Copy of James Clear Final Physics Lab Report #1

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School

University of Alabama *

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520

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Physics

Date

Apr 3, 2024

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pdf

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Uploaded by BarristerFang1573

Title of experiment: Hooke’s Law & Simple Harmonic Motion Name: James Clear Date Performed: 01/23/24 Date Due: 01/30/24 Date Handed in: 01/30/24 Name of Partner(s): Alexia Luciano Introduction (Purpose/Hypothesis/Theory) The purpose of this experiment was to test a theory on Hooke’s law. Hooke's Law states that, “the force that is needed to extend and or shorten a spring by a proportional distance, is directly related to the proportion of that distance.” The first step of this experiment begins with determining the spring constant, k. A well developed understanding of Hooke's Law is gained by carefully examining the springs and the in response that is to follow from a known applied force. The second following phase of the experiment focuses on exploring simple harmonic motion. Simple harmonic motion is a repeated movement where a mass is attached to a spring, which in turn causes the spring to go through elongation or compression from the spring's original position length and then oscillate through its equilibrium position. There were five separate sections of data, and four different instances of data collection with necessary materials, which was completed with careful and precise experimentation. Data Part 1a: Determining k for a single spring Blue spring: Measured spring constant = 26 N/m Blue spring: Actual spring constant = 20 N/m Red spring: Measured spring constant = 12 N/m Red spring: Actual spring constant = 10 N/m

Green spring: Measured spring constant = 43 N/m Green spring: Actual spring constant = 40 N/m Part 1b: Parallel combinations of springs Equilibrium (starting) position of hook bar, 0.130 m = y 0 Mass hanging on springs Weight (force) hanging on springs Position of hook bar Displacement of hook bar from equilibrium 0.15 kg 1.47 0.137 m 0.003 m 0.20 kg 1.96 0.140 m 0.006 m 0.25 kg 2.45 0.143 m 0.009 m 0.30 kg 2.94 0.154 m 0.020 m 0.35 kg 3.43 0.162 m 0.028 m 0.40 kg 3.92 0.173 m 0.030 m Part 1c: Series combination of springs Equilibrium (starting) position of hook bar, 0.305 m = y 0 Mass hanging on springs Weight (force) hanging on springs Position of hook bar Displacement of hook bar from equilibrium 0.07 kg 0.686 0.318 m 0.013 m 0.10 kg 0.980 0.340 m 0.035 m 0.12 kg 1.17 0.370 m 0.065 m 0.15 kg 1.47 0.398 m 0.093 m 0.17 kg 1.66 0.418 m 0.105 m 0.20 kg 1.96 0.449 m 0.144 m

Part 2a: Amplitude variation for a spring A(m) △ t 1 (s) △ t 2 (s) △ t 3 (s) △ t (s) σ t (s) T (s) σ T (s) 0.18 6.19 6.26 6.33 6.26 0.070 0.626 0.007 0.19 6.22 6.54 6.26 6.34 0.541 0.634 0.054 0.20 7.02 7.54 7.22 7.24 0.262 0.726 0.026 0.22 7.21 7.04 7.11 7.12 0.085 0.712 0.0085 0.24 6.92 6.31 7.01 6.74 0.380 0.675 0.003 Part 2b: Mass variation for a spring M (kg) △ t 1 (s) △ t 2 (s) △ t 3 (s) △ t (s) σ t (s) T (s) T 2 (s 2 ) σ T (s) σ T 2 (s) 0.1 kg 5.53 5.52 5.77 5.603 0.144 0.5603 0.333 0.0144 0.00021 0.2 kg 7.56 7.31 7.65 7.506 0.176 0.7506 0.585 0.0176 0.00031 0.25 kg 7.75 8.01 8.01 7.923 0.150 0.7923 0.641 0.0150 0.00023 0.30 kg 7.88 7.99 8.15 8.067 0.136 0.8060 0.664 0.0136 0.00018 0.35 kg 8.85 8.54 8.77 8.721 0.161 0.8720 0.769 0.0161 0.00026 0.40 kg 9.31 9.55 9.63 9.497 0.167 0.9497 0.927 0.0167 0.00028 Sample Calculations: Part 1a: Determining k for a single spring Red spring: Measured spring constant of red spring = 12 Actual spring constant of red spring (instructor given value) = 10 Percent error equation = measured value − true value / (truevalue) × 100, equation; = 12 − 10 ÷ (10) ×100 = 20% Red spring percent error = 20% Part 2a: Amplitude variation for a spring 1. Calculate the mean △ t, and standard deviation, σ t of the three trials for each amplitude. - The formula for standard deviation (SD) is: σ = √(∑(x−¯x) ( x − x) 2 /n) - Mean sample; 6.19 + 6.26 + 6.33 = 6.26 = △ t

2. Calculate the period T , from △ t/10 and record the data. - Sample; 6.26/10 = 0.626 = T 3. Calculate the uncertainty in the period, σ t , as σ t /10, and record the data. - Sample; 0.07/10 = 0.007 = σ T Part 2b: Mass variation for a spring 4. Calculate the mean △ t, and standard deviation, σ t of the three trials for each amplitude. - The formula for standard deviation (SD) is: σ = √(∑(x−¯x) ( x − x) 2 /n) - Mean sample; 5.53 + 5.52 + 5.77 = 5.603 = △ t 5. Calculate the period T, from △ t/10 and record the data. - Sample; 5.603/10 = 0.5603 = T 6. Calculate the uncertainty in the period, σ t , as σ t /10, and record the data. - Sample; 0.144/10 = 0.0144 = σ T 7. If both sides of Equation 2 are squared, the result is: T 2 = 4π 2 M / k. This states that T 2 is proportional to M with 4π 2 /k as the slope. Calculate T 2 and record in your data table. - Slope = 1.785 = 4π 2 /k = 39.44/1.785 = 22.1 8. Calculate the uncertainty in the square of the period, σ T 2 , and record the data. - Sample; 0.0144 2 = 0.00021 = σ T 2 Graphs/Charts: Graph 1: This graph illustrates the relationship between period and amplitude. However, the graph does not show any notable correlation between the two variables, period and amplitude. This falls aligns with the understanding that period is independent of the amplitude, because when amplitude is altered, period remains as similar values as shown above.

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