Lab Manual PHY2048L for current 2021 PDF

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Florida International University

GENERAL PHYSICS LABORATORY 1 MANUAL Edited Fall 2019

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Florida International University Department of Physics

Physics Laboratory Manual for Course PHY 2048L Contents Course Syllabus Grading Rubric Estimation of Uncertainties

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Experiments 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Graph Matching Ball Toss and Error Analysis Projectile Motion Newton’s First and Third Laws Newton's Second Law Atwood's Machine Static and Kinetic Friction Kinetic and Potential Energy Momentum, Energy and Collisions Conservation of Angular Momentum & Rotational Dynamics Simple Harmonic Motion Sound Waves and Beats

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COURSE SYLLABUS LAB COORDINATOR Email: Please use Canvas Inbox UPDATES Updates to the lab schedule, make-up policy, etc. may be found on Canvas. CLASS MEETINGS • During Fall and Spring Semesters classes start the second week of the semester and end the week prior to the final exam week. • Students that have missed their own section may attempt to make-up by attending another section during the time the same experiment is conducted (see PantherSoft for available sections). Admission for make-up is granted by the Instructor on site, no reservation, no guaranteed seating. • Students must sign in each class meeting to verify attendance. ACTIVE LEARNING One of the important goals of this lab course is to strengthen your understanding of what you have learned in the classroom. You will be working in groups and encouraged to help each other by discussing among yourselves any difficulties or misconceptions that occur to you. Apart from the instructor in charge, student Learning Assistants (LA) will be on hand to encourage discussion, for example by posing a series of questions. LAB REPORTS You will be required to submit a lab report at the end of the class period. The format of the report is dictated by the experiment. As you work your way through the experiment, following the procedures in this manual, you will be asked to answer questions, fill in tables of data, sketch graphs, do straightforward calculations, etc. You should fulfill each of these requirements as you proceed with the experiment. Any preliminary questions could be answered before coming to the lab, thereby saving time. This way, you will effectively finish the report as you finish the experiment. Note that for experiments that require them, blank or partially filled in data tables are provided on separate perforated pages in this manual at the end of the experiment. You may carefully tear them out along the perforation and staple them to the rest of your report. GRADES • The weekly lab reports and your active participation will determine your grade in the course. Each week you will receive 30% for active participation and up to 70% for your lab report. • A missed assignment or lab will receive a ZERO grade. • Lab reports are to be handed in before you leave the lab. • THERE IS NO FINAL EXAM • The grading system is based on the following scale although your instructor may apply a "curve" if it is deemed necessary. In addition, “+” and “-“may be assigned in each grade range when appropriate. o A: 90-100%

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o B: 75-90% o C: 60-75% o D: 45-60% WHAT YOU NEED TO PROVIDE Calculator with trig. and other math functions including mean and standard deviation.

AT THE END OF CLASS. 1. Disconnect all sensors that you have connected. 2. Report any broken or malfunctioning equipment. 3. Arrange equipment tidily on the bench. DROPPING THE LECTURE BUT NOT THE LAB If you find it necessary to drop the lecture course, PHY 2048 or PHY 2053, you do not also have to drop this lab course, PHY 2048L. However, you will need to see a Physics Advisor and get a waiver.

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GRADING RUBRIC Expectations for a successfully completed experiment and lab report are indicated in the following rubric. Note that not every scientific ability in the rubric may be tested in every experiment. Therefore the graders will determine the maximum number of points attainable for a report (14), add on participation points (6), and indicate your score out of 20. Grade

Scientific ability Attempt to answer Preliminary Questions Able to draw graphs/diagrams

Able to present data and tables

Able to analyze data

Able to answer Analysis questions

Able to conduct experiment as evidenced by the quality of results

Missing (0 pt)

Inadequate (1 pt)

No attempt to answer Preliminary Questions No graphs or Graphs/drawings drawings poorly drawn with provided missing axis labels or important information is wrong or missing No data or Not all the tables relevant data and provided tables are provided

No data analysis or analysis contains numerous errors No Analysis questions answered

