Physics067 - Lab3 - Simple Pendulum Lab

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Feb 20, 2024

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Simple Pendulum Lab Worksheet PHYS 101 Complete the following exercises as a group and turn in a single document with the names of group members. Afrah Maisa Shaik Bahodir Jumaboyev Zo Ganbayar Matthew Attieh Iggy Scholl Show work and calculations. An Excel spreadsheet is recommended to compile data. Time Period and Length Measure the time period of your pendulum in the manner described in the lab manual. Make measurements for at least 3 values of l by tying the string at different lengths. Put your data in the table below. To reduce error in your measurements, allow the pendulum to make 5 complete swings (from starting point -> other side -> back to starting point is one complete swing). Measure the time it takes for five swings and then divide by 5 to get the time for a single period. Angle = 45 l 1 =0.45m l 2 =0.30m l 3 =0.40m T (s) T (s) T (s) Multiple trials 1.45 1.22 1.374 1.44 1.14 1.376 1.44 1.14 1.364 Average 1.44 1.16 1.372
T^2 2.07 1.36 1.88 Using T values, plot l vs T 2 , as described in the lab manual. Add a trendline to your plot and take note of the slope in the trendline equation. Find the slope of the trendline? Slope = 4.8 As described in the lab manual, this slope is theoretically (4 𝜋 2 / g ). Use the result for the slope to make an experimental prediction for g . g exp = → 4.8 = 4𝜋 2 /𝑔 g = 8.22 m/s 2 Given that g = 9.8 m/s 2 , how accurate is the prediction? from this experiment Report a percent error using the procedure outlined in the lab manual. Percent error =100* ( (8.22-9.8)/9.8) = 16.12 % Knowing the uncertainties in the time and length measurements, it is possible to calculate the uncertainty in the experimental prediction for g exp . (See lab manual for details.) This uncertainty will be different for each string length. Calculate the uncertainty for each string length and report results. Δl = 1 mm = 0.001 m ΔT = 10 ms = 0.01 s
String length Δg g Δg/g L1 = 0.45 m 0.029 8.22 0.00353 L2 = 0.30 m 0.039 8.22 0.00474 L3 = 0.40 m 0.032 8.22 0.00389 Time Period vs. Amplitude Now investigate the relationship between amplitude or how far you’ve lifted the pendulum and period, T . Keeping the length of your pendulums fixed at 100cm (or any desired length), measure the period in the same manner as before, while varying the angle (x) that you’ve released the pendulum from. Measure T for various values of x . Enter data in the table below. It is okay to not know the specific angle, simply chose a specific location to release the pendulum from for x1 and do a different angle/location for x2 and x3 X 1 X 2 X 3 String l 0.40m 15 30 50 T 1.326 1.362 1.356 1.332 1.324 1.406 1.344 1.358 1.426 Average T 1.334 1.348 1.396 To determine if changing the amplitude had any effect on the period, plot x vs T and add a trendline with a trendline equation. Following the procedure in the lab manual, calculate the relative percent variation in the T measurements from your x vs T data. Show your work and report your result in the space below. Relative % variation =((1.396-1.334)/1.396)*100=4.44%
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Analysis Questions and Further Considerations: 1. How does the calculated uncertainty in g exp for the shortest and longest values of l compare to the percent error in g exp ? What does this suggest about how the length of the string affects the experimental prediction? Hint: Refer to the lab manual for a derivation of uncertainty in g. A shorter string length leads to a higher relative uncertainty in the measurement of g. This is likely because the period T of a pendulum, which is used to calculate g, is less for shorter strings. This means that any small timing errors or other experimental inaccuracies will constitute a larger proportion of the total period- increasing the relative uncertainty. This suggests that using a longer pendulum could reduce the relative error in g(exp), likely because the longer period gives a larger time interval to measure, reducing the impact of any timing inaccuracies. It also indicates that the precision of timing measurements must be higher when using shorter pendulums to maintain the same level of accuracy in determining g. 2. How does the relative % variation in T for the x vs T measurements compare to the precision of the timekeeping instruments (stopwatch)? If they are different, why might that be? In the x vs T trials we got slightly different results for each trial with a percent error of 4.44%. This may be due to the stop watch not being precise, but more likely the slight differences are due to the people stopping and starting the watch not being able to be super exact and precise with the timing. 3. How would the period of a simple pendulum be affected if it were located on the moon instead of the earth? ( g earth =6 g moon ). The pull decreases which increases the time period due to the fact that g value in the moon is of the value on Earth. This means the pendulum will have a decreased acceleration due to the gravity and take longer to complete its oscillation.
4. What effect would the temperature have on the time kept by a pendulum clock if the pendulum rod increases in length with an increase in temperature? The temperature increasing causes the length of the pendulum to increase, creating a greater period in its swing. This would make the pendulum oscillation slightly longer than expected since it would take a longer amount of time to swing back and forth. 5. We have neglected any effect due to air resistance on the motion of the pendulum. The justification for this is the assumption that the energy loss due to air resistance is a small fraction of the maximum kinetic energy of the pendulum. Suppose for the same fixed length of the string, you were to compare bobs made of steel, wood, and foam of the same size. How would the motion (the time period T and the amplitude of oscillation) be affected? The wood, foam, and steel bobs all have different densities, therefore if the bobs are all the same size they would all have different masses as well. The motion of the pendulum would not be affected by the different materials even though they would have different masses. This is because no matter somethings mass, everything will fall at the same rate.