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DEPARTMENT OF PHYSICS AND ASTRONOMY APPALACHIAN STATE UNIVERSITY Online Lab Assignment: Simple Pendulum PHY 1104, Section Date: Name: ● This lab will be conducted online and each student will submit an individual lab report . You are allowed to work on the lab content with another student, but you MUST SUBMIT YOUR OWN UNIQUE images, data, calculations, graphs, explanations, conclusions, etc. Copying items on Lab Assignments or re-using a lab completed in a previous semester (even your own work from a previous semester) constitutes an academic integrity code violation and will be brought before the Office of Student Conduct. ● Read the Introduction and complete the Pre-lab Activity and the Online Quiz for the lab on Asulearn. The Pre-Lab Activity involves predictions, conceptual questions and background information that can be done before you arrive, saving you time during the lab. Many of the Online Quiz questions are based on the Pre-lab activity so it is best that you do the Pre-Lab Activity BEFORE starting the Quiz. The Pre-lab will be turned in and graded as part of the lab assignment. ● You need to make a copy of this document and save to your own google drive using “File>Make a Copy” in order to have editing permission. ● To submit hand-drawn sketches or calculations take a CLEAR picture and save it to a file. You may insert the picture into your lab document in the appropriate locations using "Insert>Image". ● To submit graphs or tables from Vernier Graphical Analysis or Vernier Video Analysis, you can either: "File>Export Graph" or take a screenshot of the graph and save to a file. Insert the graph or table into your lab document in the appropriate locations using "Insert>Image". Purpose Predict and test how the period of motion is affected by the amplitude, mass, gravitational acceleration, and length of a simple pendulum. Apply the results of the period from varying the length of the pendulum to find the acceleration due to gravity. Necessary Equipment PhET Pendulum Lab HTML5 simulator You will use a simulator to explore the harmonic motion of a simple pendulum. The simulator is from the PhET Interactive Simulations project at the University of Colorado Boulder. i. From your web browser, go to https://phet.colorado.edu/en/simulation/pendulum-lab . You can also look for “phet pendulum lab” from a search engine and choose an appropriate result. There is a description of required software ii. Open the simulation by clicking on the arrow over the diagram. You also have the option to download the simulation and run it from a different browser PHY 1104: Simple Pendulum, Page | 1 212 Jan 31 2023 NICO PURCELL

DEPARTMENT OF PHYSICS AND ASTRONOMY APPALACHIAN STATE UNIVERSITY iii. Select the far-right icon (“Lab”) to open the lab. You should see the following display: Vernier Graphical Analysis App : Graphical Analysis is a free software available on multiple platforms that is used to analyze data, plot and apply curve fits. This help document is available to help you download and get started with Graphical Analysis. Introduction: Simple Pendulum A Simple Pendulum: A simple pendulum consists of a mass m attached by a comparatively light string of length L to a point of support P, as seen in figure 1. When the mass is set in motion, it will oscillate back and forth. As the mass oscillates, gravity acts as a restoring force to always pull the mass back toward the equilibrium position, where the net force on the mass is zero. For a simple pendulum such as that shown in Figure 1, the equilibrium position is at the bottom of the path of the mass, at the location where the angle from the vertical axis, θ, is zero. Once the mass m is displaced from its equilibrium position by an angle θ , it will experience a net restoring force due to the component of the gravitational force which points toward the equilibrium position. In this case, the restoring force has a magnitude of (1) ࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? = ࠵?࠵?࠵?࠵?࠵?θ PHY 1104: Simple Pendulum, Page | 2

DEPARTMENT OF PHYSICS AND ASTRONOMY APPALACHIAN STATE UNIVERSITY (2) ࠵? = 2π ࠵? ࠵? Since all measurements need to be made in the base SI units, the period of oscillation T is measured in seconds, the distance between the pivot point and the center of mass of the bob L is measured in meters, and the local acceleration due to gravity g is measured in units of meters per second per second. Review Documents As this is the second lab for General Physics 2, you should review some aspects of the physics lab that were introduced both in the previous lab and in General Physics 1. You will be responsible for the proper use of topics such as Graphing, Measurement Error (Uncertainty), Significant Figures, and Error Analysis. Grading Rubrics for graphs, tables, and predictions are also included. Links to each topic are below. Refresher on Measurement Error : This is a quick summary of measurement error. For a more complete description, please use the document: Introduction to Measurements and Error . Significant figures : How to use significant figures correctly in your calculations for physics lab. Error Analysis : Describes how to compare final answers using percent difference and percent error. Also outlines possible experimental errors. Graphing : How to use graph theoretical equations to find experimental values using curve fits. Student Checklists on Formatting : Use these checklists to make sure that you are submitting your work using proper formatting techniques for physics lab. PHY 1104: Simple Pendulum, Page | 4

