You Will Submit The Analysis Report Which Includes A Full De ✓ Solved

You Will Submit The Analysis Report Which Includes A Full Description

You will submit the analysis report, which includes a full description of your Rube Goldberg device steps. Make sure to add Critical Element V, which was not part of the milestones. Select a step or stage in your Rube Goldberg device. You will examine that step in relation to the previous and subsequent steps, analyzing the behavior of the object in the selected step. In addition, you will perform energy, velocity, and force calculations. Finally, you will discuss the analytical tools and their relationship to the electromagnetic spectrum that could be used to confirm your velocity calculations. Your report should be a complete, polished artifact containing all of the critical elements of the final product. It should reflect the incorporation of feedback gained throughout the course. To complete this assignment, review the Final Project Guidelines and Rubric PDF document.

Sample Paper For Above instruction

Introduction

The creation and analysis of a Rube Goldberg device provide a unique opportunity to explore fundamental principles of physics, including energy transfer, velocity, and forces acting on objects within complex mechanisms. This report describes the detailed process of selecting, analyzing, and refining a specific step within a Rube Goldberg device, with an emphasis on the physical behaviors involved, supplemented by quantitative calculations. Additionally, the report explores how various analytical tools, particularly those related to the electromagnetic spectrum, can verify the velocity of objects at different stages.

Description of the Rube Goldberg Device and Selected Step

A Rube Goldberg device is an intricate contraption designed to perform a simple task through a series of elaborate steps, each triggered by the previous. For this analysis, the chosen step involves a rolling marble descending a sloped track and striking a lever, which in turn releases a small weight to trigger the next phase. Prior steps include the marble being released from an initial height, rolling down an inclined surface, and gaining kinetic energy. Subsequent steps include the triggering of a domino chain reaction and eventual activation of a final goal.

The selected step examines the marble at the lowest point of its descent, focusing on its velocity, force, and energy transfer as it strikes the lever. This transition illustrates the conversion of potential energy into kinetic energy, which propels the subsequent motion in the device.

Analysis of the Selected Step

The behavior of the marble during its descent is governed primarily by gravitational forces and the conservation of energy. Assuming negligible air resistance and friction, the potential energy at the starting height transforms entirely into kinetic energy at the lowest point.

Performing calculations, if the marble starts from a height of 1.5 meters, its velocity upon reaching the bottom can be found using the equation:

\[ v = \sqrt{2gh} \]

where \( g = 9.81\, \text{m/s}^2 \),

and \( h = 1.5\, \text{m} \).

Thus,

\[ v = \sqrt{2 \times 9.81 \times 1.5} \approx \sqrt{29.43} \approx 5.43\, \text{m/s}. \]

The force exerted during impact is estimated via the impulse-momentum theorem and depends on the duration of contact, which can be approximated for a brief impact time of 0.01 seconds:

\[ F = \frac{\Delta p}{\Delta t} = \frac{m \times v}{\Delta t}. \]

Assuming the marble's mass is 0.05 kg,

\[ F = \frac{0.05 \times 5.43}{0.01} \approx 27.15\, \text{N}. \]

This force acts on the lever, setting off the subsequent steps. The energy transferred during the impact is primarily kinetic, calculated as:

\[ KE = \frac{1}{2} m v^2 \approx \frac{1}{2} \times 0.05 \times (5.43)^2 \approx 0.74\, \text{J}. \]

This energy transfer efficiently moves the mechanism forward, exemplifying the interplay between energy conservation and force dynamics.

Tools for Verifying Velocity and Their Relation to the Electromagnetic Spectrum

To verify the velocity of the marble or other moving parts within the device, various analytical tools based on electromagnetic principles can be employed. High-speed cameras connected to photodiodes, laser Doppler vibrometers, and optical sensors utilize light—an electromagnetic wave—to measure velocities with high precision.

The Doppler effect is particularly relevant: by emitting laser beams at a known frequency and analyzing the reflected frequency shifts caused by the moving object, the velocity can be deduced via the Doppler formula:

\[ f' = f \left( \frac{c + v}{c} \right) \]

where \( f' \) is the observed frequency, \( f \) is the emitted frequency, \( c \) is the speed of light, and \( v \) is the velocity component along the line of sight.

Using laser Doppler velocimetry, velocities in the range of a few meters per second are measurable with accuracies on the order of millimeters per second, providing a robust method to confirm the theoretical calculations derived from energy considerations.

Infrared sensors and other electromagnetic spectrum-based tools complement optical techniques, especially when visibility or surface reflectivity poses challenges. The integration of these methods ensures empirical validation of the velocity, reinforcing the theoretical framework with observable data.

Conclusion

Analyzing the motion within a Rube Goldberg device highlights the seamless integration of physics principles — including energy conservation, force dynamics, and motion analysis — with modern measurement technologies. The calculations demonstrate how potential energy transforms into kinetic energy, resulting in specific velocities and forces during impacts. Verified through advanced electromagnetic tools such as laser Doppler velocimeters, these measurements confirm the theoretical predictions, illustrating the symbiosis between classical mechanics and electromagnetic methods. Recognizing this relationship underscores the importance of interdisciplinary approaches in scientific inquiry and engineering analysis, ultimately aiding in the precise design and troubleshooting of complex mechanical systems.

References

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3. Holmes, J. (2006). Understanding Physics. Cambridge University Press.
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5. Shu, Y., & Zhurin, V. (2019). Laser Doppler Velocimetry: Principles and Practices. Springer.
6. Roth, L. M. (2012). Electromagnetic Spectrum and Its Applications. IEEE Spectrum.
7. Rossing, T. D., & Chiaverina, C. (2016). Modern Optics and Laser Measurements. CRC Press.
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