Table 3
	                       
    A     = Trial Number
    B     = Total momentum before in kg.m/s
    C     = Total momentum after in kg.m/s
    D     = Absolute value of difference in momentums
    E     = Percent Error

 A       B            C            D            E
=====================================================    
Collisions, both moving
 1      0.058610    0.04622     0.01239294     21.14
 2      0.009295    0.00641     0.00288858     31.08
 3      0.022247    0.00978     0.0124628      56.02
 4      0.008130    0.00009     0.00803677     98.85
 5      0.067066    0.05390     0.01316168     19.62

 1      0.081604    0.07293     0.00867892     10.64
 2      0.072394    0.07185     0.00053912      0.74
 3      0.021058    0.01434     0.00671496     31.89
 4      0.048650    0.04719     0.00146381      3.01
 5      0.047221    0.04751     0.00029310      0.62

 1      0.357793    0.27100     0.08679695     24.26
 2      0.270996    0.24562     0.02537367      9.36
 3      0.310008    0.21312     0.09689193     31.25
 4      0.245622    0.20610     0.03952510     16.09
 5      0.314949    0.17054     0.14440695     45.85

	Table 4
                      
    A     = Trial
    B     = Mass of glider 1 in kg
    C     = Velocity of glider 1 before collision, coupling, or 
            explosion in m/s
    D     = Velocity of glider 1 after collision, coupling, or 
            explosion in m/s
    E     = Momentum of glider 1 before in kg.m/s
    F     = Momentum of glider 2 after in kg.m/s

 A       B            C            D            E           F  
=============================================================== 
Collisions, one stopped
 1      0.23295     0.8264       0.0000     0.192510     0.000000
 2      0.23295     0.7639       0.0000     0.177951     0.000000
 3      0.23295     0.8591       0.0000     0.200127     0.000000
 4      0.23295     0.6935       0.0000     0.161551     0.000000
 5      0.23295     0.7337       0.0000     0.170915     0.000000

 1      0.28322     1.0140       0.0000     0.287185     0.000000
 2      0.28322     0.6920       0.0000     0.195988     0.000000
 3      0.28322     0.7616       0.0000     0.215700     0.000000
 4      0.28322     0.6757       0.0000     0.191372     0.000000
 5      0.28322     0.6246       0.0000     0.176899     0.000000

 1      0.23295     0.8584       0.0000     0.199964     0.000000
 2      0.23295     0.7639       0.0000     0.177951     0.000000
 3      0.23295     0.9363       0.0000     0.218111     0.000000
 4      0.23295     1.1390       0.0000     0.265330     0.000000
 5      0.23295     0.8306       0.0000     0.193488     0.000000

	Table 5

    A     = Trial Number
    B     = Mass of glider 2 in kg
    C     = Velocity of glider 2 before collision, coupling, or 
            explosion in m/s
    D     = Velocity of glider 2 after collision, coupling, or 
            explosion in m/s
    E     = Momentum of glider 2 before in kg.m/s
    F     = Momentum of glider 2 after in kg.m/s

 A       B            C            D            E           F
=================================================================
Collisions, one stopped    
 1      0.23295     0.0000       0.7418     0.000000     0.172802
 2      0.23295     0.0000       0.6831     0.000000     0.159128
 3      0.23295     0.0000       0.7722     0.000000     0.179884
 4      0.23295     0.0000       0.6211     0.000000     0.144685
 5      0.23295     0.0000       0.6588     0.000000     0.153467

 1      0.23295     0.0000       1.0050     0.000000     0.234115
 2      0.23295     0.0000       0.6725     0.000000     0.156659
 3      0.23295     0.0000       0.7413     0.000000     0.172686
 4      0.23295     0.0000       0.6720     0.000000     0.156542
 5      0.23295     0.0000       0.6017     0.000000     0.140166

 1      0.28322     0.0000       0.6854     0.000000     0.194119
 2      0.28322     0.0000       0.6035     0.000000     0.170923
 3      0.28322     0.0000       0.7491     0.000000     0.212160
 4      0.28322     0.0000       0.9200     0.000000     0.260562
 5      0.28322     0.0000       0.6540     0.000000     0.185226

