Description For each trial, calculate the difference between m1 and m2. Enter the result in the col ...
Description For each trial, calculate the difference between m1 and m2. Enter the result in the column labeled mdiff. For each trial, calculate the total mass in grams. Enter the result in the column labeled mT. Note that for Part II, there is a column in the table for 1/mT. Disconnect all sensors and choose New from the File menu. Plot a graph of acceleration vs. mdiff, using the Part I data. Based on your analysis of the graph, what is the relationship between the mass difference and the acceleration of an Atwood’s machine? NOTE When printing graphs, save the trees by selecting only the pages that you really want to print. Similarly, plot a graph of acceleration vs. 1/mT, using the Part II data. Based on your analysis, what is the relationship between total mass and the acceleration of an Atwood’s machine? Are your results consistent with the theoretical expression that you derived for the acceleration? Use the slope of the graph in Part I, together with the total mass, mT to obtain the acceleration due to gravity, g. Also obtain g using the slope of the graph in Part II. How do your values compare with each other and with the "textbook value"? If there are differences, what factors do you think might be responsible? UNFORMATTED ATTACHMENT PREVIEW Florida International University GENERAL PHYSICS LABORATORY 1 MANUAL Edited Fall 2019 0 Florida International University Department of Physics Physics Laboratory Manual for Course PHY 2048L Contents Course Syllabus Grading Rubric Estimation of Uncertainties 2 4 5 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 9 13 20 24 30 35 39 46 51 56 61 66 1 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% 2 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. 3 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 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 Data analysis is mostly correct but complete with some lack of no errors 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 All questions answered correctly Results indicate a proficient level of experimental ability 4 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 + 185 ? = 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 + 015 . 2 3 = 01 . m 5 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 Absolute error in x, ?x = 0.22 + 01 . 2 + 01 .2 = 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 + 0.02 2 = 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 c. The absolute uncertainty in the slope is given by: , where n 2 n is the number of data points. ? 7 M ax .s lo pe e n i l t s e B 1 4 e p .slo in M Extension(mm) 1 2 1 0 8 6 4 2 3 4 5 6 7 M a s s ( k g ) F i g . 1 G r a p h o f e x t e n s i o n v s . m a s s 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. 8 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 Figure 1 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 9 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. 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 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 10 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. . A new 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. . A new 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. 11 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. 12 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 would show these changes. Is there a mathematical pattern to the changes in velocity? What is the accompanying pattern to the position vs. time graph? What would the acceleration vs. time graph look like? In this part of the experiment, you will use a Motion Detector to collect position, velocity, and acceleration data for a ball thrown straight upward. Analysis of the graphs of this motion will answer the questions asked above. Motion Detector Figure 1 OBJECTIVES • Collect position, velocity, and acceleration data as a ball travels straight up and down. • Analyze position vs. time, velocity vs. time, and acceleration vs. time graphs. • Determine the best-fit equations for the position vs. time and velocity vs. time graphs. • Determine the mean acceleration from the acceleration vs. time graph. MATERIALS computer Labquest Mini Logger Pro Vernier Motion Detector volleyball or basketball wire basket PRELIMINARY QUESTIONS 1. Consider the motion of a ball as it travels straight up and down in freefall. Sketch your prediction for the position vs. time graph. Describe in words what this graph means. 13 2. Sketch your prediction for the velocity vs. time graph. Describe in words what this graph means. 3. Sketch your prediction for the acceleration vs. time graph. Describe in words what this graph means. PROCEDURE 1. Connect the Vernier Motion Detector to a digital (DIG) port of the interface. Set the Motion Detector sensitivity switch to Ball/Walk. 2. Place the Motion Detector on the floor and protect it by placing a wire basket over it. 3. Open the file “06 Ball Toss” from the Physics with Vernier folder. 