Excellent Notebook Example

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Apr 3, 2024

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Lab Notebook: <Excellent Notebook Example> P a g e 1 | 5 Name Awesome Physics Student Station # Lab Group Members Other Awesome Physics Students Instructions: Please increase space as necessary. Make sure your notebook is legible, clear, and well organized. Method We found the spring constant by linearizing data from the Pasco car oscillating system. Materials: • Pasco car, mass of 250g • 4 masses for car, each with a mass of 250g • Track with spring attachments, ruler on track resolution 0.001m • Level • Stopwatch, resolution 0.01 s • Tape to mark the track • 2 matching springs with same spring constant, k=3.4kg/s^2 Procedure: 1. level track 2. check car wheels for good spin 3. attached identical springs to both sides of the car and attached to the hooks on the track 4. place car wheels in grooves on the track and test the oscillation 5. 10 trials for each mass, starting with just the car and adding 1 bar for each data set

Lab Notebook: <Excellent Notebook Example> P a g e 2 | 5 6. timing 3 periods and dividing by 3 for the time of one period, stopwatch resolution of 0.01s 7. from the rest position, pull the cart 9.5cm + .1cm, measured using ruler on the track and put a small piece of tape at the center rest position and the initial release position of the car. 8. Find the average period using =AVERAGE in Excel 9. Find the standard deviation =STDEV.S 10. Find the uncertainty in the mean =STDEV.S()/SQRT(10) 11. Make a plot of mass v period 12. Linearize data: square period and plot mass v period squared and add equation to plot 13. Calculate k using the slope from the linearized equation 14. Find uncertainty of period squared using error propagation 15. Find the uncertainty of the slope using max-min method Data We omitted one trial on the last set of data because the stopwatch wasn’t hit correctly and took a new data point. Original data point was 6.05/3. All other data was included. Mass (kg) 0.25 0.5 0.75 1 1.25 Trial 1 (s) 0.896667 1.233333 1.523333 1.74 1.953333 Trial 2 (s) 0.896667 1.243333 1.526667 1.723333 1.983333 Trial 3 (s) 0.89 1.243333 1.536667 1.736667 1.976667 Trial 4 (s) 0.876667 1.22 1.546667 1.736667 1.956667 Trial 5 (s) 0.873333 1.266667 1.5 1.763333 2.006667 Trial 6 (s) 0.876667 1.276667 1.526667 1.753333 1.956667 Trial 7 (s) 0.886667 1.243333 1.513333 1.736667 2.013333 Trial 8 (s) 0.9 1.243333 1.526667 1.766667 1.986667 Trial 9 (s) 0.886667 1.256667 1.506667 1.783333 2.013333 Trial 10 (s) 0.883333 1.25 1.526667 1.783333 1.95 Average Period (s) 0.886667 1.247667 1.523333 1.752333 1.979667 Standard Deviation 0.009296 0.016105 0.013699 0.021026 0.025164 Uncertainty in the mean (s) 0.00294 0.005093 0.004332 0.006649 0.007957 Average Period Squared (s^2) 0.786178 1.556672 2.320544 3.070672 3.91908 Uncertainty of Average Period Squared (s^2) 0.005213 0.012709 0.013198 0.023303 0.031506

Lab Notebook: <Excellent Notebook Example> P a g e 3 | 5 Data Analysis Spring Equation: 𝑇 = 2𝜋√ 𝑚 𝑘 Linearized Spring Equation: 𝑇 2 = 4𝜋 2 𝑚 𝑘 Error propagation for uncertainty of Period Squared: 𝛿 𝑇 2 = 2 ⋅ 𝛿 𝑇 ⋅ 𝑇

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Lab Notebook: <Excellent Notebook Example> P a g e 4 | 5 Figure 1: This plot shows the mass and the average period data. The relationship is a root curve. The uncertainty bars are included but covered by the points. Figure 2: Linearized plot of mass and period squared. Uncertainty bars are added but covered by the points. 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0.2 0.4 0.6 0.8 1 1.2 1.4 Period (s) Mass (kg) Mass and Period

Lab Notebook: <Excellent Notebook Example> P a g e 5 | 5 Conclusion We measured the spring constant to be 𝑘 = 1.27 𝑘𝑔 𝑠 2 ± 0.07 𝑘𝑔 𝑠 2 which is a bit less than we anticipated of 1.7kg/s^2. In order to find the uncertainty in the slope and then k, we first did error propagation to find the uncertainty of the period squared values so that we could add them as vertical uncertainty bars on our linearized plot. The uncertainty bars were practically eclipsed by the data points which enabled me to have very tight-fitting max and min slope estimates. The low uncertainty value we found using the max min slope method to estimate the uncertainty in the slope and then find the uncertainty in k leads me to have a high level of confidence in the precision of our data, but the distance from the expected value of 1.7 leads me to believe that there is some kind of systematic error in our experiment as our data did not produce a highly accurate value. This could be due to the track not being perfectly level, despite our best efforts, the wheels on the cart not moving as freely as they were originally designed to do (we did switch out our first cart because one of the wheels was not turning properly) or that the springs had previously been deformed past their limits and thus the spring constant would not be equal to what we expected. When collecting our data we always pulled the car to the left, but after we had finished collecting our data we tested pulling the car the same distance to the right and found that there is no difference in period when this happens. This makes sense as there is no provision in the theoretical model equation about distance from an equilibrium point. We also included the mass of the car in our mass values as the mass was not insignificant but in fact equal to the mass of each bar that was later added to the system. We found it really interesting that we perceived the 3 periods to be drastically slower each time another bar was added to the car and did notice that the distance travelled by the car in each period away from the resting point at equilibrium decreased more rapidly with more mass. This indicates that there may be a point at which the model equation isn’t valid with too much mass for certain spring constants and would be interesting to look at further. If we were to do this lab again, we would want to find a way to have smaller mass increases for each data set and spend more time making sure the cart wheels move freely on a perfectly leveled track.

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