PY 120 Laboratory Manual

Wayne Warrick Passaic County Community College Laboratory Manual PY-120 Physics I

Laboratory Manual PY-120 Physics I Laboratory Passaic County Community College Professor: Wayne Warrick Introduction As part of the Passaic County Community College physics course sequence, the laboratory is a required and integral component to all offered physics courses within the Biological and Physical Sciences Department. This manual will act as a comprehensive reference guide for students to follow during each laboratory experiment. The following pages will detail the laboratory grading criteria, expected report format, laboratory safety and etiquette protocol, and detailed instructions for each experiment. Each laboratory section of this manual includes the necessary theoretical background, pertaining to physics, in order for students to perform each experiment. The laboratory aspect of physics, as with any physical or life science course, represents a necessary part to gather not only an adequate understanding of physics but to obtain a solid foundation which will benefit students of all STEM majors. This is why it is highly recommended to read through this manual, ahead of time, so that you are prepared to not only follow along in the lab, but to actively engage with each of your colleagues and understand each experiment. Additional references, links, and helpful websites are listed within each experiment section. Copyright: Wayne Warrick, 2022 Laboratory Manual Authored by Wayne Warrick May 2019 Rev: July 2023

1 Laboratory Requirements PY-120 Physics I Laboratory Passaic County Community College Professor: Wayne Warrick The laboratory portion of the course counts towards 25% of the final course grade. Unless otherwise stated, each experiment will require a written report. Each lab report will be graded out of a total of 10 points. The required format for lab reports is detailed in the Laboratory Report Format section of this manual and a Sample Report is provided on Blackboard. Laboratory assessment is divided into the following categories: Prelab, Participation, Experimental Data Collection, and the submitted Lab Report. Each of these categories and grading criteria is explained below. Prelab The prelab is intended to prepare students for the laboratory experiment. Before handling sensitive apparatus, equipment, or computer-controlled data collection tools, etc., it is necessary to have an adequate understanding of the experiment. The prelab will test your knowledge and comprehension of the physics required to perform the experiment and demonstrate each student’s level of procedural preparedness. The prelab for each experiment can be found in the lab manual. Do not print these pages out. Read the lab manual in preparation for the week’s upcoming experiment and be able to correctly answer at least three out of five of the prelab questions. All of the answers to the prelab questions can be found in the lab manual. When you arrive to the lab the instructor will hand out the prelabs. You will have 15 minutes to complete and submit. The prelabs will be graded as soon as they are handed in. Students who do not pass the prelab are not permitted to perform the experiment for that week and will receive a grade of zero for the lab report. Read Ahead! It is imperative to read the lab manual and lab procedures prior to performing each experiment. Participation Laboratory attendance is mandatory. Students are expected to answer the prelab questions, participate in the experiment, collect data, and answer questions posed by the instructor. Additional details regarding the attendance portion of the lab can be found on the course syllabus. Lab Safety The instructor will discuss the safety aspects of each experiment at the beginning of the laboratory. Experimental Data During each lab experiment, students will collect data, often a lot of data. Sometimes this is manual data, read from protractors, meter sticks, and scales, other times it is data from electronic instrumentation. It is required that each student record their data from each experiment in a lab notebook. Report Lab reports are required for each experiment. Each group will submit one lab report corresponding to each lab. All parts of the lab report must be typed up. The only exceptions are sketches and calculations, which can be hand-written. If there are multiple trials, it is only necessary to show calculations for one trial. The format for the report can be found in the Laboratory Report Format section of this lab manual. A sample lab report can be found on Blackboard. The lab report must adhere to this format.

