Andrew Parmelee lab 2

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Dec 6, 2023

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Parmelee 1 Andrew Parmelee Professor White General Physics I November 20 th 2023 Exploration 19: Momentum Lab Report 2

Parmelee 2 Introduction: Purpose of this lab: The purpose of this lab was to investigate situations where the momentum of a system is not conserved. The main objective was to measure and analyze the effects of an external force on the momentum of a dynamics cart, considering factors that include velocity, force, and impulse. The setup included using the cart, motion detector, force sensor, rubber band, and LoggerPro software to collect and analyze data. What did we test? We ran several trials of the cart moving along a track and bouncing off the end of the track. The cart was propelled using a rubber band. We measured the sensors on the test rig that provided velocity and force associated with the cart as it moved in the system. Based on these measurements we calculated the difference in momentum before and after the cart bounced and changed direction on the track. We also calculated the impulse of the bounce. What are we trying to justify? By studying the data and figuring out the percent difference, it allows us to compare impulse determined from force measurements over time to the change in momentum determined from velocity measurements. In addition, we can look at the percentage differences between different trials to determine how consistent the test is overtime. This test is intended to give us insights into how well impulse and momentum can be determined with experiments.

Parmelee 3 Procedure: What did we do? We conducted this experiment using a dynamics cart, motion detector, force sensor, rubber band, and LoggerPro software for analyzing the data. We began the test by calibrating the force sensor and ensuring that the setup was aligned appropriately. We weighed the mass of the cart and then we attached a rubber band between the cart and the end of the track. To provide the cart with uniform pull of the rubber band we pulled the cart backward for each trial to the same starting spot along the track. While monitoring the sensors with the software, we released the cart, enabling it to move forward via the pull of the rubber band. The cart bounced off of the end of the track, and then moved in the opposite direction. We did multiple trials and captured the data with screen shots from the LoggerPro software. Results: With a motion detector we captured the velocity of the cart as it moved forward, bounced, and moved backward on the track. With a force sensor we measured the force acting on the cart as it bounced. We then calculated changes in velocity and momentum between before and after the cart bounced. We also calculated the impulse from the force data at the bounce. From the data from these trials, we calculated percent difference values. We also calculated the percent difference between the measured impulses to the changes in momentum. These measurements and calculations are shown in the following table and graphs. Mass of Cart: 0.666 Kg

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Parmelee 4 Trial Final velocity vf (m/s) (max) Initial Velocity Vi (m/s) (min) Difference in Vi (m/s) Change in Momentum Δp (kg.m/s) Impulse J J (N.s) % Difference Between Δp and J 1 Missing .9676 Unknown Unknown 98.39 Unknown 2 0.7801 -1.048 1.8281 1.2175 107 195.5% 3 0.9511 -1.249 2.2001 1.4653 69.75 191.77% Percent Difference between Trial 2 and 3 19.8% 17.5% 18.5% 18.5% 42.1% 1.9% Trial 2

Parmelee 5 Trial 3

Parmelee 6 Calculations:

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Parmelee 7 Footnotes for test data  We had to run a 3rd trial on a different day because we forgot to take a screenshot of the graph with the correct data of the 1st trial. Thus, I ignored the 1 st trial data, and made my calculations and comparisons only using trials 2 and 3.  We also made a mistake and didn’t capture the mean velocity correctly. The brackets were in the wrong spots, so instead I used the max and min velocities for the initial and final values in my table.  The value for the impulse in the graphs seems significantly higher than the example in the instructions for the lab. For example, the lab example says that the integral for the Force is 0.588 N*s, but our graph says the integral is 107 N*s for Trial 2 and 69.75 N*s for Trial 3.  We likely made a mistake in using the software to calculate the impulse accurately. Conclusion: Did we Justify It? We were unable to justify an accurate comparison between change in momentum and impulse. Our maximum and minimum velocity measurements and corresponding momentum differences are probably sufficient to use because their percentage errors are less than 20%. However, the Impulse calculations from the software appear to be 100 times too high based on the example we were given in the instructions. Possibly the reason for this could have been that the software has the wrong scale for impulse, or the force sensor was not calibrated correctly. Another possibility is that we didn’t use the software correctly to determine the impulse. When comparing the trials to each other, trial 2 had a smaller change in momentum. However, when comparing the trials, trial 2 had a larger impulse. This also suggests that our impulse

Parmelee 8 measurements are not accurate. I would have expected trial 2 to have a smaller impulse than trial 3 because the change in momentum was smaller. Also, our percentage of errors between impulse and change in momentum came out to nearly 200%, which is much higher than 20%. Thus, our test results did not justify our expectations. Overall, this experiment aimed to explore determining and comparing impulse and change of momentum. However, our likely inaccurate impulse calculations highlight the need for adjustments in our experiment. We may be able to address these problems by using the software correctly, and/or calibrating the force sensor correctly.

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