Bouncy Collision (one moving, one stationary)
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Graphs
Solid red or blue line = Position Dashed red or blue line = Velocity Dotted red or blue line = Momentum Green Line = Total momentum |
Calculations
Initial Momentum = Mass * Initial Velocity = 0.252 kg * 0.66 m/s = 0.16632 kg m/s
Final Momentum = Mass * Final Velocity = 0.252 kg * 0.6 m/s = 0.1512 kg m/s
Percent Difference = |.1512-.16632| / 0.16632 = 9.09%
Initial Momentum = Mass * Initial Velocity = 0.252 kg * 0.66 m/s = 0.16632 kg m/s
Final Momentum = Mass * Final Velocity = 0.252 kg * 0.6 m/s = 0.1512 kg m/s
Percent Difference = |.1512-.16632| / 0.16632 = 9.09%
Conclusion
This experiment did prove that momentum is conserved. The initial and final momentum of the carts are 9.09% off but this is still a fairly small margin considering the numbers. This error could have been caused by inaccuracies with the best fit lines in logger pro as they are not 100% accurate to the actual line.
This experiment did prove that momentum is conserved. The initial and final momentum of the carts are 9.09% off but this is still a fairly small margin considering the numbers. This error could have been caused by inaccuracies with the best fit lines in logger pro as they are not 100% accurate to the actual line.
Bouncy Collision (both moving)
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Graphs
Solid red or blue line = Position Dashed red or blue line = Velocity Dotted red or blue line = Momentum Green Line = Total momentum |
Calculations
Initial Momentum = Mass A * Initial Velocity A + Mass B * Initial Velocity B = 0.252 kg * 0.32 m/s + 0.252 * -0.38= -0.01512 kg m/s
Final Momentum = Mass A * Final Velocity A + Mass B * Final Velocity B = 0.252 kg * 0.32 m/s + 0.252 * -0.38 = -0.0126 kg m/s
Percent Difference = |.0126-.01512| / 0.01512 = 16.67%
Initial Momentum = Mass A * Initial Velocity A + Mass B * Initial Velocity B = 0.252 kg * 0.32 m/s + 0.252 * -0.38= -0.01512 kg m/s
Final Momentum = Mass A * Final Velocity A + Mass B * Final Velocity B = 0.252 kg * 0.32 m/s + 0.252 * -0.38 = -0.0126 kg m/s
Percent Difference = |.0126-.01512| / 0.01512 = 16.67%
Conclusion
In this test the percent difference was 16.67 which while higher than the previous test you can still assume momentum is conserved as while the numbers have a large percent difference this is only because they are very small values and they are actually near each other as can be seen on the graph. Velocity could also be being lost to friction which would decreases the calculated momentum
In this test the percent difference was 16.67 which while higher than the previous test you can still assume momentum is conserved as while the numbers have a large percent difference this is only because they are very small values and they are actually near each other as can be seen on the graph. Velocity could also be being lost to friction which would decreases the calculated momentum
Sticky Collision (one moving, one stationary)
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Graphs
Solid red or blue line = Position Dashed red or blue line = Velocity Dotted red or blue line = Momentum Green Line = Total momentum |
Calculations
Initial Momentum = Mass B * Initial Velocity B = 0.252 kg * 0.43 m/s = 0.10836 kg m/s
Final Momentum = (Mass A + Mass B) * Final Velocity A and B = (0.252 kg + 0.252 kg )* 0.17 m/s = 0.08568 kg m/s
Percent Difference = |.08568-.10836| / 0.10836 = 20.93%
Initial Momentum = Mass B * Initial Velocity B = 0.252 kg * 0.43 m/s = 0.10836 kg m/s
Final Momentum = (Mass A + Mass B) * Final Velocity A and B = (0.252 kg + 0.252 kg )* 0.17 m/s = 0.08568 kg m/s
Percent Difference = |.08568-.10836| / 0.10836 = 20.93%
Conclusion
So this collision led to a percent difference of 20.93% between initial and final momentum. But similarly to the other experiments both the initial and final momentum are very small values that are still very close even if they are off from each other by a higher percent. This inaccuracy could be caused by bad data being taken by the motion sensor as it picked up the velocity of the carts. If the experiment was repeated it can be assumed the momentum values would be closer as the momentum is conserved.
So this collision led to a percent difference of 20.93% between initial and final momentum. But similarly to the other experiments both the initial and final momentum are very small values that are still very close even if they are off from each other by a higher percent. This inaccuracy could be caused by bad data being taken by the motion sensor as it picked up the velocity of the carts. If the experiment was repeated it can be assumed the momentum values would be closer as the momentum is conserved.
Sticky Collision (both moving)
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Graphs
Solid red or blue line = Position Dashed red or blue line = Velocity Dotted red or blue line = Momentum Green Line = Total momentum |
Calculations
Initial Momentum = Mass A * Initial Velocity A + Mass B * Initial Velocity B = 0.252 kg * 0.18 m/s + 0.252 * -0.71= -0.13356 kg m/s
Final Momentum = (Mass A + Mass B) * Final Velocity A and B = (0.252 kg + 0.252 kg) * -0.22 m/s = -0.11088 kg m/s
Percent Difference = |-.11088 + .13356| /0.13356 = 16.98%
Initial Momentum = Mass A * Initial Velocity A + Mass B * Initial Velocity B = 0.252 kg * 0.18 m/s + 0.252 * -0.71= -0.13356 kg m/s
Final Momentum = (Mass A + Mass B) * Final Velocity A and B = (0.252 kg + 0.252 kg) * -0.22 m/s = -0.11088 kg m/s
Percent Difference = |-.11088 + .13356| /0.13356 = 16.98%
Conclusion
This experiment led to a difference in initial and final momentum of 16.98% but like the others the percent difference isn't what is important, it is the actual difference between initial and final momentum. The values are very small so a small error with the motion sensor can lead to the momentum being slightly off and because of how small the momentum are this small change will effected the percent difference greatly. So this experiment shows momentum is conserved.
This experiment led to a difference in initial and final momentum of 16.98% but like the others the percent difference isn't what is important, it is the actual difference between initial and final momentum. The values are very small so a small error with the motion sensor can lead to the momentum being slightly off and because of how small the momentum are this small change will effected the percent difference greatly. So this experiment shows momentum is conserved.
Explosion (neither is moving, then both are moving)
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Graphs
Solid red or blue line = Position Dashed red or blue line = Velocity Dotted red or blue line = Momentum Green Line = Total momentum |
Calculations
Initial Momentum = 0 kgm/s (neither cart is moving)
Final Momentum = Mass A * Final Velocity A + Mass B * Final Velocity B = 0.252 kg * 0.82 m/s + 0.252 * -0.82 = 0 kg m/s
Percent Difference = 0%
Initial Momentum = 0 kgm/s (neither cart is moving)
Final Momentum = Mass A * Final Velocity A + Mass B * Final Velocity B = 0.252 kg * 0.82 m/s + 0.252 * -0.82 = 0 kg m/s
Percent Difference = 0%
Conclusion
The percent difference of this experiment was 0% so momentum was conserved. While there is initially no momentum because the two carts with equal masses are moving at the same velocity their momentum is canceled out and is still 0 together as a system.
The percent difference of this experiment was 0% so momentum was conserved. While there is initially no momentum because the two carts with equal masses are moving at the same velocity their momentum is canceled out and is still 0 together as a system.
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