Introduction

• Introduction, Policies, and Procedures
  • Lab Enrollment
    
    You must be officially registered through the Registrar's Office for the Physics lab section you attend; otherwise you may not receive credit for the entire Physics course...
  • Lab Attendance and Missed Labs
    
    You are expected to attend all scheduled labs that correspond to your physics course...
  • Goals of the Introductory Physics Labs at UNC-CH
    
    The Art of Experimentation: The introductory laboratory should engage each student in significant experiences with experimental processes and design...
  • Preparation for Lab and Pre-Lab Assignments
    
    Study the experiment you will be performing before you come to lab...
  • What to bring to lab
    
    Lab manual, Laboratory data sheets, Pre-lab assignment, Scientific calculator (preferably with statistical functions), A pen...
  • Laboratory Work
    
    At the beginning of each lab, your instructor will spend 15 to 20 minutes giving an overview of the experiment you will perform...
  • Lab Reports
    
    Lab reports must be typed or printed clearly in ink. Each report must include a cover page, an abstract, a summary of your experimental results (including your original data sheet and any additional notes, tables, or graphs), and a discussion of your findings...
  • Lab Report Submission and Deadlines
    
    Lab reports are generally due at the next lab period after the experiment is performed; however your lab instructor may be able to give more immediate feedback if you submit your report before your next lab session (this is particularly encouraged for the first lab report)...
  • Lab Report Grading
    
    Reports are graded on a 100-point scale as follows...
  • Lab Grades
    
    Lab scores are reported to your physics course instructor, who counts it as part (usually 25%) of your overall course grade...
  • Lab Exam
    
    A physics laboratory practicum is administered near the end of the semester and counts as 20% of your final lab average...
  • Laboratory and the Honor Code
    
    The Department of Physics and Astronomy fully supports the Code of Student Conduct, as expressed in the document "The Instrument of Student Judicial Governance for the University of North Carolina at Chapel Hill" (1991)...
  • Safety
    
    Always keep safety in mind when working in a laboratory situation...
• Lab Expectations
  • Assignments
    
    Lab assignments are common for all students taking the lab...
  • Expectations of a Physics Lab Student
    
    A procedure will not be provided for you, and no printers are available in the lab rooms...
  • Grading
    
    Each lab consists of a PreLab and LabReport assignment...
  • Plagiarism and Working Together
    
    Complete all WebAssign free-response questions in your own words...
  • Attendance
    
    Arrive on time, if you are more than 10 minutes late for your scheduled lab, you may be asked to leave and you may not be able to make up the lab...
• Concepts Survey
  • Concepts Survey
    
    A concepts survey is administered at the beginning and end of the semester to see how much each student has learned...
• Measurements and Error Analysis
  • The Uncertainty of Measurements
    
    Some numerical statements are exact: Mary has 3 brothers, and 2 + 2 = 4...
  • Types of Errors
    
    Measurement errors may be classified as either random or systematic, depending on how the measurement was obtained (an instrument could cause a random error in one situation and a systematic error in another)...
  • Estimating Experimental Uncertainty for a Single Measurement
    
    Any measurement you make will have some uncertainty associated with it, no matter the precision of your measuring tool...
  • Standard Deviation
    
    To calculate the standard deviation for a sample of N measurements...
  • Standard Deviation of the Mean (Standard Error)
    
    When we report the average value of N measurements, the uncertainty we should associate with this average value is the standard deviation of the mean, often called the standard error (SE)...
  • Anomalous Data
    
    The first step you should take in analyzing data (and even while taking data) is to examine the data set as a whole to look for patterns and outliers...
  • Fractional Uncertainty Revisited
    
    When a reported value is determined by taking the average of a set of independent readings, the fractional uncertainty is given by the ratio of the uncertainty divided by the average value...
  • Propagation of Uncertainty
    
    Suppose we want to determine a quantity f, which depends on x and maybe several other variables y, z, etc...
  • The Upper-Lower Bound Method of Uncertainty Propagation
    
    An alternative, and sometimes simpler procedure, to the tedious propagation of uncertainty law is the upper-lower bound method of uncertainty propagation...
  • Significant Figures
    
    The number of significant figures in a value can be defined as all the digits between and including the first non-zero digit from the left, through the last digit...
  • Use of Significant Figures for Simple Propagation of Uncertainty
    
    By following a few simple rules, significant figures can be used to find the appropriate precision for a calculated result for the four most basic math functions, all without the use of complicated formulas for propagating uncertainties...
  • Uncertainty, Significant Figures, and Rounding
    
    For the same reason that it is dishonest to report a result with more significant figures than are reliably known, the uncertainty value should also not be reported with excessive precision...
  • Combining and Reporting Uncertainties
    
    In 1993, the International Standards Organization (ISO) published the first official worldwide Guide to the Expression of Uncertainty in Measurement...
  • Conclusion: "When do measurements agree with each other?"
    