Data analysis contains a number of errors indicating substantial lack of understanding Less than half the questions unanswered or answered incorrectly

Little or no experimental ability as evidenced by poor quality of results

Results indicate a marginal level of experimental ability

Needs improvement (2 pt)

Graphs/drawings have no wrong information but a small amount of information is missing Data and tables are provided but some information such as units is missing Data analysis is mostly correct but some lack of understanding is present Less than a quarter of the questions unanswered or answered incorrectly Results indicate a reasonable level of experimental ability with room for improvement

Adequate (3 pt) Answers to Preliminary Questions attempted Graphs/drawing s contain no omissions and are clearly presented Complete set of data and tables with all necessary information provided Data analysis is complete with no errors

All questions answered correctly

Results indicate a proficient level of experimental ability

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ESTIMATION OF UNCERTAINTIES The purpose of this section is to provide you with the rules for determining the uncertainties in your experimental results. All measurements have some uncertainty in the results due to the fact you can never do a perfect experiment. We begin with the rules for estimating uncertainties in individual measurements, and then show how these uncertainties are to be combined to produce the uncertainty in the final result. The “absolute uncertainty” in a measured quantity is expressed in the same units as the quantity itself. For example, length of table = 1.65 ± 0.05 m or, symbolically, L ± L. This means we are reasonably confident that the length of the table is between 1.60 and 1.70 m, and 1.65 m is our best estimate. If L is based on a single measurement, it is often a good rule of thumb to make L equal to half the smallest division on the measuring scale. In the case of a meter rule, this would be 0.5 mm. Other considerations, such as a rounded edge to the table, may make us wish to increase L. For example, in the diagram, the end of the table might be estimated to be to be at 35.3 ± 0.1 cm or even 35.3 ± 0.2 cm.

If the same measurement is repeated several times, the average (mean) value is taken as the most probable value and the “standard deviation” is used as the absolute uncertainty. Therefore if the length of the table is measured 3 times giving values of 1.65, 1.60 and 1.85m, the average value is 165 + 1 60 + 185 = 170 m 3 The deviations of the 3 values from the average are -0.05, -0.10 and +0.15m, and the standard deviation sum of squares of deviations = number of measurements

So now we express the length of the table as 1.7 ± 0.1 m. Note: Your calculator should be capable of providing the mean and standard deviation automatically. Excel can also be used to calculate these quantities.

=

0 .052 + 010 . 2 + 0 15 . 2 3

. m = 01

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Generally it is only necessary to quote an uncertainty to one, or at most two, significant figures, and the accompanying measurement is rounded off (not truncated) in the same decimal position. “Fractional uncertainty” or “percentage uncertainty” is the absolute uncertainty, expressed as a fraction or percentage of the associated measurement. In the above example, the fractional uncertainty, L/L is 0.1/1.7 = 0.06, and the percentage uncertainty is 0.06 x 100 = 6%. Rules for obtaining the uncertainty in a calculated result. We now need to consider how uncertainties in measured quantities are to be combined to produce the uncertainty in the final result. There are 2 basic rules: A) When quantities are added or subtracted, the absolute uncertainty in the result is equal to the square root of the sum of the squares of the absolute uncertainties in the quantities. B)

When quantities are multiplied or divided, the fractional uncertainty in the result is equal to the square root of the sum of the squares of the fractional uncertainties in the quantities.

Examples 1.

In calculating a quantity x using the formula x = a + b - c, measurements give a = 2.1 ± 0.2 kg b = 1.6 ± 0.1 kg c = 0.8 ± 0.1 kg Therefore, x = 2.9 kg 2

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Absoluteerror in x, x = 0.2 + 01 . + 01 .

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= 0.2 kg

The result is therefore x = 2.9 ± 0.2 kg 2.

