Collision 1: Bouncy - Moving / Stationary
Setup: One cart moves towards a stationary cart and hits it, and the carts bounce off of each other
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Blue solid line - Position for Cart A Red solid line - Position for Cart B Blue dashed line - Velocity for Cart A Red dashed line - Velocity for Cart B Blue dotted line - Momentum for Cart A Red dotted line - Momentum for Cart B Green line - Total Momentum |
Calculations:
Initial Momentum = Mass * Initial Velocity = 0.252 kg * 0.66m/s = 0.16632 kgm/s
Final Momentum = Mass * Final Velocity = 0.252 kg * 0.6 m/s = 0.1512 kgm/s
Percent Difference = |.1512-.16632|/0.16632 = 9.09%
Initial Momentum = Mass * Initial Velocity = 0.252 kg * 0.66m/s = 0.16632 kgm/s
Final Momentum = Mass * Final Velocity = 0.252 kg * 0.6 m/s = 0.1512 kgm/s
Percent Difference = |.1512-.16632|/0.16632 = 9.09%
Note: The time of collision makes it look like there is no momentum for a short time, and this is a source of uncertainty for our measurements.
Conclusion:
The goal of the momentum lab was to test 5 different types of collisions and to see if momentum was conserved within the system like it is supposed to be. In this collision, Cart A is moving at a velocity of 0.66 m/s and Cart B is still, and then after the collision Cart A stops and Cart B moves with a velocity of 0.6 m/s. After calculating the momentum, I found a 9.09% difference between the two values. This isn't surprising because the numbers are extremely small, so I can conclude that momentum was conserved and that this experiment proved what I was hoping to prove.
The goal of the momentum lab was to test 5 different types of collisions and to see if momentum was conserved within the system like it is supposed to be. In this collision, Cart A is moving at a velocity of 0.66 m/s and Cart B is still, and then after the collision Cart A stops and Cart B moves with a velocity of 0.6 m/s. After calculating the momentum, I found a 9.09% difference between the two values. This isn't surprising because the numbers are extremely small, so I can conclude that momentum was conserved and that this experiment proved what I was hoping to prove.
Collision 2: Bouncy - Both Moving
Setup: Push two carts towards each other (moving in opposite directions) and let them hit each other and bounce off
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Green solid line - Position for Cart A Orange solid line - Position for Cart B Green dashed line - Velocity for Cart A Orange dashed line - Velocity for Cart B Green dotted line - Momentum for Cart A Orange dotted line - Momentum for Cart B Purple line - Total Momentum |
Calculations:
Initial Momentum = Mass A * Initial Velocity A + Mass B * Initial Velocity B = 0.252 kg * 0.32m/s + 0.252 * -0.38= -0.01512 kgm/s
Final Momentum = Mass A * Final Velocity A + Mass B * Final Velocity B = 0.252 kg * 0.32m/s + 0.252 * -0.38 = -0.0126 kgm/s
Percent Difference = |.0126-.01512|/0.01512 = 16.67%
Initial Momentum = Mass A * Initial Velocity A + Mass B * Initial Velocity B = 0.252 kg * 0.32m/s + 0.252 * -0.38= -0.01512 kgm/s
Final Momentum = Mass A * Final Velocity A + Mass B * Final Velocity B = 0.252 kg * 0.32m/s + 0.252 * -0.38 = -0.0126 kgm/s
Percent Difference = |.0126-.01512|/0.01512 = 16.67%
Conclusion:
In this collision, Cart A is moving at a velocity of 0.32 m/s and Cart B is moving at a velocity of -0.38 m/s, so the carts are moving towards each other. Once they collide, they bounce off of each other and travel in opposite directions; Cart A has a velocity of -0.31 m/s and Cart B has a velocity of 0.26 m/s. There was a 16.67% difference in these values which is a little more concerning, but since the numbers are so small and there is a small force of friction that would affect the velocity values, I can still conclude that the momentum of the system was conserved.
In this collision, Cart A is moving at a velocity of 0.32 m/s and Cart B is moving at a velocity of -0.38 m/s, so the carts are moving towards each other. Once they collide, they bounce off of each other and travel in opposite directions; Cart A has a velocity of -0.31 m/s and Cart B has a velocity of 0.26 m/s. There was a 16.67% difference in these values which is a little more concerning, but since the numbers are so small and there is a small force of friction that would affect the velocity values, I can still conclude that the momentum of the system was conserved.
Collision 3: Sticky - Moving / Stationary
Setup: One cart moves towards a stationary cart and hits it, but they stick together
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Red solid line - Position for Cart A Black solid line - Position for Cart B Red dashed line - Velocity for Cart A Black dashed line - Velocity for Cart B Red dotted line - Momentum for Cart A Black dotted line - Momentum for Cart B Orange line - Total Momentum |
Calculations:
Initial Momentum = Mass B * Initial Velocity B = 0.252 kg * 0.43m/s = 0.10836 kgm/s
Final Momentum = (Mass A + Mass B) * Final Velocity A and B = (0.252 kg + 0.252 kg )* 0.17m/s = 0.08568 kgm/s
Percent Difference = |.08568-.10836|/0.10836 = 20.93%
Initial Momentum = Mass B * Initial Velocity B = 0.252 kg * 0.43m/s = 0.10836 kgm/s
Final Momentum = (Mass A + Mass B) * Final Velocity A and B = (0.252 kg + 0.252 kg )* 0.17m/s = 0.08568 kgm/s
Percent Difference = |.08568-.10836|/0.10836 = 20.93%
Conclusion:
This collision involves Cart A staying still and Cart B moving at a velocity of 0.43 m/s, and then when the carts collide, they stick together and continue to travel in the same direction that Cart B was traveling with a velocity of 0.17 m/s. The percent difference between the initial and final momentum values was 20.93%, so my velocity measurements were probably not as precise as they could have been, but overall it makes sense to assume that the momentum was conserved.