4. Collect data. During data collection you will toss the ball straight upward above the Motion Detector and let it fall back toward the Motion Detector. It may require some practice to collect clean data. To achieve the best results, keep in mind the following tips: • Hold the ball approximately 0.5 m directly above the Motion Detector when you start data collection. • A toss so the ball moves about 0.5 m above the detector works well. • After the toss, catch the ball at a height of 0.5 m above the detector and hold it still until data collection is complete. • Use two hands and pull your hands away from the ball after it starts moving so they are not picked up by the Motion Detector. When you are ready to collect data, click as you have practiced. to start data collection and then toss the ball 5. Examine the position vs. time graph. Repeat Step 4 if your position vs. time graph does not show an area of smoothly changing position. Check with your instructor if you are not sure whether you need to repeat the data collection. ANALYSIS 1. Print or sketch the three motion graphs. The graphs you have recorded are fairly complex and it is important to identify different regions of each graph. Click Examine, , and move the mouse across any graph to answer the following questions. Record your answers directly on the printed or sketched graphs. a. Identify the region when the ball was being tossed but still in your hands: Examine the velocity vs. time graph and identify this region. Label this on the graph. Examine the acceleration vs. time graph and identify the same region. Label the graph. b. Identify the region where the ball is in free fall: Label the region on each graph where the ball was in free fall and moving upward. Label the region on each graph where the ball was in free fall and moving downward. c. Determine the position, velocity, and acceleration at specific points. On the velocity vs. time graph, decide where the ball had its maximum velocity, just as the ball was released. Mark the spot and record the value on the graph. On the position vs. time graph, locate the maximum height of the ball during free fall. 14 Mark the spot and record the value on the graph. What was the velocity of the ball at the top of its motion? What was the acceleration of the ball at the top of its motion? 2. What does a linear segment of a velocity vs. time graph indicate? What is the significance of the slope of that linear segment? 3. The graph of velocity vs. time should be linear. To fit a line to this data, click and drag the mouse across the free-fall region of the motion. Click Linear Fit, . 4. How closely does the coefficient of the t term in the fit compare to the accepted value for g? 5. The graph of acceleration vs. time should appear to be more or less constant. Click and drag the mouse across the free-fall section of the motion and click Statistics, . 6. How closely does the mean acceleration compare to the values of g found in Step4? Error Analysis INTRODUCTION In this experiment, you will use different apparatus to determine the acceleration of a freely falling object. Once you have done this, you will address the following questions: How do I decide if the value I obtained is “close enough” to the accepted value? If I were to repeat the experiment several times, within what range would I expect my values to fall? This experiment affords you the opportunity to understand variations in experimentally determined data. OBJECTIVES In this experiment, you will Determine the value of the acceleration of a freely falling object. Compare your value with the accepted value for this quantity. Learn how to describe and account for variation in a set of measurements. Learn how to describe a range of experimental values. MATERIALS Vernier data-collection interface Logger Pro or LabQuest App Vernier Photogate foam pad to cushion impact Picket Fence clamp or ring stand to secure Photogate 15 Picket fence Figure 1 PREAMBLE In this experiment, you will use software which records the elapsed time between some regularly occurring events. When the Picket Fence (a strip of clear plastic with evenly spaced dark bands) passes through a Photogate, the device notes when the infrared beam of the photogate is blocked by a dark band and measures the time elapsed between successive “blocked” states. The software uses these times and the known distance from the leading edge of a dark band to the next to determine the velocity of the picket fence as it falls through the photogate. The elapsed time from Blocked state to Blocked state decreases as the picket fence accelerates in free fall through the photogate.? PROCEDURE 1. Connect the photogate to one of the digital inputs on the interface and start the datacollection program. If the photogate has a sliding door, make sure it is open. 2. Check to see if the sensor is working by passing your hand between the infrared LED and the detector. The gate Status should change from “Unblocked” to “Blocked.” 3. Fasten the photogate to a support rod or ring stand so that the arms of the photogate are horizontal (see Figure 1). 4. Open the file "Picket Fence" in folder Lab02 on the desktop. 5. Change the graph setup to view only the velocity vs. time graph. 6. Place something soft on the table or floor to cushion the picket fence as it strikes the surface. 