PHYSICS LAB Newton's Law Printed Names: Signatures: Date: Lab Section: Instructor: GRADE: PHYSICS DEPARTMENT JAMES MADISON UNIVERSITY Revision August 2003
NEWTON S SECOND LAW Purpose: 1. To become familiar with the air track as a system for minimizing the effects of friction. 2. To verify Newton s second law. 3. To examine analysis techniques. 4. To develop sound methods to ensure experiments are working. One important goal of this lab is to present the student with the process of performing experiments. A good experimentalist is continually examining and questioning. There will be questions posed in the manual that are designed to alert the student to important issues. In future experiments students will be expected to raise these kinds of questions on their own. Materials: Photogate with LabPro, Logger Pro software, airtrack with air source, gliders, weight hanger, balance, and assorted masses. PART 1: THEORY The system shown in Fig. 1 consists of two masses, m1 and m2 connected by a massless, inextensible string which passes over a massless, frictionless pulley. When Newton s second law is applied to the system the following equations result: mass 1: m1a = T (1) mass2: m2a = m2g -T (2) mass 1 mass 2 Figure 1 60
where T is the tension in the string. If equations (1) and (2) are added, the resulting equation of motion is (m1 + m2) a = m2g. (3) You will check the validity of equation (3) experimentally with the aid of an almost frictionless air track. A. Constant accelerating force In this part of the exercise, we will keep the acceleration force F a = m2g constant and check the dependence of the acceleration a on the total mass m1 + m2. Since equation (3) may be rewritten as with a = [1/(m1+m2)]F a (4a) F a = m2g (4b) we see that the graph of the acceleration versus the RECIPROCAL of the total mass (m1+m2) should be a straight line THROUGH THE ORIGIN with a slope equal to F a. B. Constant total mass In this part of the exercise, we will keep the total mass m1 + m2 constant and check the dependence of the acceleration a on the acceleration force F a = m2g. Since equation (3) may be rewritten as a = F a/(m1+ m2) (5a) with F a = m2g (5b) we see that the graph of the acceleration versus the accelerating force should be a straight line THROUGH THE ORIGIN with slope equal to the reciprocal of the total mass: slope = 1/(m1+m2). (5c) 61
PART II EXPERIMENTAL TECHNIQUES A. The air track In performing the experiment we will make use of the air track. The air track is a device which provides an approximately frictionless system for mechanics experiments. A glider coasts on a thin layer of air which prevents it from making contact with the metal surface of the track. pickett fence photogate glider Figure 2: Experimental Apparatus B. Measuring the acceleration We will use the Logger Pro software with the plastic picket fence mounted on the top of a glider to measure the acceleration of the glider. The experimental apparatus is shown in Figure 2. To set up the Logger Pro software open the experimental setup file "Newton's Law". Use the "Open" item on the "File" menu. You will find the file in the Intro Physics folder on the desktop. This file configures the photogate and sets up the collection mode. This setup uses the photogate to measure the time interval between the arrival of the dark areas of the picket fence at the photogate. From this time and the distance between the areas on the picket fence (already initialized in Logger Pro to be 5.0 cm) the average velocity and average acceleration are calculated and recorded. Examine the setup before proceeding. PART III: MEASUREMENTS AND ANALYSIS Good technique There are several aspects of this experiment that may be new to the experimenter. How should one proceed in order to successfully perform the measurement? First try to understand what will be recorded and why it is being measured. Because we want to explore the motion of objects under the influence of applied forces, the experiment is designed to measure time intervals. Given the distance moved by the glider and the time interval, velocity and acceleration can be calculated 1. The goal of this experiment is to compare the 1 In a well designed experiment the methods used should be questioned as to their validity. For this lab, in the interest of time, the student can assume that these procedures are adequate. 62
acceleration measured to the acceleration predicted by Newton s law from a measured force and a measured mass. List these three quantities on your data sheet. Some questions that should be answered by the experimenter are (Use the questions to guide your thinking.) :?? What forces are being applied??? Which ones are relevant according to the ideal design??? Which ones may influence the experiment because the experiment is not ideal??? What object is actually experiencing the force and moving (think about this question)??? How does one measure the applied force? Briefly summarize your response to the above question by writing a paragraph in a text box in Excel. Understanding the measurement will prevent the student from performing the experiment incorrectly. Try to reduce the physics that you are investigating to a straightforward statement. In addition to clearly defining the measurement, good experimentalists test their equipment. If the photogate is designed to directly measure time intervals then test it. Turn on the air track. Collect data. Move the glider by hand very slowly through the photogate. You can manipulate the motion in very simple ways so that you can examine what is actually being measured. First try some movements and note what is recorded by Logger Pro. Then perform more controlled motions where you predict what the results should be. With a watch you can roughly measure time intervals and compare. From your observations describe what starts the data recording and what is measured. Logger Pro produces a table of values t, x, v and a. You should be able to ascertain how the times and positions are measured. (Velocities and accelerations are derived from this data. The