Experimental Physics I
Experimental Physics I PHY 344
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This 4 page Class Notes was uploaded by Clement Bernier on Wednesday October 21, 2015. The Class Notes belongs to PHY 344 at Syracuse University taught by Britton Plourde in Fall. Since its upload, it has received 9 views. For similar materials see /class/225642/phy-344-syracuse-university in Physics 2 at Syracuse University.
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Date Created: 10/21/15
January 2009 Phy 344 Introductory Measurement Procedures and Error Analysis Introduction A measurement of any physical quantity is not complete unless the experimenter speci es hisher uncertainties in performing the measurement Such error analysis is crucial to give the experimental results meaning7 so that they can be compared with theoretical predictions or related measurements Fortunately there are standardized procedures for estimating measurement uncertainties and propagating these errors through various calculations In this introductory project for Phy 3447 you will work on several exercises involving simple measurements and learn these error analysis procedures that will be important for the rest of the experiments you will perform in the lab this semester7 as well as throughout your future scienti c career This project should be possible to complete after the rst few class periods While working on these exercises7 you will learn the general procedure for maintaining a lab notebook7 which should include sketches7 descriptions7 tables of data7 calculations7 plots7 and a discussion of your results Please see the course syllabus for more details about the lab notebooks You will also become familiar with the Origin plotting and analysis software that will be useful for many of the experiments you will perform throughout the semester For this project you will submit your lab notebook only and will not be expected to turn in a separate lab report Required Reading Read chapters 1 5 and chapter 8 of the Taylor error analysis textbook Exercises A Measuring Disks In this exercise7 you will measure the circumference and diameter for several disks and estimate the associated uncertainties Following the procedures de tailed in the textbook7 you will propagate the error through a calculation of the ratio of the circumference to the diameter for each disk 1 Choose ve disks from the supply7 covering a wide range of sizes Make a table in your notebook with columns for diameter7 circumference7 the associated measurement uncertainties7 and two nal columns for the ratio of the circumference to the diameter and its uncertainty 3 Measure the diameter of each disk and estimate your uncertainty7 both in resolving the scale on the ruler and in ensuring that the diameter is properly de ned 00 Devise a technique for measuring the circumference of each disk7 perhaps making a exible measuring tape from a strip of paper Consider possible sources of error in this measurement and estimate the uncertainty 7 For each disk7 compute the ratio of the circumference to the diameter Cf Using the appropriate technique for propagating errors7 determine the un certainty in these ratios 03 After measuring all ve disks7 compute the mean of your distribution for the ratio of circumference to diameter and the standard deviation of the mean This can be done easily with the statistics functions in Origin Review Chapter 4 of Taylor7 particularly section 457 for guidance 5 Using your measured data7 plot circumference vs diameter for each disk7 including error bars based on your estimated uncertainties Determine the best t to a linear dependence using Origin along with the error in the best t line Compare these values7 both from step 6 and step 7 along with their asso ciated uncertainties7 to 7139 00 3 Describe possible sources of systematic error in this measurement and dis cuss possible methods for quantifying and reducing these B Oscillations of a Pendulum For a simple pendulum with length L7 recall that the period is given by T 27h Lg By measuring T and L7 while keeping track of uncertainties7 you will compute a value for 9 You will also explore the possibility of using repeated measurements to reduce the uncertainty in a particular quantity 1 Arrange a pendulum at your lab bench by attaching a clamp to the edge of the table and selecting a string and bob Obtain a timer and get a feel for its stopping and starting mechanism 3 Measure the length of the pendulum and record your measurement uncer tainty Consider carefully how the length should be de ned 00 Start the pendulum oscillating with an amplitude that is not too large Consider the consequences of a large amplitude swing and discuss this in your notebook r e Cf 03 5 00 3 Using a stopwatch7 record the period for one oscillation of the pendulum Repeat this measurement ten times Compute the mean7 standard devia tion7 and standard deviation of the mean for these measurements What should you quote for your best measurement value and associated uncer tainty for this period What is the dominant source of the measurement error Use the stopwatch to measure the time for the pendulum to complete ten oscillations Determine the period and the uncertainty associated with this measurement Repeat this procedure ten times 7 so7 ten trials7 each trial consisting of ten oscillations of the pendulum Perform the same statistical analysis on your data as in step 4 Compare your uncertainty in this measurement of the pendulum period with that from step 4 Discuss potential problems with this measurement approach Use your measurements of the pendulum period and the length to deter mine your best value for the acceleration due to gravity near the surface of the earth Compare this with the accepted value for 9 Change the length of the string on your pendulum and measure the pe riod using the multiple oscillation method from step 5 Assuming your uncertainty from step 5 is reasonable7 you may take this value for the un certainty in the new measurement ofthe period without repeating multiple measurements Adjust the length ofthe pendulum two more times and measure the period for each so that you obtain four data points of length and period Plot these data along with error bars in Origin in such a way that a linear t will have a slope which can be compared with 9 Describe possible sources of systematic error in this measurement and dis cuss possible methods for quantifying and reducing these C Measurements of Height with a Quadrant The quadrant is a simple device for measuring height by sighting to a particular point and measuring the angle above the horizontal This will provide another situation for practicing estimating uncertainties and propagating errors7 includ ing techniques for dealing with a nonlinear function review section 35 from Taylor 1 In order to translate the angular measurement from the quadrant into a height7 you will also need to measure the distance from your observation 3 3 9 4 Cf 03 point to the base of the object being studied This can be done by measur ing the size of your stride7 then pacing off the distance Devise a procedure for characterizing your uncertainty in this measurement ln addition7 you will need to measure the height of your observation point 7 estimate the uncertainty in this measurement Draw a sketch in your notebook of the relevant geometry for such a height measurement using a quadrant7 labeling the various lengths and angles Discuss possible sources of error in the reading ofthe angle on the quadrant and estimate your measurement uncertainty for this quantity Use your quadrant to measure the height of the ceiling in the lab room Room 3777 that is7 the distance from the oor to the ceiling Propagate the errors to determine the uncertainty in your calculation of the ceiling height and compare your calculated value to a direct measurement using a ruler Using the same technique7 go outside and measure the height ofthe Physics Building along with the associated uncertainty Describe possible sources of systematic error in this measurement and dis cuss possible methods for quantifying and reducing these D Measuring a Distribution of Resistances In this exercise7 you will measure many nominally identical resistors then study the distribution of the measured resistances Review Chapter 5 in Taylor H D 00 7 CH Choose a bag of nominally identical resistors from the supply table with labeled values of at least 1 k9 Measure the resistance of each resistor with an ohmmeter and record the value in your notebook Repeat this for at least 50 resistors with the same labeled resistance values Plot these resistance values in a histogram using Origin Explore the effects of choosing different bin sizes Compute the mean of this distribution There is a straightforward way to do this with Origin 7 ask a TA or the instructor for help if necessary Compute the standard deviation7 again7 using the statistics tools in Origin Compute the standard deviation of the mean Using this7 compare the mean value of your distribution with the labeled value on the package of resistors
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