DEPARTMENT OF PHYSICS AND ASTRONOMY APPALACHIAN STATE UNIVERSITY Lab Activities: Simple Pendulum Pre-Lab Activity: Making Predictions The simulation shows a simple pendulum with a mass ( m) , suspended on the end of a string of length (L), with a fixed pivot point as shown in the diagram at the right. This mass is also called the pendulum bob. When the mass is displaced to a small initial angle and released, the mass will swing back and forth in periodic motion. The period (T) is the time it takes to complete one whole swing while the amplitude ( θ ) is the angle of release relative to the vertical. The acceleration due to gravity is shown as ( g ) in the figure. Using the information discussed in the introduction, make the following predictions about the motion of the pendulum. You are graded on the detail of your prediction, not on if it matches the conclusions you reach in the actual experiment. As part of the learning process it is important to compare your predictions with your results. Do not change your predictions! Question 1: (2pt) How does the period of the pendulum depend on the amplitude of the swing? Explain your answer using details about the equation for the period of a simple pendulum. Question 2: (2pt) How does the period of the pendulum depend on the mass of the pendulum bob? Explain your answer using details about the equation for the period of a simple pendulum. Question 3: (2pt) How does the period of the pendulum depend on the length of the pendulum?Explain your answer using details about the equation for the period of a simple pendulum. PHY 1104: Simple Pendulum, Page | 5 The period doesn't depend on the amplitude just the length e gravity allouding to the equation The period doesn't depend on mass Just the length gravity a cording to the equation for period

DEPARTMENT OF PHYSICS AND ASTRONOMY APPALACHIAN STATE UNIVERSITY Report your measurement of period of the pendulum, T , with its uncertainty in the proper format of with the ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?ℎ ࠵?࠵?࠵?࠵?࠵? ± ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?ℎ ࠵?࠵?࠵?࠵?࠵? same number of decimal places and units of seconds. If you need to review how to determine the uncertainty in a measurement, read the resource: Reference on Measurement Error . Don’t forget to include units! T 1 = b) Repeat the previous question for amplitudes of 2°, 3°, 4°, and 5° . List the period for all amplitudes 1°to 5°, with their uncertainties, in the table below. Amplitude ( ° ) Period (s) Uncertainty in period (s) 1 2 3 4 5 Question 5: (1pt) Use Graphical Analysis using the license code: gasRe6uJtu, to plot your data of Period vs. Amplitude. This help document is available to help with Graphical Analysis. To do this: 1. Start a Manual Entry Experiment. 2. Enter the Amplitude values in the X column. Then use the column options (three dots at the top of column X) to change the name and units. 3. Enter the Period values in the y column. Then use the column options to change the name and units. 4. Use the Graph Tools (bottom left corner) and choose “ Edit Graph Options ” to add a title to your graph and to set the scaling to “ Always Show 0 ”. a) Scale the window displaying your graph. This may be the Graphical analysis window itself. Minimize the window so that the title and all data is still easily viewed, but the window is as small as possible. This scales the text and data points so you can easily read it after exporting the graph. Export your graph image to a file (click on the file name at the top left and choose “Export>Image”,) or take a screenshot of your graph, to insert below. You may need to play with the scaling of the window to get an easy to read graph.Insert your graph of Period for Varying Amplitude in the space below. Make sure that you follow the checklist for graphs to get full credit. Make sure to set the y-axis scaling to “ Always Show 0 ”. PHY 1104: Simple Pendulum, Page | 7 2.0063 0.00015 2.00635 0.00015 2 00645 0.00015 2 00665 0.00015 2 00695 0100015 2 00725 0.00015

DEPARTMENT OF PHYSICS AND ASTRONOMY APPALACHIAN STATE UNIVERSITY Question 6: (2pts) Observe the shape of your graph. Determine the relationship between the amplitude and the period of a simple pendulum. How does your prediction compare with the results of your experiment? Summarize both your prediction and experimental results and describe the similarities and differences below. Question 7: (2pts) Test your prediction “How does the period of the pendulum depend on the mass of the pendulum bob?” , complete the following: a) Keep the amplitude at 5° , the length at 1.00 m and gather data for different masses as follows: 0.50 kg, 0.80 kg, 01.20 kg, and 1.50 kg . List the period for all pendulum lengths, with their uncertainties, in the table below. Mass (kg) Period (s) Uncertainty in period (s) 0.50 0.80 1.20 1.50 b) Use Graphical Analysis to plot your data of Period for Varying Mass . Make sure that you set your column names and units appropriately, add a title to your graph PHY 1104: Simple Pendulum, Page | 8 period us amplitude for a pendulum amplitude degrees The graph shows a straight horizontal line w a slope of zero This confirms my prediction that the Period is independent of amplitude 2 0070 0 0001 2 0010 0.0001 2 0070 0 0001 2 0070 0 0001

