Instruction Manual Manual No. 012-10461A Physical Pendulum Set Model No.
Model No. ME-9833 Physical Pendulum Set Table of Contents Equipment ................................................................................................... 3 Introduction................................................................................................. 4 Basic Setups ............................................................................................... 4 Background Information............................................................................
Physical Pendulum Set Model No. ME-9833 Physical Pendulum Set Model No. ME-9833 Equipment 4 3 5 2 6 1 Included Equipment Recommended Equipment 1. Pendulum Bar, 28 cm Rotary Motion Sensor (PS-2120 or CI-6538) 2. Offset Hole Base and Support Rod (see PASCO catalog) 3. Solid Disk Super Pulley with Clamp (ME-9448A) 4. Thin Ring Mass and Hanger Set (ME-8979) 5. Thick Ring PASCO Computer Interface (see PASCO catalog) 6. Irregular Shape Vernier Caliper (SF-9711) 7. Mounting Screws (qty.
Model No. ME-9833 Physical Pendulum Set Introduction The Physical Pendulum Set consists of six parts: pendulum bar (28 cm), offset hole, solid disk, thin ring, thick ring, and irregular shape. This set of objects allows the study of physical pendula, moments of inertia, and the parallel axis theorem.
Physical Pendulum Set Model No. ME-9833 Setting Up the Rotary Motion Sensor and Interface Connect the Rotary Motion Sensor to the interface and connect the interface to a computer. For the PASPORT Rotary Motion Sensor, connect the sensor’s plug to a compatible PASPORT interface (e.g., USB Link, PowerLink, Xplorer, Xplorer GLX). For the ScienceWorkshop Rotary Motion Sensor, connect the yellow plug to digital channel 1 and the black plug to digital channel 2 of a compatible ScienceWorkshop interface (e.g.
Model No. ME-9833 Physical Pendulum Set τ = Iα = r⊥F For the basic setup for measuring moment of inertia shown in Figure 2, τ = rT where T is the tension in the string and r is the radius of the step pulley to which the string is attached. The net force ΣF = mg – T = ma is the difference between the tension, T, and the weight, mg, of the hanging mass. Therefore, the tension, is T = mg – ma where “a” is related to the angular acceleration, α, by a = rα.
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Model No. ME-9833 6. Put the object to be measured onto the shaft of the sensor above the three step pulley. Secure it in place with one of the mounting screws. Physical Pendulum Set Mounting screw 7. Measure and record the mass, m, of a mass hanger. 8. Attach the mass hanger to the end of the string that is draped over the Super Pulley. Data Recording: Center of Gravity 1. Wind the string about the step pulley so that the mass hanger is just below the Super Pulley. Hold the irregular shape in place. 2.
Physical Pendulum Set 2. Use calipers to carefully measure the distance, Lcg, from the center of gravity to one of the other pivot points on the irregular shape. Record the measurement as Lcg, the distance from the center of gravity to the pivot point. Model No. ME-9833 Measure Lcg 3. Replace the irregular shape on the Rotary Motion Sensor by attaching it with one of the mounting screws through the pivot point that you used for the measurement. Data Recording: Parallel Axis 1.
Model No. ME-9833 Physical Pendulum Set 1.Repeat the procedure for the other two ‘legs’ of the irregular shape. Determine whether or not the moment of inertia about the parallel axis (the pivot point) is equal to the sum of the moment of inertia about the center of mass plus ML2cm. 2.Repeat the procedure for another physical pendulum object, such as the solid disk.
Physical Pendulum Set Model No. ME-9833 Experiment 2: Minimum Period for an Oscillating Bar Equipment Item Item PASCO Interface and DataStudio software Base and Support Rod Rotary Motion Sensor Metric ruler 28-cm Bar from Physical Pendulum Set The first section outlines the calculation of the distance from the pivot point to the center of mass of a long bar that produces the minimum period of oscillation for the bar at small amplitudes.
Model No. ME-9833 Physical Pendulum Set Measurement of Period for Different Lcg Equipment Setup 1. Measure and record the length, L, of the bar. 2. Mount the Rotary Motion Sensor on a support rod so that the shaft of the sensor is horizontal (parallel to the table). 3. Use a mounting screw to attach the bar to the shaft of the sensor through the first hole above the center hole of the bar. In other words, attach the bar so the pivot point is 2 cm above the center of gravity. Computer Setup 1.
Physical Pendulum Set Model No. ME-9833 2. Double click the label of the new Table display in the Summary panel to open the Data Properties window. Give the table a Measurement Name of ‘Period versus Length’, an ‘X’ Variable Name of ‘Length’ with ‘cm’ for units, and a ‘Y’ Variable Name of ‘Period’ with ‘s’ for units. 3. Find the period of oscillation for the ‘2 cm’ setup. (a) Click the ‘Smart Cursor’ button in the toolbar. (b) Move the Smart Cursor to one of the first peaks of Angular Position.
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Physical Pendulum Set Model No. ME-9833 Experiment 3: Moment of Inertia Based on Period of Oscillation Equipment Item Item PASCO Interface and DataStudio software Balance Rotary Motion Sensor Vernier caliper Physical Pendulum Set Mass and Hanger Set Base and Support Rod String or thread Use the period of oscillation of a physical pendulum to calculate the moment of inertia. Measure the moment of inertia and compare the measured value to the calculated value.
Model No. ME-9833 Physical Pendulum Set 4. Use a mounting screw to attach the disk to the shaft of the sensor through a hole on the edge of the disk. Computer Setup: Period of Oscillation 1. Connect the sensor to a PASCO interface and connect the interface to a computer. 2. On the computer, start the DataStudio program. Set up the program so that it has a Graph display of Angular Position (rad) versus Time (s). 3. Open the ‘Setup’ window and increase the sampling rate from 10 Hz to 100 Hz. 4.
