The Simple Pendulum - Worksheet 010422

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Drexel University *

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152

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Mechanical Engineering

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Dec 6, 2023

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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. Ben Nordeman _____________________ _____________________ _____________________ 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. l 1 = l 2 = l 3 = .50m .30cm .40cm T (s) T (s) T (s) Multiple trials 1.368 0.996 1.206 1.38 1.01 1.216 1.314 1.02 1.23 Average 1.354 1.0087 1.217 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. 1

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 f(x) = 3.63 x Length(m) vs T^2(s) Length (m) T^2(s^2) Find the slope of the trendline? Slope = 3.6287 As described in the lab manual, this slope is theoretically (4 ? 2 / g ). Use the result for the slope to make an experimental prediction for g . g exp = 4pi^2/3.6287 = 10.8795 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 = (10.8795 -9.81) /9.81 x 100% = 10.9% 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.  g/g= sqrt(((2  T)/Tn)^2+(  l/l)^2)= sqrt(((2*0.01)/1.0087)^2+(0.001/.30)^2) = 0.01046 m  g/g= sqrt(((2  T)/Tn)^2+(  l/l)^2)= sqrt(((2*0.01)/1.217)^2+(0.001/.40)^2) = 0.00859 m  g/g= sqrt(((2  T)/Tn)^2+(  l/l)^2)= sqrt(((2*0.01)/1.354)^2+(0.001/.50)^2)= 0.00765 m 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. 2

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 .23 .20 .15 T 1.34 1.26 1.18 1.32 1.266 1.19 1.31 1.263 1.2 Average T 1.323 1.263 1.19 To determine if changing the amplitude had any effect on the period, plot x vs T and add a trendline with a trendline equation. 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 1.1 1.15 1.2 1.25 1.3 1.35 f(x) = 1.64 x + 0.94 X vs T X ( m) T(s) 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 =(1.376-1.323/1.376)x100% =3.8% 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. 3

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The error goes down as the length goes up, which makes sense as this will have less chance of error. They are a 10 th of the percent error of 10 which shows that partially not measuring the length right can be a big cause in the percent error of a value in an experiment. 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? The difference is 0.05, which is lower than the usual error for stopwatches, but this still causes a 3.2 % relative time variation, which makes a difference in the calculations. This might be due to the error also causing the time to be closer to the actual time theoretically. 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 ). This can be seen in the equation for a period where g is in the bottom of the fraction so the lower the g would make the period increase compared to earth. 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? Increase in length would increase period because they directly proportional as the length goes up so does the period. 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? Well, the denser the object is, the less it will be affected by air resistance, so steal would barely be affected by air resistance, and that's why we said it's so small for this experiment but for like 4

wood and more so for foam air resistance would have a factor because these are less dense materials. 5