M3.6 Laboratory Report 8

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Broward College *

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2053L

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Mechanical Engineering

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Oct 30, 2023

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M3.6 Laboratory Report 8 10/22/23 PHY2053L Purpose: The purpose of this lab is to investigate the relationship between force applied and the extension of a spring using the PhET simulation. The experiment involves a single spring with a force constant of 200N/m in Part

1, two springs in parallel with the same force constant in Part 2 and exploring elastic potential energy in Part 3. By conducting these experiments, I aim to understand how the force applied affects the spring’s extension and explore the concept of elastic potential energy stored in a spring. Introduction: Springs are ubiquitous in our daily lives, from the suspension systems of vehicles to the functioning of everyday objects like doors and mattresses. Understanding how springs respond to applied forces is essential in various fields, including engineering and physics. Hooke’s Law, formulated by the English scientist Robert Hooke in the 17 th century, provides a fundamental framework for comprehending the behavior of springs. Procedure: In the first part of the experiment, I used the PhET simulation to measure the extensions from the equilibrium position. I did this by employing a single spring with a force constant of 200 N/m. In the next part, I used the Systems tab to capture the extensions of two springs arranged in parallel. The next part the focus is shifted to determining the values of elastic potential energy as well as the corresponding applied forces. These calculations were based on the extension measurements provided by the simulation. To visualize and analyze this data effectively, I used the Vernier graphing tool, which enabled me to create graphs illustrating the relationship between elastic potential energy and extension. Furthermore, I utilized this graph to extrapolate the expected value of elastic potential energy at an extension of 0.7 meters. Data and Data Evaluation: Part 1 – Using one spring of force constant 200 N/m Force Applied (N) Extension (m) 1 N 0.005 m 10 N 0.050 m 50 N 0.250 m 60 N 0.300 m

90 N 0.450 m 100 N 0.500 m The magnitude of the applied force is contingent upon the spring’s elongation. As the force acting on the spring increases, its length will correspondingly increase in a direct proportion. In practical terms, for every 1 Newton of applied force, the extension is in a direct proportion of 0.005 meters. For example, when 50 N of force is applied, the resulting extension is 0.250 meters, and when 100 N of force is exerted, the extension extends to 0.500 meters. Diagram: Part 2 – Using two springs of force constant 200 N/m in parallel Force Applied (N) Extension (m) 1 N 0.003 m 10 N 0.025 m 50 N 0.125 m

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60 N 0.150 m 90 N 0.225 m 100 N 0.250 m The extension measurements obtained from the double spring system in the second experiment are approximately half as accurate as those in the initial experiment. In this study, the measurements increase by 3 units, while in the first experiment, they increased by 5 units. Part 3 – Elastic PE stored in a spring Displacement/Extension (m) Force Applied (N) Elastic PE (J) 0.1 10 N 0.5 J 0.2 20 N 2.0 J 0.3 30 N 4.5 J 0.4 40 N 8.0 J 0.5 50 N 12.5 J 0.6 60 N 18.0 J Graph:

Elastic PE = 24.5 J The relationship between the square of the extension and elastic potential energy is characterized by an inverse proportionality. When the extension is doubled, the PE also doubles. Based on the data, extensions of 0.2 and 0.4 millimeters correspond to 2.0 and 8.0 Joules of potential energy, respectively. Conclusion: In summary, the experiment revealed a clear relationship between the force applied and the spring’s extension. As the force increased, the spring’s extension also increased. In the initial part of the experiment, I observed a 0.005-meter extension when a 1 Newton force was applied. The second section of the experiment demonstrated that connecting two springs effectively halved the extension for the same force. For instance, the data illustrated an extension of 0.003 meters for a 1 N force, nearly half of what I observed in the first part. By plotting the data in the graph, I was able to

make predictions regarding the elastic potential energy in the final section for an extension of 0.7 meters.

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