2 Lab Report Grading Criteria Each lab report is graded out of 10 points. The grading is based on the following criteria: • Was the report submitted by the due date? Refer to the syllabus. • Does the report adhere to the Laboratory Report Format? • Does the report include the abstract? • Does the abstract include a brief summary of the critical results, values and findings from the experiment? Critical results are numerical values that you consider to be the most critical. • Does the lab report contain and present all of the required experimental data? • Does the report contain applicable data tables? • Does the lab report contain data analysis and all of the required calculations? • Does the report contain all of required plots, with title, axes labeled and units? • Were all of the questions answered correctly and in complete sentences? • Does the lab report contain plagiarized content? If points are deducted from a report, feedback will be provided on Blackboard. Please review this feedback to make corrections to future lab reports. Careful! If a lab report contains data, pictures, answers, etc. obtained from external sources, for example, the Internet, other lab groups, etc., this will count as plagiarism, and the group will receive a zero for that report. Lab Report Submission The completed lab reports must be submitted electronically as one file. The report should be a Microsoft Word document so that Blackboard SafeAssign can easily read it. All PCCC students have free access to Microsoft Office which includes Word and Excel. The group must decide who will be responsible for submitting the report. The completed lab report must be submitted through Blackboard SafeAssign. Emailed reports will not be accepted. The due date for each report can be found on the course syllabus. If the lab report is not submitted on time, 25% will be deducted every day after the due date. Reports submitted a fraction of a full day late will receive a proportional fraction of the deduction. Late reports must also be submitted through Blackboard SafeAssign. If a student is repeating the course, they are not permitted to submit the same lab report from a previous semester. Lab Final Exam There will be a cumulative lab final exam at the end of the semester based on the experiments performed in the lab. The lab final exam will count towards 20% of the lab portion of the course. Prepare for this exam be reviewing previous experiments as found in the lab manual. As a reminder, if a student fails the lab portion of the course, the student will receive a failing grade (F) for the course. Please review the course syllabus for additional details regarding the laboratory policies.

4 Laboratory 1 Data Acquisition and Data Analysis PY-120 Physics I Laboratory Passaic County Community College Professor: Wayne Warrick Introduction The objective of this laboratory is to introduce students to data acquisition and data analysis techniques used in physics. Students will acquire data by performing a simple kinematic experiment. By the end of the lab, students should be able to analyze data, perform calculations involving experimental error, determine the standard deviation, calculate error propagation, and perform graphical analysis. 1. Experimental Error All measurements have some type of error. An error is not a "mistake," rather it is an inherent part of the measurement process. Measurement error is the difference between the measured or observed value (quantity) and its “true” value. By “true” value, we mean a recognized standard or agreed upon accepted value. Accuracy of a measurement is how close the measured value is to the standard value of the quantity being measured. Therefore, errors reduce the accuracy of a measurement. There are two main categories of measurement errors: random errors and systematic errors. Random errors , as the name suggests, are unpredictable during the experiment. They are caused by unknown or unpredictable occurrences in an experiment, e.g., temperature variations, electrical noise, mechanical vibrations, etc. When a measurement is repeated, the next value is unpredictable due to fluctuations in readings of the apparatus or in your interpretation of the instrument. We cannot usually control random errors. All of the statistical methods discussed here only hold for random errors. Regardless of the type of instrument you use to make a measurement, you need to either calibrate, or verify the instrument is calibrated. When the instrument is not calibrated correctly, systematic error will result where the measured values are consistently inconsistent with the standard values. If you can identify the error, it might be possible to eliminate it. Zero error is a type of systematic error which occurs when the instrument does not read zero when it should. Think of a bathroom scale that is not correctly calibrated and reads 5 lb. at the zero mark. Each measurement will be consistently offset by +5 lb. For example, if your “true” weight is 135 lb., the offset scale will read 140 lb. Errors that occur in an experiment that are not random or systematic can be classified as personal errors and can include mistakes made by the experimenter. While looking at an analog scale, viewed from the wrong angle, your eyes will distort the reading, due to what is called parallax error . For example, when you look down at your car gas gauge, the pointer looks like it is on the E, but when you place your head back a little, and observe the gauge straight on, the pointer is slightly above the E mark. In the case of a ruler, tape measure, or any apparatus which has gradations, the smallest gradation is called the least count. The reading error is one-half of the least count. For a standard ruler the least count is 1.0 mm. The reading error is, ± 0.5 mm. If you measure the length of a tube as 9.36 cm, you would report this as 9.36 ± 0.05 cm. Notice that the error has the same number of decimal places as the measurement. If you require high precision a Vernier caliper or micrometer should be used instead. The precision of a measurement is a measure of how reproducible experimental values are, i.e., how close a number of measurements of the same quantity agrees with each other. The deviation of data is called the range. The smaller the range, the more precise the result. The precision is also limited by random errors and instrument limitations. This can usually be reduced by repeating the measurements.

