M3.5 Laboratory Report 7

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Broward College *

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2053L

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Aerospace Engineering

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Oct 30, 2023

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docx

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M3.5 Laboratory Report 7 Worksheet PHY2053L 10/15/2023 Purpose: The purpose of this experiment is to explore the concept of the conservation of mechanical energy in the context of the PhET simulation. This experiment aims to study how kinetic and gravitational potential energy

are related, and how various factors, such as height, mass, friction, and gravity, impact the distribution of energy within the system. By conducting this experiment, I intend to gain a deeper understanding of the fundamental principles of energy conservation and apply these concepts to real-world scenarios. Introduction: The primary focus will be on the conservation of mechanical energy, which is the principle that the total mechanical energy of a system remains constant when only conservative forces, like gravity, are at play. This experiment will examine how different heights, masses, levels of friction, and gravitational fields influence the distribution of energy within the simulation. Procedure: To get started, I’ll access the PhET simulation. In the first part of the experiment, I’ll delve into the dependence of height, mass, friction, and gravity on the distribution of mechanical energy. I’ll begin by selecting the “Measure” tab within the simulation, familiarizing myself with the available options. Then, I’ll conduct experiments by releasing the skater from various heights, adjusting friction settings, and exploring different gravitational fields. I’ll record the data for kinetic, potential, and total energy as per the instructions. In the second part of the experiment, I’ll use the Energy measuring tool to calculate height from potential energy and speed from kinetic energy at a specific point on the ramp. Finally, I’ll move on to the “Graphs” tab to examine energy graphs and analyze how they represent the conservation of energy in the system. Data and Data Evaluation: Part l: Dependance of height, mass, friction, and gravity Part 1 Dependance of Height: Energy (J) Height (6 m) Height (4 m) Height (2 m)

Kinetic 493.7 J 1579.4 J 2689.3 J Potential 3487.3 J 2401.6 J 1227.3 J Total 3981.0 J 3981.0 J 3981.0 J In this part of the experiment, I observed a shift in energy distribution. Initially, there was a greater amount of potential energy compared to kinetic energy as the skater started from higher positions. However, as the skater descended to lower heights, the balance shifted, with kinetic energy becoming dominant over potential energy. It’s noteworthy that, regardless of height, the total energy in the system remained constant. Part 1.2 Dependance of Friction: Energy (J) Friction–None Friction-Medium Friction-Lots Kinetic 37.3 J 30.4 J 28.9 J Potential 2371.3 J 2375.2 J 2376.0 J Thermal 0.0 J 2.9 J 3.6 J Total 2408.6 J 2408.6 J 2408.6 J In this part of the experiment, I observed that with an increase in friction, there was a corresponding rise in thermal energy. However, it’s important to highlight that the overall energy within the system remained constant. As friction increased, kinetic energy decreased, but potential energy saw an increase. Part 1.3 Dependance of Gravity: Energy (J) Moon Earth Jupiter Kinetic 1.0 J 37.8 J 241.8 J Potential 392.0 J 2369.8 J 5850.2 J Total 393.0 J 2407.3 J 6092.0 J With variations in gravity settings, both kinetic and potential energy exhibited changes, increasing simultaneously. Furthermore, the total energy within the system altered in response to the shifts in gravity. Notably, despite these changes, due to the consistent height, potential energy consistently outweighed kinetic energy in each scenario. Part 1.4 Dependance of Mass:

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Energy (J) Mass = 25 kg Mass = 55 kg Mass = 85 kg Kinetic 15.7 J 34.6 J 53.3 J Potential 987.3 J 2172.1 J 3356.9 J Total 1003.1 J 2206.7 J 3410.4 J With an increase in mass, there was a noticeable simultaneous rise in both kinetic and potential energy. This change in mass had a direct impact on the total energy within the system, leading to an overall increase. Part ll: Calculate speed or height from information about a different position Using a skater that weighs 60 kg with gravity set at 9.8 m/s 2 , the simulation gave the Potential energy as 1599.6 J. (PE) = mgh = 60 kg x 9.8 m/s 2 x 2.72 m = 1,599.36 J Using the same parameters as the previous scenario, the Kinetic energy given by the simulation is 1838.8 J. (KE) = 0.5mv 2 = 0.5(60 kg)(7.83 m/s) 2 = 1,839.27 J Overall, my calculations were very close to the ones given by the simulation, with only a few decimals off. Part lll: Energy Graphs Observing the graphs, I could see that each graph serves as a visual representation of the kinetic, potential, and thermal energy levels concerning the skater’s position on the ramps, ranging from the highest to the lowest points. These graphs provide a quantitative depiction to the conservation principle underlying the transformation process, where energy levels shift based on the specific transformations taking place during the skater’s path. Conclusion:

In summary, my observations reveal intriguing patterns across various aspects of the experiment. When examining the impact of height, it became evident that, initially, potential energy dominated over kinetic energy, but as the skater descended to lower heights, the balance shifted in favor of kinetic energy. Crucially, the overall energy within the system remained constant, regardless of the height. In context of friction, an interesting connection emerged. As friction increased, so did thermal energy, while the total energy remained unaltered. Simultaneously, the rise in friction caused a reduction in kinetic energy and a surge in potential energy. Shifting our focus to gravity, it was apparent that adjustments in gravitational force influenced both kinetic and potential energies, resulting in changes in the total energy of the system. However, due to consistent altitude, potential energy consistently outweighed kinetic energy in each scenario. When it came to mass, increasing it led to a simultaneous elevation of both kinetic and potential energy, thereby augmenting the total energy within the system. Part ll provided further insights, as I applied the kinetic and potential energy formulas, obtaining results mostly consistent with the simulation. This reaffirms the direct proportionality of potential energy to factors like mass, height, and gravity, and kinetic energy’s connection with mass and velocity. Finally, the graphs served as visual representations of the skater’s energy dynamics, showcasing how potential, kinetic, and thermal energy levels fluctuated as the skater traversed the ramps. These graphs quantitatively embodied the conservation principle, illustrating how energy transformed at varying levels depending on the specific conversion processes.