This collision involves Cart A staying still and Cart B moving at a velocity of 0.43 m/s, and then when the carts collide, they stick together and continue to travel in the same direction that Cart B was traveling with a velocity of 0.17 m/s. The percent difference between the initial and final momentum values was 20.93%, so my velocity measurements were probably not as precise as they could have been, but overall it makes sense to assume that the momentum was conserved.
Collision 4: Sticky - Both Moving
Setup: Two cars moving towards each other and then they run into each other, but they stick together and start traveling in the direction of the car that had a greater velocity initially.
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Orange solid line - Position for Cart A Blue solid line - Position for Cart B Orange dashed line - Velocity for Cart A Blue dashed line - Velocity for Cart B Orange dotted line - Momentum for Cart A Blue dotted line - Momentum for Cart B Red line - Total Momentum |
Calculations:
Initial Momentum = Mass A * Initial Velocity A + Mass B * Initial Velocity B = 0.252 kg * 0.18m/s + 0.252 * -0.71= -0.13356 kgm/s
Final Momentum = (Mass A + Mass B) * Final Velocity A and B = (0.252 kg + 0.252 kg) * -0.22 m/s = -0.11088 kgm/s
Percent Difference = |-.11088 + .13356|/0.13356 = 16.98%
Initial Momentum = Mass A * Initial Velocity A + Mass B * Initial Velocity B = 0.252 kg * 0.18m/s + 0.252 * -0.71= -0.13356 kgm/s
Final Momentum = (Mass A + Mass B) * Final Velocity A and B = (0.252 kg + 0.252 kg) * -0.22 m/s = -0.11088 kgm/s
Percent Difference = |-.11088 + .13356|/0.13356 = 16.98%
Conclusion:
In this collision, Cart A has a velocity of 0.18 m/s and Cart B has a velocity of -0.71 m/s, so the carts are traveling towards each other. When the carts collide, they stick together and continue to travel in the same direction that Cart B was traveling with a velocity of -0.22 m/s. I found a percent difference of 16.98% which is pretty consistent with my other percent difference values, so I am continuing to conclude that the momentum of the system was conserved.
In this collision, Cart A has a velocity of 0.18 m/s and Cart B has a velocity of -0.71 m/s, so the carts are traveling towards each other. When the carts collide, they stick together and continue to travel in the same direction that Cart B was traveling with a velocity of -0.22 m/s. I found a percent difference of 16.98% which is pretty consistent with my other percent difference values, so I am continuing to conclude that the momentum of the system was conserved.
Collision 5: Explosion
Two carts start attached to each other and then we press the button that separates them and they move away from each other.
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Green solid line - Position for Cart A Black solid line - Position for Cart B Green dashed line - Velocity for Cart A Black dashed line - Velocity for Cart B Green dotted line - Momentum for Cart A Black dotted line - Momentum for Cart B Orange line - Total Momentum |
Calculations:
Initial Momentum = 0 kgm/s (neither cart is moving0
Final Momentum = Mass A * Final Velocity A + Mass B * Final Velocity B = 0.252 kg * 0.82m/s + 0.252 * -0.82 = 0 kgm/s
Percent Difference = 0%
Initial Momentum = 0 kgm/s (neither cart is moving0
Final Momentum = Mass A * Final Velocity A + Mass B * Final Velocity B = 0.252 kg * 0.82m/s + 0.252 * -0.82 = 0 kgm/s
Percent Difference = 0%
Conclusion:
The explosion starts with the carts together and not moving, and then when we press the button, the carts quickly move away from each other. Cart A had a velocity of 0.82 m/s and Cart B had a velocity of -0.82 m/s. Since the carts had identical velocities to start and at the end, the percent difference between the two momentum values is 0%. Therefore, it is clear that the momentum was conserved in the system; there originally was no momentum at all, and then the positive momentum of Cart A and the negative momentum of Cart B cancel each other out.
The explosion starts with the carts together and not moving, and then when we press the button, the carts quickly move away from each other. Cart A had a velocity of 0.82 m/s and Cart B had a velocity of -0.82 m/s. Since the carts had identical velocities to start and at the end, the percent difference between the two momentum values is 0%. Therefore, it is clear that the momentum was conserved in the system; there originally was no momentum at all, and then the positive momentum of Cart A and the negative momentum of Cart B cancel each other out.
Sources of Uncertainty
Since there is a small force of friction between the carts and the track, this affected our velocity values because the carts slowed down a little bit. Therefore, the momentum values are affected as well, and this is a source of uncertainty that is one of the factors for the percent difference values that I found. Another source of uncertainty is finding the velocity measurements. I used the linear regression tool on LoggerPro to find the slope of the position time graphs, which fixes the potential problem of trying to eyeball the numbers. However, I still had to choose the correct time periods to find the slope of the graphs, and since all of our graphs came out as smooth lines, at times it was difficult to distinguish the correct starting point.
Links To My Graphs
Bouncy- Moving / Stationary
Bouncy- Both Moving
Sticky- Moving / Stationary
Sticky- Both Moving
Explosion
Bouncy- Both Moving
Sticky- Moving / Stationary
Sticky- Both Moving
Explosion
Impulse and Momentum Notes.pdf | |
File Size: | 444 kb |
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