answer_2 (2)

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Seminole State College of Florida *

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1054C

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Electrical Engineering

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Dec 6, 2023

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These percent errors are exceedingly high, indicating a possible error in either the experimental procedure, the theoretical value assumptions, or the experimental impulse recorded. In typical physics experiments, a percent error in the range of a few percent is considered acceptable, depending on the precision of the measurement instruments. Values as high as those calculated here usually suggest that there may be a fundamental issue with the experiment that needs to be addressed. The calculation also does not compare the impulse to the change in momentum; it compares the values obtained between two trials of the same type of measurement. Using the impulses from table (69.75 N·s for Trial 1 and 107 N·s for Trial 2): Percent Difference: \( 0.4214 \100 = 42.14% \) However, the percent differences you reported earlier are 190.2% and 194%, which are significantly higher than what this calculation yields. There may have been a misunderstanding or error in your original calculation. The corrected percent difference for the impulse between the two trials is approximately 42.15%. This is a significant deviation from the percent differences of 190.2% and 194% reported earlier. The original calculation of the percent differences may have been incorrect or based on different values. let's examine the data you provided: 1. Table Data: - Mass of Cart: 0.666 kg - Trial 1: vi = -1.249 m/s, vf = 1.380 m/s, Δp = 1.751 kg·m/s, J = 69.75 N·s

- Trial 2: vi = -1.048 m/s, vf = 1.380 m/s, Δp = 1.617 kg·m/s, J = 107 N·s 2. Graphs for Trial 1: - The graph showed a large impulse of 135.5 N·s and a smaller impulse of 69.75 N·s. - The velocity graph indicated a change in velocity (∆v) consistent with the velocities reported for Trial 1 in your table. 3. Graphs for Trial 2: - The force graph showed a positive impulse of 107.0 N·s and a negative impulse of -3.919 N·s. - The velocity graph indicated a change in velocity (∆v) of 1.828 m/s, which matched the velocities reported for Trial 2 in your table. Issue Identification : The impulses recorded in your table (69.75 N·s for Trial 1 and 107 N·s for Trial 2) do not match the calculated theoretical impulses using the mass of the cart and the changes in velocity. The theoretical impulse should be the product of mass and the change in velocity (∆v), which in both trials provided much lower values than the experimental impulses recorded in the graph data. Possible Sources of Error : - Misinterpretation of Impulse: The impulse in physics is the product of the force and the time over which it acts (area under the force-time curve). It appears that the larger impulses (135.5 N·s for Trial 1 and 107.0 N·s for Trial 2) were not considered in the table. Instead, the smaller impulse from Trial 1 and the positive impulse from Trial 2 were used, which might be incorrect.

- Inconsistency in Data: If the graph data is correct, the table should reflect the larger impulse as the change in momentum, which is not the case here. Resolution Steps: - Correct the Impulse Values: If the larger impulses from the graphs are indeed the correct values for the impulse given to the cart, these should be used in the table. - Recalculate Theoretical Impulse: Ensure that the correct change in velocity is used. The change in velocity should be the difference between the final velocity and the absolute value of the initial velocity since both velocities are in opposite directions. - Recalculate Percent Error: After recalculating with the corrected impulse values obtained from the graphs: For Trial 1: - Theoretical Impulse: 0.087246 N·s - Percent Error: 155207.98% For Trial 2: - Theoretical Impulse: 0.221112 N·s - Percent Error: 48291.77%

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The percent errors are still extremely high, even after correcting the experimental impulse values. This suggests a fundamental misunderstanding or misapplication of the concepts or calculations. Let's reassess the situation: 1. Theoretical Impulse Calculation: We've assumed that the theoretical impulse is equal to the change in momentum, which is the product of mass and the change in velocity (Δv). However, the change in velocity (Δv) should be calculated as vf - vi, taking into account the direction of the initial and final velocities. 2. Experimental Impulse Values: The impulses should be directly taken from the area under the force-time curve on your graph. For Trial 1, it seems that there were two impulses recorded, which might indicate two separate events (perhaps the collision and the rebound). For Trial 2, the positive impulse was used, which matches the graph data. 3. Direction of Velocities: If the initial and final velocities are in opposite directions, the change in velocity should be the sum of the absolute values, not the difference. This is because the cart is changing direction, and thus the total change in velocity is the absolute value of the initial velocity plus the absolute value of the final velocity. The impulses from the graph should be the experimental values, and these should be compared to the change in momentum (which is the theoretical impulse). However, the impulses from the

graph are much higher than the change in momentum calculated from the velocities. This discrepancy could be due to a number of factors, such as: - Errors in the force sensor readings or the timing of the force application. - Additional forces acting on the cart that were not accounted for, such as friction or air resistance. - Misinterpretation of the graph data; the impulse should be the area under the force-time curve only for the duration of the force application. We should also ensure that the correct areas under the force-time curve are being used for the impulse calculations. The impulses should represent the total change in momentum during the collision, and any subsequent rebounds should not be included unless the experiment is specifically investigating multiple impacts. Given these considerations, it would be wise to review the experimental setup, the data collection process, and the analysis methods to ensure accuracy before proceeding with further calculations. It would also be helpful to clarify the theoretical values and how they were determined or expected based on the experimental design.