student does not need to discover the algorithm used to find v and a.) Summarize in a text box in Excel what and how Logger Pro measures the data. A. Constant accelerating force Measure the mass of the glider and record this value, m g, on your spreadsheet clearly labeled with appropriate units. Also include an estimate of the uncertainty in your measurement. An example is shown below. mass of cart 510 grams uncertainty in mass 16 grams estimated based on reproducibility & ability to read the scale In this exercise it is essential that the air track be level. The leveling adjustment knob is at the end of the track away from the pulley. Now place one glider somewhere near the middle of the track so that it is not moving. Turn on the air source and level the track by turning the knob at the end of the airtrack. The airtrack is level when the glider has little or no tendency to slide all the way over to one end of the track. Initially turn the leveling screw one complete turn at a time. Try to get the track level to within about a quarter turn of the screw. 63
After the track is level, attach the mass hanger and string to the glider as shown in Fig. 2. Start with an accelerating mass of m2 = 50 grams. With the airtrack operating, hold the glider at the end of the air track and start the program. The event timer is triggered by the passage of the glider through the photogate. Once you have acquired your data you should examine the data. Verify and demonstrate that your measurement works. Plot the data for a trial (x vs t and v vs t). Examine mean, SD, SDM for the acceleration column. Fit the velocity versus time data to a straight line. Compare the slope from the fit to the average of the accelerations. Repeat the measurement a few times and compare. Consider the following questions. Are the values reasonable? Does the fitted curve pass close enough to all the data points? Do similar measurements give similar results? How close should results be to each other? What did you expect? If you predicted incorrectly do you understand why? How do you expect acceleration to depend on time? How can you examine the data to verify this expected behavior? If verified, what method do you suggest for estimating the acceleration from the measurements of acceleration? How do you expect the velocity to depend on time? How can you examine the data to verify this expected behavior? If verified, what method do you suggest for estimating the acceleration from the measurements of a velocity? To complete the above analysis include in your spreadsheet: 1 sample data table from Logger Pro (do not submit all your data), a plot and a fit of the velocity versus time, a plot and comments on the position versus time, the analysis of the acceleration column (mean, SD, SDM) and a statement with your overall analysis of these measurements. NOTE: Instructors will not do your analysis. Make sure it is clear what conclusions should be drawn, why the tables and plots are included. Imagine that the reader is familiar with the experiment but may not have the manual. At this point you are ready to record data efficiently. You remain vigilant that problems are not ruining your data but you should be able to quickly record the necessary data for parts A and B below. Look at how much time remains in the lab period. Cut, paste and save the data before leaving. The analysis can then be done outside the lab if necessary. Now proceed to study how the acceleration changes as the mass of the glider changes. Analyze each measurement by fitting the velocity versus time and by averaging the acceleration data. Repeat the 64
experiment adding 50 g to the glider. Continue to add mass so that the following mass values have been measured: m1 = m g = mass of glider (all measurements done with 50 grams on the string) m1 = m g + 50 g m1 = m g + 100 g m1 = m g + 150 g m1 = m g + 200 g (attach 50 grams to the glider), (glider plus 100 grams attached to the glider), In order to keep the glider sliding evenly on the track surface, add half of the additional mass to each side of the glider. You will need to summarize this part of the experiment. Put your results for acceleration into a table. (To keep your data organized you may use different worksheets.) m2 = 50 grams Accelerating force F a = m2g m1 uncertainty acceleration uncertainty acceleration uncertainty (velocity data) (acceleration data) Once you have obtained an acceleration value for each mass plot a graph of the acceleration a versus the reciprocal of the total mass [1 /(m1 +m2)]. Include comments on your result. Compare the slope of the graph with the theoretical value of F a = m2g. Use that result to determine if your experimental value excludes the theoretical value of g to 95%. (You should tabulate your comparison in the spreadsheet). Part A requires a table, plot and comment. B. Constant total mass Start with 200 grams attached to the glider and m2 = 50 g. The constant total mass for Part II will then be m1 + m2 = m g + 250 g. Remove 20 grams from the glider and add the same 20 grams to the accelerating mass m2, and find the acceleration for this system as before. Repeat this step until you have measured the acceleration for the following values of m2: 70 g, 90 g, 110 g and 130 g. Graph the acceleration, a, versus the accelerating force F a = m2g. Determine the slope of the graph. Comment on the result. Compare the slope of the graph with the theoretical value of [1/(m1 +m2)]. Part B requires a table, plot and comment. 65
Item Summary: Basic measurement == physics. Summary: Equipment operation. Measurement of mass Evaluation of the experiment ( analyze first measurement, repeat, summarize) Data recorded by adding mass to glider (table) Plot of a vs 1/(m1+m2), comments on validity of result Comparison of expected vs observed values for the applied force. Data recorded by moving mass to the hanging position (table) Plot of acceleration vs applied force, comments Comparison of expected vs observed for total mass Instructors evaluation 66
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