In calculating a quantity x using the formula x = ab/c, measurements give a = 0.75 ± 0.01 kg b = 0.81 ± 0.01 m c = 0.08 ± 0.02 m Therefore x = 7.59375 kg (by calculator).  0.01 2  0.012  0.02 2 x =  Fractional uncertainty in x,  +  = 0.25  +  0.75   0.81  0.08  x Absolute uncertainty in x, x = 0.25  7.59375 = 2 kg (to one significant figure) The result is therefore x = 8 ± 2 kg Note: the value of x has to be rounded in accordance with the value of x. If x had been calculated to be 0.003 kg, the result would have been x = 7.594 ± 0.003 kg. 3. The following example involves both rule A and rule B. In calculating a quantity x using the formula x = (a + b)/c, measurements give 6

a = 0.42 ± 0.01 kg b = 1.63 ± 0.02 kg c = 0.0043 ± 0.0004 m3 Therefore x = 476.7 kg/m3 Absolute uncertainty in a + b = 0.012 + 0.022 = 0.02 kg Fractional uncertainty in a + b = 0.02 / 2.05 = 0.01 Fractional uncertainty in c = 0.0004 / 0.0043 = 0.093 Fractional uncertainty in x = 0.0932 + 0.012 = 0.094 Absolute uncertainty in x, x = 0.094 476.7 = 40 kg/m3 (to one significant figure) The result is therefore x = 480 ± 40 kg/m3 Note that almost all of the uncertainty here is due to the uncertainty in c. One should therefore concentrate on improving the accuracy with which c is measured in attempting to decrease the uncertainty. Uncertainty in the slope of a graph Often, one of the quantities used in calculating a final result will be the slope of a graph. Therefore we need a rule for determining the uncertainty in the slope. Graphing software such as Excel can do this for you. Another way to do this is “by hand” as follows: In drawing the best straight line (see figure on following page), 1. The deviations of the data points from the line should be kept to a minimum. 2. The points should be as evenly distributed as possible on either side of the line. 3. To determine the absolute uncertainty in the slope: a. Draw a rectangle with the sides parallel to and perpendicular to the best straight line that just encloses all of the points. b. The slopes of the diagonals of the rectangle are measured to give a maximum slope and a minimum slope. max slope - min slope , where n c. The absolute uncertainty in the slope is given by: 2 n is the number of data points.

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What has been described above is known as “standard uncertainty theory”. In this system, a calculated result, accompanied by its uncertainty (the standard deviation s), has the following properties: There is a 70% probability that the “true value” lies within the ± s of the calculated value, a 95% probability that it lies within the ± 2s, a 99.7% probability that it lies within ± 3s, etc. We may therefore state that the “true value” essentially always lies within plus or minus 3 standard deviations from the calculated value. Bear this in mind when comparing your result with the expected result (when this is known). Some final words of warning It is often thought that the uncertainty in a result can be calculated as just the percentage difference between the result obtained and the expected (textbook) value. This is incorrect. What is important is whether the expected value lies within the range defined by your result and uncertainty. Uncertainties are also sometimes referred to as “errors.” While this language is common practice among experienced scientists, it conveys the idea that errors were made. However, a good scientist is going to correct the known errors before completing an experiment and reporting results. Erroneous results due to poor execution of an experiment are different than uncertain results due to limits of experimental techniques.

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Lab 1. Graph Matching One of the most effective methods of describing motion is to plot graphs of position, velocity, and acceleration vs. time. From such a graphical representation, it is possible to determine in what direction an object is going, how fast it is moving, how far it traveled, and whether it is speeding up or slowing down. In this experiment, you will use a Motion Detector to determine this information by plotting a real-time graph of your motion as you move across the classroom. The Motion Detector measures the time it takes for a high-frequency sound pulse to travel from the detector to an object and back. Using this round-trip time and the speed of sound, the interface can determine the distance to the object; that is, its position. It can then use the change in position to calculate the object’s velocity and acceleration. All of this information can be displayed in a graph. A qualitative analysis of the graphs of your motion will help you develop an understanding of the concepts of kinematics.

board to increase reflection

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OBJECTIVES Analyze the motion of a student walking across the room. Predict, sketch, and test position vs. time kinematics graphs. Predict, sketch, and test velocity vs. time kinematics graphs.

MATERIALS computer Labquest Mini Vernier Motion Detector

board meter stick masking tape

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PRELIMINARY QUESTIONS 1. Below are four position vs. time graphs labeled (i) through (iv). Identify which graph corresponds to each of the following situations and explain why you chose that graph. a. b. c. d.