7. Hold the picket fence vertically just above the photogate, start collecting data, and release the picket fence. Make sure that it does not strike the photogate as it passes through the arms. 8. Perform a linear fit on the graph of velocity vs. time. Print or sketch a copy of your graph. Take a moment to discuss what the slope and intercept of the line of best fit represent. When printing, choose Print Graph under the File menu on Logger Pro. DO NOT use Print as it will print all pages including the data file. 16 9. Based on your discussion, predict whether either of these quantities would change if you were to drop the picket fence through the photogate from a higher point. Test your prediction. 10. To see how repeatable the values of the slope are, repeat Steps 7 and 8 to obtain a total of 5 sets of resdings. Record your values of the slope and intercept in the table. 11. You may quit the data-collection program for now but do not disassemble your apparatus. You will return to it later. EVALUATION OF DATA 1. How do you account for the fact that the values of the slope were nearly the same, whereas the values of the intercept were much more variable? 2. It is highly unlikely that you obtained identical values of the slope of the best-fit line to the velocity vs. time graph for each of your trials. How might you best report a single value for the acceleration due to gravity, ag, based on your results? Perform the necessary calculation. 3. How does your experimental value compare to the generally accepted value (from a text or other source)? One way to respond to this question is to determine the percent difference between the value you reported and the generally accepted value. Note that if you simplify your units of slope, they will match those of the reported values of ag. 4. Your determination of the percent difference does little to answer such questions as, “Is my average value for ag close enough to the accepted value?” or “How do I decide if a given value is too far from the accepted value?” A more thorough understanding of error in measurement is needed. Every time you make a measurement, there is some random error due to limitations in your equipment, variations in your technique, and uncertainty in the best-fit line to your data. Errors in technique or in the calibration of your equipment could also produce systematic error. We’ll address this later in the experiment. In order to better understand random error in measurement, you must return to your experimental apparatus to collect more data. 5. Begin the data-collection program "Picket Fence" in folder Lab02 as you did before and drop the picket fence through the photogate another 20 times, bringing the total number of trials to 25. Since you are now investigating the variation in the values of ag, you need only record the value of the slope of the best-fit line to the velocity-time graph for each trial. Record the value of the slope in the Table on page 19. 6. Launch the Logger Pro file Lab02-histogram. Enter your values of slope in the Table on page 19. 7. In your discussion, you will decide how best to configure the features of the histogram so as to represent the distribution of your values in the most meaningful way. To do this, choose Options>>Additional Graph Options>>Histogram Options, and adjust the settings under the Bin and Frequency Options tab. 8. Determine the average value of ag for all 25 trials. How does this compare with the value you obtained for the first 5 trials? In which average do you have greater confidence? Why? 9. In what range (minimum to maximum) do the middle 2/3 of your values fall? In what range do roughly 90% of the values closest to your average fall? 17 10. One way to report the precision of your values is to take half the difference between the minimum and maximum values and use this result as the uncertainty in the measurement. Determine the uncertainty in this way for each range of values you determined in Step 9. 11. In what place (tenths, hundreds, thousandths) does the uncertainty begin to appear? Discuss whether it is reasonable to report values in your average beyond the place in which the uncertainty begins to appear. Round your average value of ag to the appropriate number of digits and report that value plus the uncertainty. 18 Slope (m/s2) Intercept (m/s) 19 Lab 3. Projectile Motion You have probably watched a ball roll off a table and strike the floor. What determines where it will land? Could you predict where it will land? In this experiment, you will use a projectile launcher to shoot a ball horizontally from a table top. Using your knowledge of physics, you will be able to determine the launch speed. You will also be able to get the launch speed by measuring the horizontal range as a function of the launch angle. OBJECTIVES Use a Mini Launcher to project a ball horizontally onto the floor Apply concepts from two-dimensional kinematics to determine the launch speed. Use the Mini Launcher to determine the horizontal range of a ball as a function of the launch angle. Use an appropriate graph to obtain an average value for the launch speed.. MATERIALS computer Labquest Mini Logger Pro Mini Launcher level meter stick or metric measuring tape carbon paper steel ball goggles plumb bob PRELIMINARY QUEST