	Table 6
	                       
    A     = Trial Number
    B     = Total momentum before in kg.m/s
    C     = Total momentum after in kg.m/s
    D     = Absolute value of difference in momentums
    E     = Percent Error

 A       B            C            D            E
=====================================================    
Collisions, one stopped    
 1      0.192510    0.172802     0.019708   10.24
 2      0.177951    0.159128     0.018822   10.58
 3      0.200127    0.179884     0.020243   10.12
 4      0.161551    0.144685     0.016866   10.44
 5      0.170915    0.153467     0.017448   10.21

 1      0.287185    0.234115     0.053070   18.48
 2      0.195988    0.156659     0.039329   20.07
 3      0.215700    0.172686     0.043015   19.94
 4      0.191372    0.156542     0.034829   18.20
 5      0.176899    0.140166     0.036733   20.77


 1      0.199964    0.194119     0.005845    2.92
 2      0.177951    0.170923     0.007027    3.95
 3      0.218111    0.212160     0.005951    2.73
 4      0.265330    0.260562     0.004768    1.80
 5      0.193488    0.185226     0.008262    4.27

	Table 7
                      
    A     = Trial
    B     = Mass of glider 1 in kg
    C     = Velocity of glider 1 before collision, coupling, or
            explosion in m/s
    D     = Velocity of glider 1 after collision, coupling, or
            explosion in m/s
    E     = Momentum of glider 1 before in kg.m/s
    F     = Momentum of glider 2 after in kg.m/s

 A       B            C            D            E           F  
=============================================================== 
Couplings, both moving
 1      0.23295     0.3440       0.0000     0.080135     0.000000
 2      0.23295     0.4864       0.0000     0.113307     0.000000
 3      0.23295     0.4978       0.0000     0.115963     0.000000
 4      0.23295     0.4292       0.0000     0.099982     0.000000
 5      0.23295     0.5869       0.0000     0.136718     0.000000

	Table 8

    A     = Trial Number
    B     = Mass of glider 2 in kg
    C     = Velocity of glider 2 before collision, coupling, or
            explosion in kg.m/s
    D     = Velocity of glider 2 after collision, coupling, or
            explosion in kg.m/s
    E     = Momentum of glider 2 before in kg.m/s
    F     = Momentum of glider 2 after in kg.m/s

 A       B            C            D            E           F    
=================================================================
Couplings, both moving
 1      0.23295     0.3310      0.00000    -0.077106     0.000000
 2      0.23295    -0.4902      0.00000    -0.114192     0.000000
 3      0.23295    -0.4785      0.00000    -0.111467     0.000000
 4      0.23295    -0.4543      0.00000    -0.105829     0.000000
 5      0.23295    -0.6472      0.00000    -0.150765     0.000000


	Table 9
	                       
    A     = Trial Number
    B     = Total momentum before in kg.m/s
    C     = Total momentum after in kg.m/s
    D     = Absolute value of difference in momentums
    E     = Percent Error

 A       B            C            D            E
==========================================================	
Couplings, both moving
     1     0.003028     0.000000     0.003028         7.75
     2    -0.000885     0.000000     0.000885        11.43
     3     0.004496     0.000000     0.004496        11.19
     4    -0.005847     0.000000     0.005847        10.64
     5    -0.014047     0.000000     0.014047        15.18

Table 10

Lost to data corruption

Table 11

Explosions, different masses
 1      0.27946     0.0000       0.2139     0.000000     0.059776
 2      0.27946     0.0000       0.1749     0.000000     0.048878
 3      0.27946     0.0000       0.2904     0.000000     0.081155

	Table 12
	                       
    A     = Trial Number
    B     = Total momentum before in kg.m/s
    C     = Total momentum after in kg.m/s
    D     = Absolute value of difference in momentums
    E     = Percent Error