An object at rest An object moving in the positive direction with a constant speed An object moving in the negative direction with a constant speed An object that is accelerating in the positive direction, starting from rest

2. Below are four velocity vs. time graphs labeled (i) through (iv). Identify which graph corresponds to each of the following situations. Explain why you chose that graph. a. An object at rest b. An object moving in the positive direction with a constant speed c. An object moving in the negative direction with a constant speed d. An object that is accelerating in the positive direction, starting from rest

PROCEDURE Part I Preliminary Experiments

1. Connect the Motion Detector to a digital (DIG) port of the interface. Set the sensitivity switch to Ball/Walk. 2. Place the Motion Detector so that it points toward an open space at least 4 m long. Use short strips of masking tape on the floor to mark the 1 m, 2 m, 3 m, and 4 m positions from the Motion Detector. 3. Open the file “01a Graph Matching” from the Physics with Vernier folder. Monitor the position readings. Move back and forth and confirm that the values make sense. 4. Use Logger Pro to produce a graph of your motion when you walk away from the detector with constant velocity. To do this, stand about 1 m from the Motion Detector, hold the board against your back to improve the reflection of the high frequency sound pulses, and have

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your lab partner click begin to click.

. Walk slowly away from the Motion Detector when you hear it

5. Examine the graph. Sketch a prediction of what the position vs. time graph will look like if you walk faster. Check your prediction with the Motion Detector. NOTE When printing graphs, save the trees by selecting only the pages that you really want to print. Part II Position vs. Time Graph Matching

6. Open the experiment file “01b Graph Matching.” A position vs. time graph with a target graph is displayed. 7. Decide how you would walk to produce this target graph. 8. To test your prediction, choose a starting position and stand at that point. Click to start data collection. When you hear the Motion Detector begin to click, walk in such a way that the graph of your motion matches the target graph on the computer screen. 9. If you were not successful, repeat the process until your motion closely matches the graph on the screen. Print or sketch the graph with your best attempt showing both the target graph and your motion data. 10. Choose Clear All Data from the Data menu, and then click Generate Graph Match, target graph is displayed. Repeat Steps 7–9 using the new target graph.

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11. Answer the Analysis questions for Part II before proceeding to Part III. Part III Velocity vs. Time Graph Matching

12. Open the experiment file “01d Graph Matching.” A velocity vs. time graph is displayed. 13. Decide how you would walk to produce this target graph. 14. To test your prediction, choose a starting position and stand at that point. Click to start data collection. When you hear the Motion Detector begin to click, walk in such a way that the graph of your motion matches the target graph on the screen. It will be more difficult to match the velocity graph than the position graph. Repeat the process until your motion closely matches the graph on the screen. Print or sketch the graph with your best attempt showing both the target graph and your motion data. 15. Choose Clear All Data from the Data menu, and then click Generate Graph Match, target graph is displayed. Repeat Steps 13–14 using the new target graph.

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16. Remove the masking tape from the floor. 17. Proceed to the Analysis questions for Part III.

ANALYSIS Part II Position vs. Time Graph Matching

1. Describe how you walked for each of the graphs that you matched.

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2. Explain the significance of the slope of a position vs. time graph. Include a discussion of positive and negative slope. 3. What type of motion is occurring when the slope of a position vs. time graph is zero? 4. What type of motion is occurring when the slope of a position vs. time graph is constant? 5. What type of motion is occurring when the slope of a position vs. time graph is changing? Test your answer to this question using the Motion Detector. Part III Velocity vs. Time Graph Matching

6. Describe how you walked for each of the graphs that you matched. 7. What type of motion is occurring when the slope of a velocity vs. time graph is zero? 8. What type of motion is occurring when the slope of a velocity vs. time graph is not zero? Test your answer using the Motion Detector.

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Lab 2. Ball Toss and Error Analysis Ball Toss When a juggler tosses a ball straight upward, the ball slows down until it reaches the top of its path. The ball then speeds up on its way back down. A graph of its velocity vs. time wou...