Physical Pendulum Set Model No. ME-9833 Analysis 1. Calculate the moment of inertia using the period, T, the mass, M, and the distance from the pivot point to the center of gravity, Lcg. 2 T MgL cg - – ML 2 cg I cg = -----------------------2 4π 2. Record the calculated value for the moment of inertia in the Data Section. Measurement: Moment of Inertia Equipment Setup 1. Set up the Rotary Motion Sensor horizontally on a support rod with the three step pulley on top.
Model No. ME-9833 Physical Pendulum Set 2. Select a region of the first run of angular velocity data and select ‘Linear Fit’ from the ‘Fit’ menu. 3. Record the value of the slope as the first value of angular acceleration around the center of gravity. 4. Repeat the process for the other two runs of data. 5. Find the average angular acceleration, αcg, and record it in the Data Section. 6. Calculate the net torque, τ = rm(g - rα). 7.
Physical Pendulum Set Model No. ME-9833 Experiment 4: Use a Physical Pendulum to Measure the Acceleration Due to Gravity, g The purpose of this experiment is to use a physical pendulum to measure the acceleration due to gravity.
Model No. ME-9833 Physical Pendulum Set Procedure: Measurement of Period Equipment Setup 1. Measure and record the length, a, and width, b, of the bar. 2. Measure and record the mass, M, of the bar. 3. Mount the Rotary Motion Sensor on a support rod so that the shaft of the sensor is horizontal (parallel to the table). Figure 4-1: Equipment setup 4. Use a mounting screw to attach the bar to the shaft of the sensor through the hole at the end of the bar.
Physical Pendulum Set Model No. ME-9833 2. Click ‘Start’ to begin recording data. After about 30 seconds, click ‘Stop’ to end recording data. Data will appear in the graph of angular position versus time and also in the graph of period versus time. 3. Repeat the process for two more trials. Analysis 1. Determine the average period of oscillation, T, for the pendulum bar and record the value in the Data Section. 2. Assume that the center of gravity is at the midpoint of the pendulum bar.
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Physical Pendulum Set Model No. ME-9833 Appendix A: Specifications Item Dimensions Irregular shape Lcg 1 = 0.051, Lcg 2 = 0.044, Lcg 3 = 0.035, thickness = 0.00635 m Solid disk Diameter = 0.08 m, thickness = 0.00635 m Thin ring Outside diameter = 0.085 m, inside diameter = 0.075 m, thickness = 0.00635 m Thick ring Outside diameter = 0.08 m, inside diameter = 0.04964 , thickness = 0.00635 m Offset hole Outside diameter = 0.096 m, diameter of hole = 0.043 m, thickness = 0.
Model No. ME-9833 Physical Pendulum Set If you are using ScienceWorkshop, click and drag the Graph icon from the list under ‘Displays’ to the measurement name under ‘Data’ that you want to display. An empty Graph display will open with the measurement name on the vertical axis and ‘Time’ on the horizontal axis. To change the measurement shown in the Graph display, click and drag the measurement name from the list under ‘Data’ to the vertical axis of the Graph display.
Physical Pendulum Set Model No. ME-9833 Appendix D: Teacher’s Notes Sample Data for Experiment 1: Parallel Axis Theorem The table shows typical data for the parallel axis theorem using the irregular shape physical pendulum object. The three columns of data are for the three ‘legs’ of the irregular shape object. Table 1: Parallel Axis Theorem for Irregular Shape Item (units) 1 2 3 Object irregular shape A irregular shape B irregular shape C Mass of object, M (kg) 0.06339 0.06339 0.
Model No. ME-9833 Physical Pendulum Set 3. How do you know that the center hole is the center of gravity? Answers will vary. One way to confirm that the center hole is the center of gravity is to balance the irregular shape on a fingertip. Sample Data for Experiment 2: Minimum Period of an Oscillating Bar The screenshot shows typical data for the length from the pivot point to the center of gravity of an oscillating pendulum bar and the corresponding period of oscillation for each length.
Physical Pendulum Set Model No. ME-9833 1 2 2 2 2 1- 2 ----L + L cg – 2L cg = ------ L – L cg = 0 12 12 1 L cg = ---------- L 12 Data Section Length of pendulum bar: 28 cm Calculated value for length that gives minimum period: 8.0829 cm Measured value for length that gives minimum period: 8 cm Percent difference: 1.02% Questions 1.
Model No. ME-9833 Physical Pendulum Set Sample Data for Experiment 3: Moment of Inertia Based on Period of Oscillation Determine the calculated moment of inertia and the measured moment of inertia and record the results in the Data Section. Table 3: Data Section Item Value Item Value Mass of solid disk, M: 0.08818 kg Mass of hanger, m: 0.00512 kg Distance from pivot to center of gravity, Lcg: 0.40 m Average angular acceleration, αcg: 8.87 rad/s2 Average measured period of oscillation, T: 0.
Physical Pendulum Set Model No. ME-9833 Sample Data for Experiment 4: Use a Physical Pendulum to Measure the Acceleration Due to Gravity, g. The following are typical data for the experiment. Data Section Length of pendulum bar, a: 0.28 m Width of pendulum bar, b: 0.015 m Mass of pendulum bar, M: 0.70 kg Average period of oscillation, T: 0.876 s Distance from pivot to center of gravity, Lcg: 0.14 m Calculated value for the moment of inertia about the center of gravity, Icg: 0.
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