 A       B            C            D         E
=====================================================        
Explosions, equal masses 
 1      0.000000   -0.014777     0.014777   5.04
 2      0.000000   -0.012828     0.012828   7.92
 3      0.000000   -0.015395     0.015395   7.07

Explosions, different masses
 1      0.000000   -0.021270     0.021270   6.24
 2      0.000000   -0.050798     0.050798   5.40
 3      0.000000   -0.025280     0.025280   8.35

Calculations for Angular Momentum

Moment of Inertia = Sum of all m.r2's

Angular Momentum  = Angular Velocity * Moment of Inertia

Absolute Difference = Angular momentum before - 
			Angular momentum after    
     
Percent Error = Absolute Difference / 
		Angular momentum before * 100
     
	                        Table 1
                    
        Object                Mass(g) Radius(cm)   mr2(kg.m2)
    ==========================================================
    original disc              712.05      12.75    0.000908
    large disc                 743.41      12.75    0.000948
    metal bar                  621.74      14.05    0.000874
    small disc                 107.48       5.60    0.000060
    masses(1)                  200.55       3.50    0.000070
    masses(2)                  300.55       5.60    0.000168

	Table 2

       A     = Reading
       B     = Angular Velocity(rad/s)
       C     = Moment of Inertia Before in kg.m2
       D     = Angular Momentum before in rad.kg.m2/s

     A     B           C              D
    ==============================================
    Original disc + large disc, trial 1
     1    17.47     0.00090786       0.015860
     2    16.99     0.00090786       0.015425
     3    16.47     0.00090786       0.014953
     4    15.99     0.00090786       0.014517
     5    15.33     0.00090786       0.013918

    Original disc + large disc, trial 2
     1    18.83     0.00090786       0.017095
     2    18.56     0.00090786       0.016850
     3    18.23     0.00090786       0.016550
     4    17.94     0.00090786       0.016287
     5    17.66     0.00090786       0.016033

    Original disc + large disc, trial 3
     1    10.61     0.00090786       0.009632
     2    10.45     0.00090786       0.009487
     3    10.27     0.00090786       0.009324
     4    10.06     0.00090786       0.009133
     5    9.852     0.00090786       0.008944

	Table 3

       A     = Reading
       B     = Angular Velocity(rad/s)
       C     = Moment of Inertia After in kg.m2
       D     = Angular Momentum after in rad.kg.m2/s

     A     B           C              D
    ==============================================
    Original disc + large disc, trial 1
     1     6.49     0.00185571       0.012047
     2     6.15     0.00185571       0.011403
     3     5.81     0.00185571       0.010787
     4     5.46     0.00185571       0.010128
     5     5.08     0.00185571       0.009429

    Original disc + large disc, trial 2
     1     7.00     0.00185571       0.012997
     2     6.72     0.00185571       0.012461
     3     6.41     0.00185571       0.011895
     4     6.09     0.00185571       0.011309
     5     5.75     0.00185571       0.010663

    Original disc + large disc, trial 3
     1    4.302     0.00185571       0.007983
     2    4.057     0.00185571       0.007529
     3    3.816     0.00185571       0.007081
     4    3.566     0.00185571       0.006617
     5    3.305     0.00185571       0.006133

	Table 4

       A     = Trial
       B     = Average Angular Momentum before in rad.kg.m2/s
       C     = Average Angular Momentum after in rad.kg.m2/s
       D     = Absolute Difference
       E     = Percent Error

     A      B          C         D        E
    ==============================================
    Original Disc + big mass
     1   0.014934   0.010759 0.004175    27.96
     2   0.016563   0.011865 0.004698    28.36
     3   0.009304   0.007069 0.002235    24.03


	Table 5

       A     = Reading
       B     = Angular Velocity(rad/s)
       C     = Moment of Inertia Before in kg.m2
       D     = Angular Momentum before in rad.kg.m2/s

