Lab 1_ Springs and Elastic Potential Energy

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Apr 3, 2024

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Lab 1: Springs and Elastic Potential Energy Group #3 Ann McGinty Olivia Kawalec Lysa Korusenge Monday, January 22, 2024 iOLab Unit #4 Introduction: The purpose of this lab was to use Excel to calculate the kinetic and potential energies of a small spring, knowing the mass of the iOLab, to better understand the Law of Conservation of Energy and Hooke’s Law. This is done by experimentally measuring the mass of the iOLab in Exercise 1, graphing a parametric plot of the iOLab’s Force and Wheel position, velocity, and acceleration when a small spring is attached to it in Exercise 2, and using this data to determine how efficient the system is in Exercise 3. Exercise 1: Measure the Mass of the iOLab Remote: Data Collection In this exercise, we calibrated the iOLab, inserted the eye hook, and then selected the accelerometer and force sensors on the iOLab software. We began measuring the data, picked up the iOLab device by its toggle for a few seconds, then set it down and stopped the collection. Afterwards, we highlighted the section of the graph on the force sensor that indicated the iOLab was being held in the air. This represents the force of gravity on the iOLab. The experimental quantity for acceleration was also indicated in the accelerometer sensor’s graph. This allowed us to solve for the mass using the formula: 𝐹 𝑔 = 𝑚𝑔.
Figure 1.1 - Image of iOLab being held in the air to calculate the force due to gravity Exercise 1: Measure the Mass of the iOLab Remote: Data Analysis Figure 1.2 - Highlighted region is showing acceleration due to gravity while iOLab is stationary on table Based on the first graph, we found that Ay = -9.824 m/s^2 +/- 0.0360 m/s^2 This is our value of g (acceleration due to gravity).
Figure 1.3 - Highlighted region is showing the force of gravity when the iOLab is being held stationary in the air Based on the second graph, we found Fy = -1.992 N +/- 0.0310 N This was our value of the force due to the Earth’s gravitational pull. 𝑚 = 𝐹 𝑔?𝑎𝑣 /𝑔 𝑚 = − 1. 992 𝑁 / − 9. 824 𝑚/? 2 𝑚 = 0. 203 𝑘𝑔 𝑚 = 203 𝑔 σ 𝑚 = 𝑚 𝐹 𝑔?𝑎𝑣 /𝐹 𝑔?𝑎𝑣 ) 2 + (σ 𝑔 /𝑔) 2 σ 𝑚 = 0. 203 𝑘𝑔 (0. 0310 𝑁 / − 1. 992 𝑁) 2 + (0. 0360 𝑚/? 2 / 9. 824 𝑚/? 2 ) 2 σ 𝑚 = 0. 00325 𝑘𝑔 Therefore, the mass we obtained is m = 0.203 kg +/- 0.00325 kg.
Figure 1.4 - Image of iOLab on triple beam balance The mass value obtained from the triple beam balance is approximately 195 grams + 4.8 grams (199.8 grams, or 0.1998 kg). The uncertainty associated with this value is +/- 0.05 grams (half the smallest value that can be detected on the scale, which is 1 gram). The value calculated from the triple beam balance scale and our calculations are very similar, and also very close to the expected value of 200 grams. Exercise 1: Measure the Mass of the iOLab Remote: Conclusion The mass of the iOLab was 0.203 kg +/- 0.00325 kg, as calculated from the equation: Fg = mg. We took the force of gravity and the acceleration due to gravity from the force and the accelerometer graphs, respectively. This agrees with the expected value of 200 g for the iOLab. The mass we obtained from the triple beam balance was 199.8 g +/- 0.05 g. One potential
source of error includes holding the iOLab unsteadily in the air, causing the force of gravity measurements to be off. To minimize this error, we can keep our elbow on the table to assure that the iOLab is wobbling as little as possible. Exercise 2: Measure the Spring Constant, k, of the Short Spring: Data Collection In this exercise, we added the small spring onto the force sensor of the iOLab. The iOLab data was reset, and the force and wheel sensors (including position, velocity, and acceleration) were selected. The iOLab was pushed back and forth relative to a vertical barrier (the wall). Next, a parametric plot, plotting Force on the x-axis versus Wheel Position on the y-axis. Afterwards, two points were selected at opposite ends of the plot, and the slope of the line was obtained. This was done five times. Finally, the five values of the slope were averaged to determine the mean and corresponding standard deviation. Figure 2.1 - Image of spring being pushed against the vertical barrier (wall)
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