Lab 2 PHYSICS Palm beach

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Palm Beach State College *

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2048L

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Physics

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Oct 30, 2023

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docx

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2

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Laboratory Assignment 2: Rolling Objects on Inclined Planes Introduction: In this experiment, we explored the dynamic interplay of rolling objects on inclined planes, examining the correlation between time, distance, and the velocities attained during their descent. Our primary objective was to delve into the complex concept of moment of inertia concerning various objects released down the incline. We used a diverse array of rolling objects with different shapes to investigate the implications of rolling inertia variations. Additionally, we harnessed the power of a revolving platform to extract crucial data on radius, revolution time, and object height from the ground. Our analysis aimed to shed light on the preservation of energy in the context of moment of inertia. A) Angular Inquiry: We began by determining the inclination angle. The ruler's incline dimensions were 1.2cm for height and 30cm for length. Utilizing the inverse sine function, we calculated an inclination angle of approximately 2.29 degrees. B) Comparative Assessment: Next, we conducted a comparative analysis. We compared our calculated value for a solid sphere with the theoretical value. Our result, which amounted to -0.49, deviated from the theoretical expectation. To gain more insight, we also explored the absolute value of this result in relation to 2/5, indicating a value that seemingly fell between that of a hollow and solid sphere. C) The Big Ball: We expanded our investigation to include data for a larger ball. We carefully examined whether the measured rolling times displayed any dependency on the ball's radius. Theoretically, there should be no radius term within the equation for time ( ? ^2 = 2(1 + ? ) ? g sin( ? )). Despite this, we recognized that a larger radius corresponded to a greater mass. However, we elaborated on the idea that both moment of inertia and object inertia were proportional to mass, while acceleration correlated with weight, all of which were intertwined with mass. Consequently, we concluded that mass and radius should not affect the rolling times of the ball. E) In-depth Analysis: We furthered our exploration by including data for the cylinder and the ball. A comparative analysis was carried out to assess moments of inertia between the solid sphere and the hollow cylinder. The anticipated value based on the equation was 0.84. We calculated the average times for the cylinder and the ball, and intriguingly, they turned out to be remarkably identical. This finding raised questions regarding experimental accuracy and precision. F) Comparative Rolling Times: To delve deeper, we examined the comparative rolling times for solid and hollow cylinders. While the observed difference wasn't substantial, we resorted to Eq. 3 to compute the value of β for the solid cylinder. The intricacies of the equation were explored to facilitate a comprehensive understanding. G) Turntable Experiment: The document delved into the results of the turntable experiment, offering insights into the measurements of radius, revolution times, and object height. Subsequently, we calculated the final velocity, exploring angular velocity and the moment of inertia in the process. H) Moment of Inertia Calculations: We conducted calculations to derive the moment of inertia for both the disk and the cylinder. The moment of inertia for the disk was computed as 0.015, and for the cylinder, it was determined to be 0.014. As a final step, we consolidated these results to ascertain the moment of inertia for the turntable, arriving at a value of 0.029. Concluding Remarks: Our experiment was initiated with the ambitious goal of unraveling the complexities surrounding moment of inertia in objects navigating inclined planes. The journey, however, encountered various challenges, resulting in negative moment of inertia values. These challenges were multifaceted, encompassing both human and material factors. Object trajectories exhibited deviations from the expected straight path. Irregularities in the ruler's surface further complicated the scenario, influencing friction and, consequently, the difference in recorded times.
Additionally, human measurements suffered from imprecisions owing to disparities in reaction times. Subsequently, our analysis extended to a comparison of moments of inertia between the cylinder and the ball. The derived value of 1 didn't align with the theoretical value of 0.84, signifying potential sources of error and uncertainties. Of particular interest was the astonishing discovery that the average times for both objects yielded precisely identical results. This aspect fueled contemplation about the accuracy and precision of our experiment. Lastly, we explored the moment of inertia for the turntable, which, when compared to the calculated values for the cylinder and the disk, hinted at the potential presence of errors in one or both of these calculations
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