     A     B           C              D
    ==============================================
    Original disc + metal bar, trial 1
     1    17.53     0.00090786       0.015915
     2    17.52     0.00090786       0.015906
     3    17.25     0.00090786       0.015661
     4    16.96     0.00090786       0.015397
     5    16.75     0.00090786       0.015207

    Original disc + metal bar, trial 2
     1    16.94     0.00090786       0.015379
     2    16.96     0.00090786       0.015397
     3    16.76     0.00090786       0.015216
     4    16.54     0.00090786       0.015016
     5    16.29     0.00090786       0.014789

    Original disc + metal bar, trial 3
     1    14.12     0.00090786       0.012819
     2    13.69     0.00090786       0.012429
     3    13.45     0.00090786       0.012211
     4    13.20     0.00090786       0.011984
     5    12.92     0.00090786       0.011730

	Table 6

       A     = Reading
       B     = Angular Velocity(rad/s)
       C     = Moment of Inertia After in kg.m2
       D     = Angular Momentum after in rad.kg.m2/s

     A     B           C              D
    ==============================================
    Original disc + metal bar, trial 1
     1 9.409000     0.00178141       0.016761
     2 7.662000     0.00178141       0.013649
     3 6.098000     0.00178141       0.010863
     4 5.159000     0.00178141       0.009190
     5 4.837000     0.00178141       0.008617

    Original disc + metal bar, trial 2
     1    5.146     0.00178141       0.009167
     2    4.805     0.00178141       0.008560
     3    4.489     0.00178141       0.007997
     4    4.153     0.00178141       0.007398
     5    3.867     0.00178141       0.006889

    Original disc + metal bar, trial 3
     1    6.526     0.00178141       0.011625
     2    4.866     0.00178141       0.008668
     3    3.991     0.00178141       0.007110
     4    3.615     0.00178141       0.006440
     5    3.104     0.00178141       0.005529

	Table 7

       A     = Trial
       B     = Average Angular Momentum before in rad.kg.m2/s
       C     = Average Angular Momentum after in rad.kg.m2/s
       D     = Absolute Difference
       E     = Percent Error

     A      B          C         D        E
    ==============================================
    Original disc + metal bar
     1   0.015617   0.011816 0.003800    24.34
     2   0.015160   0.008002 0.007157    47.21
     3   0.012234   0.007875 0.004359    35.64

	Table 8

       A     = Reading
       B     = Angular Velocity(rad/s)
       C     = Moment of Inertia Before in kg.m2
       D     = Angular Momentum before in rad.kg.m2/s

     A     B           C              D
    ==============================================
    Original disc, small disc, and masses(1), trial 1
     1    15.10     0.00090786       0.013709
     2    14.80     0.00090786       0.013436
     3    14.30     0.00090786       0.012982
     4    13.74     0.00090786       0.012474
     5    13.44     0.00090786       0.012202

    Original disc, small disc, and masses(1), trial 2
     1    17.70     0.00090786       0.016069
     2    17.51     0.00090786       0.015897
     3    17.30     0.00090786       0.015706
     4    17.12     0.00090786       0.015543
     5    16.94     0.00090786       0.015379

    Original disc, small disc, and masses(1), trial 3
     1    16.23     0.00090786       0.014735
     2    16.05     0.00090786       0.014571
     3    15.81     0.00090786       0.014353
     4    15.60     0.00090786       0.014163
     5    15.41     0.00090786       0.013990

	Table 9

       A     = Reading
       B     = Angular Velocity(rad/s)
       C     = Moment of Inertia After in kg.m2
       D     = Angular Momentum after in rad.kg.m2/s

     A     B           C              D
    ==============================================
    Original disc, small disc, and masses(1), trial 1
     1    11.76     0.00096805       0.011384
     2    11.45     0.00096805       0.011084
     3    11.12     0.00096805       0.010765
     4    10.83     0.00096805       0.010484
     5    10.54     0.00096805       0.010203

    Original disc, small disc, and masses(1), trial 2
     1    14.60     0.00096805       0.014134
     2    14.37     0.00096805       0.013911
     3    14.16     0.00096805       0.013708
     4    13.90     0.00096805       0.013456
     5    13.63     0.00096805       0.013195