DEPARTMENT OF PHYSICS AND ASTRONOMY APPALACHIAN STATE UNIVERSITY b) Use Graphical Analysis to plot your data of Period for Varying Length . Make sure that you set your column names and units appropriately, add a title to your graph and to set the y-axis scaling to “ Always Show 0 ”. Export your scaled graph to a file and insert your graph of Period for Varying Length in the space below. Make sure that you follow the checklist for graphs to get full credit. Question 10: (2pts) How does your prediction compare with the results of your experiment? Summarize both your prediction and experimental results and describe the similarities and differences below. Activity Two: Measuring acceleration g due to gravity Our goal in this part of the lab is to use the model of the period of a simple pendulum to graphically find the gravitational acceleration, g . This value does vary across the globe and with altitude and therefore commonly must be measured for accurate modeling of particular scenarios. The gravitational acceleration is set as one of the parameters for your experiment, but we are mainly finding it to refresh your skills in linearizing an equation and using a graph to determine a constant in that equation. You should read the resource Graphing before continuing with this activity. In order for the period of a simple pendulum to be written as a line with the equation y = mx+b, and the slope used to determine the local acceleration due to gravity g , we must rearrange the equation. We call this linearizing the equation: PHY 1104: Simple Pendulum, Page | 10 length vs period of a pendulum length Lm The graph shows that the increase in length increased the period indicated by a positive slope This confirms my prediction that length's period are directly positively related

DEPARTMENT OF PHYSICS AND ASTRONOMY APPALACHIAN STATE UNIVERSITY ࠵? = 2π ࠵? ࠵? We will start by squaring both sides of the equation: ࠵? 2 = 4π 2 ࠵? ࠵? = 4π 2 ࠵? ࠵? If we match the rearranged equation to the equation of a line ( y = mx+b). The ࠵? 2 = 4π 2 ࠵? ࠵? length will be the independent variable and correspond to x in the equation of a line, and T 2 is the dependent variable in our equation and correspond to y in the equation of a line. This means that the slope, m = 4 π 2 /g, can be used to calculate the acceleration due to gravity, g , following the equation: g= 4 π 2 /m . The y-intercept, b , will be zero. Question 11: (1pt) Since T 2 is the value we will be using on the y-axis, we will need to calculate it for each value of Length (plotted on the x-axis). Perform your calculations to update the table below. We will not use uncertainties, however your values should have the appropriate significant figures. Length (m) Period (s) Period Squared (s 2 ) 0.50 0.60 0.70 0.80 0.90 Question 12: (1pt) Use Graphical Analysis to plot your data of Period Squared for Varying Length . Make sure that you set your column names and units appropriately. Use the Graph Tools to “Apply a Curve Fit”. Choose “Linear”. a) What is the value for the slope, m , from your curve fit? This should have units of s 2 /m. m = b) Your slope should be in the range of 3.5 s 2 /m to 4.5 s 2 /m. If it is not, DO NOT CONTINUE. Check your equation and graph or ask your instructor for help. You will discuss what you did to correct the problem in the experimental error section. (choose one using the highlight tool) Yes, my slope is in the correct range. (You may continue the lab.) PHY 1104: Simple Pendulum, Page | 11 1142 2.01 1 55 2141 1 68 2.82 1 79 3.22 1 90 3.62 4.03m 52

DEPARTMENT OF PHYSICS AND ASTRONOMY APPALACHIAN STATE UNIVERSITY Experimental Error and Conclusion: Question 15: (4pts) If your percent error was high, or your slope was initially out of the expected range, describe what you did to correct the problem. Even if your percent error was low and you performed this experiment using a simulation, there was still experimental error associated with it . Consider what experimental errors you had either collecting the data or performing the analysis that would affect the results. Experimental errors are something that you couldn’t fix at the time, but would if you were to repeat the experiment. (Note: Miscalculations, numerical rounding, or misreading instructions are NOT errors. Focus on errors with the process of collecting and analyzing the data.) Question 16: (5pts) Summarize your experiment and interpret the major results. It should include: 1) a short description of what you did and WHY it was done (what was the key physics explored); 2) your MAJOR results with values and units (NOT all values measured or calculated); 3) the accuracy of your measured values as shown by your % error values; 4) identify the improvements that would have the most impact on your accuracy and/or precision and how would you implement them in a practical manner (you do not need to reiterate what the errors were, just propose a solution for them); 5) were the goals/purposes of the lab achieved? The conclusion should be concise (not wordy) and written in paragraph form. PHY 1104: Simple Pendulum, Page | 13 I predict that the period would increase if g were to decrease because in the equation gis in the denominator position when the denominator decreases the wholenumber increases The simulation confirms this as on earth the Period was 7 78s on the moon the period was 5.82s I didn't encounter any experimental error during the experiment but I made a small error in rounding when I was performing certain calculations

DEPARTMENT OF PHYSICS AND ASTRONOMY APPALACHIAN STATE UNIVERSITY When you have completed the lab, save it as a pdf using "File>Download As> PDF Document" to submit for grading. Here is a video to show you how to convert a google doc to a PDF. All lab reports must be submitted by Friday at 11:59 PM . If you miss this deadline, please contact your lab instructor. PHY 1104: Simple Pendulum, Page | 14 Forthis experiment I analyzed a simple pendulum to determine the period if amplitude massor length affectedthe length of the period I used a simulation vernier to graph data I found that mass's amplitude did not affect the period but length does directly affect the period Period squared indicated the same result w length period There was 0 error is the calculated value of g wasthe exact same value as theactual value which is 9.80m s There was very minimal error in the experiment