lab report 8 - PHY2053L

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Broward College *

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2053L

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Mechanical Engineering

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Dec 6, 2023

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docx

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4

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Uploaded by inuyasha078

Cristian Acuna Vasquez 03/16/2020 PHY2053L Title: Energy in Simple harmonic Motion Purpose: The purpose of this experiment is to further understand and demonstrate simple harmonic motion through a simulation experiment involving a spring and different masses. Background Information: Any motion that repeats itself at regular intervals is called periodic or harmonic motion. Motion is periodic about an equilibrium position. The restoring forces are proportional to and oppositely directed to a displacement from the equilibrium position. It can be described for an oscillating mass in terms of its position, velocity, and acceleration as a function of time. energy is present in three forms for the mass and spring system. The mass , m, with velocity, can have kinetic energy KE; which results in the formula KE = ½ mv 2 . The spring can hold potential energy as well or PE elastic , which can be calculated by the formula PE elastic = ½ ky 2 . k is the spring constant and y is the extension or compression of the spring measured from the equilibrium position. The principle of this experiment, if there are no other forces experienced by the system, is conservation of energy ∆KE + ∆PE elastic = 0 Materials: computer Simulation software PhET Procedure: Using the PhET simulation software, use 50 g to 200g masses and mount them into the spring. As the mass moves up and down and it reaches equilibrium, record the kinetic energy, gravitational potential energy, elastic potential energy, thermal energy and total energy and calculate the k constant of the spring.
Data: Part I : Preliminary data collection Mass (kg) Gravitational force Force (N) Spring Displacement (m) 0.05 9.8 0.49 0.07 0.1 9.8 0.98 0.14 0.15 9.8 1.47 0.21 0.2 9.8 1.96 0.28 0.25 9.8 2.45 0.35 Part II : Determining spring constant F= -kx then k= -F/x Mass (kg) Gravitational force Force (N) Spring Displacement (m) k constant (N/m) 0.05 9.8 0.49 0.07 -7.0 0.1 9.8 0.98 0.14 -7.0 0.15 9.8 1.47 0.21 -7.0 0.17 9.8 1.68 0.24 -7.0 0.2 9.8 1.96 0.28 -7.0 0.23 9.8 2.25 0.32 -7.03 0.25 9.8 2.45 0.35 -7.0 0.28 9.8 2.74 0.39 -7.03 0.30 9.8 2.94 0.42 -7.0
Part III : Energy in Simple harmonic motion
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Results/ Calculations: Slope of force vs. position 7.016 N/m Error Analysis: In this lab, there are no errors because it was done by a simulation. In real life, air resistance could be a factor for different results Conclusion: In conclusion, we were able to calculate the spring constant k. We observed that the relationship between the slope of force vs. position graph results in the approximation of the value k of the spring. In simple harmonic motion, there is a continuous interchange of kinetic energy and potential energy. At maximum displacement from the equilibrium point, potential energy is a maximum while kinetic energy is zero. At the equilibrium point the potential energy is zero and the kinetic energy is a maximum. At other points in the motion the oscillating body has differing values of both kinetic and potential energy.