    Original disc, small disc, and masses(1), trial 3
     1    13.28     0.00103825       0.013788
     2    12.98     0.00103825       0.013476
     3    12.67     0.00103825       0.013155
     4    12.36     0.00103825       0.012833
     5    12.07     0.00103825       0.012532

	Table 10

       A     = Trial
       B     = Average Angular Momentum before in rad.kg.m2/s
       C     = Average Angular Momentum after in rad.kg.m2/s
       D     = Absolute Difference
       E     = Percent Error

     A      B          C         D        E
    ==============================================
    Original disc, small disc, and masses(1)
     1   0.012961   0.010784 0.002176    16.79
     2   0.015719   0.013681 0.002038    12.97
     3   0.014362   0.013157 0.001205     8.40

	Table 11

       A     = Reading
       B     = Angular Velocity(rad/s)
       C     = Moment of Inertia Before in kg.m2
       D     = Angular Momentum before in rad.kg.m2/s

    Original disc, small disc, and masses(2), trial 1
     1    10.30     0.00090786       0.009351
     2    10.13     0.00090786       0.009197
     3     9.97     0.00090786       0.009052

    Original disc, small disc, and masses(2), trial 2
     1    17.54     0.00090786       0.015924
     2    17.38     0.00090786       0.015779
     3    17.19     0.00090786       0.015606
     4    16.97     0.00090786       0.015406
     5    16.75     0.00090786       0.015207

    Original disc, small disc, and masses(2), trial 3
     1    19.11     0.00090786       0.017349
     2    18.95     0.00090786       0.017204
     3    18.77     0.00090786       0.017041
     4    18.57     0.00090786       0.016859
     5    18.37     0.00090786       0.016677

	Table 12

       A     = Reading
       B     = Angular Velocity(rad/s)
       C     = Moment of Inertia After in kg.m2
       D     = Angular Momentum after in rad.kg.m2/s

     A     B           C              D
    ==============================================
    Original disc, small disc, and masses(2), trial 1
     1     8.43     0.00113636       0.009574
     2     8.27     0.00113636       0.009400
     3     8.12     0.00113636       0.009224

    Original disc, small disc, and masses(2), trial 2
     1    13.55     0.00113636       0.015398
     2    13.29     0.00113636       0.015102
     3    13.02     0.00113636       0.014795
     4    12.74     0.00113636       0.014477
     5    12.48     0.00113636       0.014182


    Original disc, small disc, and masses(2), trial 3
     1    15.28     0.00113636       0.017364
     2     15.1     0.00113636       0.017159
     3     14.9     0.00113636       0.016932
     4    14.67     0.00113636       0.016670
     5    14.43     0.00113636       0.016398

	Table 13

       A     = Trial
       B     = Average Angular Momentum before in rad.kg.m2/s
       C     = Average Angular Momentum after in rad.kg.m2/s
       D     = Absolute Difference
       E     = Percent Error

     A      B          C         D        E
    ==============================================
    Original disc, small disc, and masses(2)
     1   0.009200   0.009399 0.000199     2.17
     2   0.015584   0.014791 0.000793     5.09
     3   0.017026   0.016904 0.000121     0.71

Conclusion

The results obtained in all cases tested proved that momentum is conserved. This was found to be true for both linear and angular momentum situations. Therefore our hypothesis was correct.

Percent Error

Reasons for Percent Error

Linear Collisions

  1. Surfaces were not totally frictionless so a certain amount of energy was lost due to friction.
  2. Energy during linear collisions was not totally transferred.
  3. The air track was not completely level (it has a slight dip towards the centre).

Changing Angular Momentum

  1. The moment of inertia of the centre post could not be measured.
  2. The ball bearings on which the centre post rotated had no lubricant, therefore there was a torque due to friction.
  3. When the second mass was dropped onto the original disc energy was lost because the second mass did not immediately reach the final velocity, and therefore skidding occurred.