5 From Figure 1, try to determine which target (bull’s-eye) represents accuracy and precision. Figure 1. Bull’s-eye target with black dots representing trials. Images: [1]. 2. Analysis of One or Two Measurements If you want to compare a measured value to the standard value, you need to calculate the percent error. % Error = Experimental Value − Standard Value Standard Value x 100% If the standard value is a theoretical value, i.e., obtained from theoretical calculations, the percent error can be written as, % Error = Experimental Value − Theoretical Value Theoretical Value x 100% If you want to compare two measured values to each other, you need to calculate the percent difference. % Difference = < Exp. Value 1 − Exp. Value 2 Average of these two values < x 100% Example The measured value of the acceleration due to gravity is 9.65 m/s 2 . The standard value is 9.81 m/s 2 . The % Error is -1.63 %. The minus sign indicates that the measured value is below the standard value. The % Difference is 1.64 %. The % Error and the % Difference are written with two decimal places. As a rule, the % Error and % Difference cannot have more decimal places than your measured values. 3. How to Present Data in a Report All measured values must be reported with their error. The word error is interchangeable with uncertainty. For example, you measured the mass of an object to be 10.923 g, but you were only confident of this value to within a measurement uncertainty of 0.2 g. In other words, the mass could be as high as 10.923 + 0.2 g or as low as 10.923 – 0.2 g. Notice how the 9 is the “doubtful” figure. So, if the 9 is doubtful, then for certain, the numbers that come after are even more uncertain, and can be ignored. The proper way to report this measurement is to write Mass = 10.9 ± 0.2 g. With high probability, the mass is within the range 10.7 g to 11.1 g. The uncertainty, 0.2 g, has one significant figure. In general, measurement uncertainty can only have one significant figure. Also, it is necessary to round the measured value to the same number of decimal places as the uncertainty. Make sure you are consistent when reporting uncertainty.

7 Adding or Subtracting Error Consider a function F, which is dependent on two variables a and b. We write this as F(a, b). a and b both have their own uncertainty. How can we determine the uncertainty of F(a, b)? It will help to see this through an example. F(a, b) = a + b. This means that the function adds a and b together. ࠵? = 2.5 ± 0.7࠵?/࠵? # ࠵? = 2.8 ± 0.2࠵?/࠵? # When we add a and b, we get 5.3. We do not want to simply add the absolute errors together, rather we need to use the following formula. ∆࠵? = >(∆࠵?) # + (∆࠵?) # ∆࠵? is the error associated with the function F. ∆࠵? and ∆࠵? are the absolute errors associated with a and b respectively. In this example, ∆࠵? = 0.7 and ∆࠵? = 0.2. Using the above equation, ∆࠵? = 0.73 m/s 2 . The correct way to report this is, F = 5.3 ± 0.7 m/s 2 . As a general rule, if the uncertainty of one measurement is at least three times greater than the error of another measurement, the larger error dominates. It you are measuring the same type of quantity using the same instrument, the error should be the same for each trial. Example: L 1 = 2.50 ± 0.05 cm and L 2 = 5.00 ± 0.05 cm. Determine the sum of these lengths. F = L 1 + L 2 = 7.50 ± 0.07 cm Even when subtracting values, we still add the uncertainties since overall uncertainty increases (it is compounded). Example: During a filtration experiment 4.22 ± 0.03g remains on the filter paper. The initial amount was 5.23 ± 0.03g. How much quantity was sifted from the paper? 5.23 g – 4.22 g = 1.01 ± 0.04 g Multiplying or Dividing Error Consider a function F, which is dependent on two variables v and t. We write this as F(v, t). v and t both have their own uncertainty. How can we determine the uncertainty of F(v, t)? It will help to see this through an example. F(v, t) = v × t. This means that the function takes the product of v and t. v = 15.35 ± 0.1 ࠵?/࠵? t = 8.2567 ± 0.03 ࠵? To determine the uncertainty associated with the function F, we need to use the equation. ∆࠵? = ࠵? × , - ∆࠵? ࠵? / # + - ∆࠵? ࠵? / #