    We now have the resources to answer the fundamental scientific question that was asked at the beginning of this error analysis discussion: "Does my result agree with a theoretical prediction or results from other experiments?"...
  • References
    
    Baird, D.C. Experimentation: An Introduction to Measurement Theory and Experiment Design, 3rd. ed...
• Data Analysis for Physics Labs
  • Using Excel for Data Analysis
    
    This tutorial will lead you through the steps to create a graph and perform linear regression analysis using an Excel spreadsheet...
• Measuring Instruments
  • Calipers
    
    The Vernier Caliper and the Micrometer Caliper, pictured here, are instruments for making precise measurements of length...
  • Balances
    
    The balance you will use in the laboratory is a modern, digital balance...
  • The Smart Timer
    
    In many of the exercises in this manual, you will be called upon to measure time intervals and frequencies (number of events occurring in a given time interval)...
• Graphing Techniques
  • Graphing Techniques
    
    The construction of graphs is a very important technique in experimental physics...

Laboratories

• Equilibrium of Forces Acting at a Point
  • Introduction
    
    Forces are one of a group of quantities known as vectors, which are distinguished from regular numbers (known as scalars) by the fact that a vector has two quantities associated with it, a magnitude and a direction (related to a coordinate axes of the system you are dealing with)...
  • Procedure
    
    We shall first study the equilibrium of the small ring when there are three forces acting on it...
  • Analysis
    
    Make accurate diagrams on normal rectangular graph paper showing the sum of the forces acting on the ring for both parts of the experiment above...
  • Discussion
    
    Is the condition for static equilibrium satisfied for both parts of this experimant?...
• Motion in One Dimension
  • Introduction
    
    The object of this lab is to help you gain understanding of motion in one dimension. We shall study the motion of a low friction air cart as it moves down a linear air cushioned track inclined at an angle θ...
  • Procedure
    
    In the first part of this experiment, we shall verify Eq. (1) by measuring the position of the cart as a function of time...
  • Analysis
    
    To check if the motion of the cart is described by Eq. (1), you will make a plot of t² vs. x (i.e. t² on the y-axis and x on the x-axis)...
  • Discussion
    
    Summarize your results, i.e. your two values for the acceleration together with their uncertainty...
• Projectile Motion
  • Introduction
    
    In this lab you will study the motion of a freely-falling projectile, namely a small plastic sphere...
  • Procedure
    
    Caution: Safety glasses must be worn during this experiment...
  • Analysis
    
    Calculate the average time-of-flight and the uncertainty for the short and medium ranges...
  • Discussion
    
    Did the time-of-flights for part one change with the initial velocity?...
• Work and Energy
  • Introduction
    
    The concept of energy is one of the most fundamental topics in physics...
  • Procedure
    
    Caution: Safety glasses must be worn during this experiment...
  • Analysis
    
    Calculate and compare the elastic potential energy with the kinetic energy of the ball and all the moving parts of the launcher...
  • Discussion
    
    Is energy conserved throughout this experiment?...
• Uniform Circular Motion
  • Introduction
    
    Uniform circular motion is the motion of an object traveling at a constant (uniform) speed in a circular path...
  • Procedure
    
    If the platform is not level, it will adversely affect your results. Students in the first lab of the week should have leveled the apparatus already...
  • Analysis
    
    The weight of the static mass hanging over the pulley is equal to the centripetal force, F, applied by the spring...
  • Discussion
    
    Compare the value of m obtained from your curve fit to the measured values of the rotating mass m and radius of motion r...
• Energy of a Rolling Object
  • Introduction
    
    In this experiment, we will apply the Law of Conservation of Energy to objects rolling down a ramp...
  • Procedure
    
    Level the bottom surface of the ramp and the tray...
  • Analysis
    
    Complete the data tables with the information needed to compute the initial potential energy and the translational and rotational kinetic energies for each release height...
  • Discussion
    
    To what extent was energy conserved for this experiment?...
• Empirical Analysis of a Ring Pendulum
  • Introduction
    
    If you suspend an object in the shape of a ring on a knife edge and give it a slight push, it will swing back and forth, pivoting about the equilibrium position...
  • Procedure
    
    Select a large ring and mount it on the knife edge support...
  • Analysis
    
    Compare the periods of oscillation you obtained for different amplitudes of the same ring...
  • Discussion
    
    Summarize your findings in the discussion section of your report...
• Frequency Analysis of Sound Waves
  • Theory
    
    Sound waves can be analyzed in terms of their amplitude and frequency...
  • Procedure
    
    Throughout this lab, you will use a microphone and Vernier LabPro interface connected to your CCI laptop to collect sound data, and the Vernier LoggerPro software to analyze the sound waves with frequencies that range from 20 Hz to 16,000 Hz (approximately the range that humans can hear)...
  • Discussion
    
    What differences in waveforms did you observe for the monochord and tuning forks?...
• Energy Audit
  • Introduction
    
    As you should now recognize, physics involves the study of different forms of energy...
  • Procedure
    
    Start by listing at least 15 significant ways that you "consume" energy over the course of a year...

Appendix

Instrument Accuracy

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