8 First, round each measurement so that it has the same number of decimals as the error. ∆࠵? is the error associated with the function F. ∆࠵? is the error in v. ∆࠵? is the error in t. The uncertainties under the radical are fractional or relative errors. From this example, ∆࠵? = 0.95 . It may be tempting to write the final answer as F = v × t = 127.2 ± 0.95 m . However, the error can only have one significant figure. Round the error 0.95 to 1. The error has no decimal places (refer to page 5). The final value is F = 127 ± 1 m. Example : mass = 25.0 ± 0.5 g, volume = 10.0 ± 0.1 cm 3 . Calculate the density and the percent uncertainty of the density. ࠵? = mass/volume = 2.5. The fractional error of the density is, ∆࠵? = ࠵? × , - ∆࠵? ࠵? / # + - ∆࠵? ࠵? / # ∆࠵? = 0.06 cm 3 . This can be rounded to 0.1 cm 3 . Report the density as ࠵? = 2.5 ± 0.1 cm 3 Example You measure the following linear dimensions: L = 2.0 ± 0.1 m, W = 3.5 ± 0.1 m, H = 4.0 ± 0.2 m You may be tempted to write the volume as V = 28.0 ± 2.1 m 3 . The uncertainty needs to be rounded to 2 m 3 . The final value is, V = 28 ± 2 m 3 . If you have a function of the form, F = a m b n , then you can find the error of F using the following equation. ∆F = F × , m - ∆a a / # + n - ∆b b / # If you have a function of the form, F = + ! , " - # , then you can find the error of F using the following approximation, ∆F = F × -m ∆a a + q ∆b b + p ∆c c / How to Report Error This is really a preference of the person collecting the data. A common format is: 2.50 g/cm 3 ± 3.0% The unit is placed after the measured value. The 3% is the percent error. 2.50 ± 0.07 g/cm 3 . The unit is placed after the absolute error. 0.07 is the absolute error and is 3% of the measured value. 6. Data Analysis A good experiment requires repetition, called trials. For every trial, one or more measurements are made. For every measurement, there is some inherent error. In physics, we want to perform at least three trails. All of the measured numerical values you obtain during each trial is called data. What type of data analysis you perform depends on what the experiment requires. A very common statistical quantity is the mean or average of the data. A review on how to calculate the mean can be found in the Physics Preparation Guide. Another, even more important statistical quantity is called the standard deviation.

10 Example The acceleration due to gravity (g) is measured five times in an experiment. The reported values are: 9.62, 9.65, 9.71, 9.73, 9.80 with units of m/s 2 . The average value of g is 9.70 m/s 2 . The standard value of g is 9.80 m/s 2 . The standard deviation of g is 0.07 m/s 2 . This means that values of g within the range of 9.70 ± 0.07 m/s 2 have a 68% chance of being found. Notice that the standard deviation is the uncertainty. As required, the uncertainty has one significant figure and two decimal places. The measured value of g has two decimal places. Values of g within the range 9.70 ± 2 s have a 95% chance of being found. You cannot report this as 9.70 ± 0.14 m/s 2 because the uncertainty has two significant figures. Round the uncertainty to 0.1. Now, the uncertainty has one decimal place. Round the measured value to 9.7. The correct way to report the values of g within 2 s is 9.7 ± 0.1 m/s 2 . If you have multiple trials, and each trial contains a quantity that results from error propagation, you can use the following technique. Trial 1: S 1 = Value ± Error Trial 2: S 2 = Value ± Error ... Trial N: S N = Value ± Error. The error for each trial results after using error propagation. The average value of S is simple the mean of all of the trials. The error of the average value is ∆S ( = (S /01 + Error of ࠵? 2+( ) − (S /34 − Error of ࠵? 2!5 ) S max is the largest value of S. S min is the smallest value of S. 8. Data Outliers If a data point lies beyond or outside of what was consistent with the data trend, do not ignore this. Take a close look to determine what may have caused the outlier. A test that you can use to determine if the data point is truly an outlier is to compare it to 3 ࠵? . If the data point is less than 3 ࠵? , keep it. If the data point is greater than 3 ࠵? you can exclude that data point. Be sure to discuss this as a discrepancy in the lab report.

11 Laboratory 1-Prelab Data Acquisition and Data Analysis PY-120 Physics I Laboratory Passaic County Community College Professor: Wayne Warrick Question 1 List two types of specific measurement errors you expect to encounter in this lab. Question 2 If the gradations of the meter stick are one millimeter, how will you determine the reading error of the meter stick? Question 3 Write down the expressions for percent error and percent difference. Explain the difference between percent error and percent difference. Question 4 The mass of a certain sample of material is 35.00 ± 0.5 g. Its volume is 15.0 ± 0.1 cm 3 . Calculate the density and the percent uncertainty of the density. Show all steps. Question 5 Calculate the variance and the standard deviation of the following test scores: 72, 75, 80, 86, 90. Show all steps in the calculations.

13 Step 5) Determine the average speed of the cart. Step 6) Determine the variance and standard deviation of the speed. Step 7) Calculate the error of the average value of the speed. Part 3 Step 1) Place the PASCO Fan Cart bumper at the zero (0 cm) mark on the track. Step 2) Position one student to record the distance the cart travels and another student, with a stop watch, to record the elapsed time. Instructions for the PASCO ME-6977 Fan Cart o Rotate the fan case until the pointer is aligned with the 0 o mark. o Press the POWER button once. This puts the cart in STANDBY mode. Step 3) Set the cart fan speed to MEDIUM, with no pulse duration. Step 4) Press the power button and allow the cart to move until it reaches approximately 100 cm and record the elapsed time. Step 5) Be especially careful not to let the cart drop off the table. Step 6) Perform a total of 5 trials. Record data in Table 3 . Step 7) Calculate the average velocity of the cart. Table 3 Trial # Distance (m) Time (s) 1 2 3 4 5

14 Part 4 The displacement of a car as a function of time graph is shown below. The initial velocity is zero. Step 1) By analyzing the plot below, determine the acceleration of the car. Step 2) Kinematics tells us that the displacement of an object as a function of time is given by, ࠵? 6 = ࠵? ! + ࠵? ! ࠵? + 1 2 ࠵?࠵? # The starting point of the car is the zero-reference point. The derivative of this expression as a function of time is the velocity of the car. It is not possible to differentiate directly. Step 3) Create a table in which one column is Δ࠵? and another column is Δ࠵? . Step 4) Using the provided plot, choose points x 1 , x 2 and t 1 , t 2 which are close to each other. Use these data points to determine the slope of the function. Move left to right, choose more data points, and fill in the table from Step 3. Step 5) Plot the data points from the table. This plot represents velocity as a function of time. Questions 1) What is the difference between percent error and percent difference? Explain. 2) If your work bench was sloped, what type of error would this produce? 3) If a cluster of data has a low standard deviation, what does that tell us about the spread? 4) What does the slope of the distance vs. time plot represent? 5) What is the difference between RMSE, linear regression, and “best-fit”? 6) In Part 3, if the velocity of the car is constant, what is its acceleration? 7) In Part 3, once the car accelerates, is the displacement as a function of time still linear? Explain. Include all data, graphs, tables, calculations, and answers to these questions in the lab report. 0 50 100 150 200 250 300 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Displacement (m ) Time (s) Displacement vs. Time

16 Laboratory 2-Prelab Free-Fall PY-120 Physics I Laboratory Passaic County Community College Professor: Wayne Warrick Question 1 What is the standard value for the acceleration due to gravity? Question 2 What is the purpose of the release mechanism? Question 3 How does the mass of an object affect its rate of vertical fall? Question 4 What mathematical function (linear, parabolic, hyperbolic, etc.) should the plot of the velocity of the falling ball as a function of time be? Question 5 Plot the following function: y(t) = 4.9t 2 and determine the slope and y-intercept. The plot needs to have axes and units. From this function determine the velocity and acceleration as a function of time and plot both functions.

17 Lab Procedure Materials Needed: Tape measure, two meter sticks, adhesive tape, stopwatch, ball, release mechanism Step 1) Attach and vertically position two meter sticks together using adhesive tape. Step 2) Attach the meter sticks to the edge of the workbench. Step 3) One student will position the ball close to the ground, parallel to the meter sticks, and prepare to release the ball. Another student will record the elapsed time of fall using the stopwatch. It is recommended to use the release mechanism so that no initial velocity is imparted to the ball. Step 4) At the instant the ball is released, start the stopwatch (unc. = 10 ms). This will require a lot of practice. You are likely to obtain a few anomalous results. Record your data for displacement and elapsed time to the nearest 10 ms. Step 5) For each trial, the ball should be incrementally raised to a new height, released and the elapsed time of fall recorded for a total of ten (10) trials. Be sure to include the uncertainty in your final answer for the average acceleration due to gravity. Step 6) Using graphical analysis software plot the vertical position as a function of the square of elapsed time for the ball. The y-axis scale should have units of cm for higher resolution. Step 7) Plot the velocity and acceleration of the falling ball as a function of time. Explain in your lab report why your average value of (g) is different than the standard value. Discuss observed discrepancies and what may have contributed to this. Step 8) Plot the vertical displacement of the ball as it fell using the increments of time from Table 1. Table 1 Step 9) Calculate the average value of the acceleration due to gravity, its standard deviation and the uncertainty of the mean of g. Questions 1) What does the slope of the plot y vs. t 2 represent? 2) What does human reaction time indicate? Where could this have occurred in this experiment? 3) If the mass of the ball was doubled, how would this affect the acceleration due to gravity? 4) During a free-fall experiment, a solid metal ball and a hollow metal ball are positioned at the same height and released at the same instant. The metal of each ball has the same density. Which ball has a greater inertia? Should the ball with greater inertia fall more slowly than the lighter ball? Include all data, graphs, tables, calculations, and answers to these questions in the lab report. Trial Distance (cm) t (s) t 2 (s 2 ) g (m/s 2 ) v (m/s) a (m/s 2 )