Guidance for Writing Lab Reports for PHYS 233:

Guidance for Writing Lab Reports for PHYS 233: The following pages have a sample lab report that is a model of what we expect for each of your lab reports in PHYS 233. It is written for a lab experiment that we do not actually require of you, but it uses many of the tools that are needed for the actual labs. Note carefully all of the details in the text, figures, tables, and appendices. Especially note the abstract on the cover page. A well-written abstract conveys the essential purpose of the lab as well as the general results and conclusions. A good abstract tells us that the rest of the lab report is likely well thought-out and executed. The remainder of this page reprints instructions for lab reports and their grading, taken from the course web pages. ******************************************************************************************************** Lab Reports At the end of the experiment, your team will hand in a complete lab report. This is your chance to communicate your work in a style similar to what published scientific journals would require (with a little extra info for your TA). This report must include at least these three components: A Journal: A clear and concise discussion of what you did, how you designed your experiment, and what results you got, written so that an absent student could understand and repeat your experiment. If you followed false trails that you gave up, you should explain them here with your reasons for giving them up. Data and Interpretation: A presentation of your data in a form that would be easy for an absent student to understand. Include a discussion of what your data means, what conclusions you ve drawn from your data, and a persuasive case to convince your reader that your conclusion is valid. Keep in mind that a record of raw (un-manipulated) data would never be published by a scientific journal--what of the data that you have collected is necessary to make your case? Is this data sufficient and convincing? Evaluation: After you ve had a chance to see what data and conclusions other groups have gotten, it s important to go back and reconsider what you ve done. Here is where you discuss how you could improve upon your experiment (design or analysis), in light of what you learned during lab and during the class presentations. This is also the place to expand upon the interdisciplinary nature of these labs--how are the things you have studied in other science classes connected to what you have done and learned here? Do you see other possible applications of these research ideas and experimental techniques? Title, Abstract, Introduction: These need to be highly descriptive, to encapsulate the goals, motivation, and conclusions. Criteria for grading a Lab Report: Design and thoughtfulness. Did your team do a careful and thoughtful job in creating your experiment, and was this thought reflected in the journal? Clarity and completeness. Did your team explain your experiment so that someone could reproduce it? Persuasiveness. What conclusions did your team draw from your data? Were you able to back up these conclusions with this data in a convincing way? Evaluation. After observing the experiments of other groups, were you able to critique your own lab, propose constructive changes, or explain why your experiment was better than those of your classmates? (The question you are answering in your evaluation is, If I got to re-do this experiment next week, how would I do it differently? ) pts 7 8 8 7 1

The Acceleration of Falling Objects Lab Report PHYS 233 Authors: Ada Yonath Journalist Barbara McClintock Data Interpreter Carol Greider Critic Rosalyn Yalow Checker Abstract: In this Lab for PHYS 233, our goal was to test the idea that simple objects fall with a constant acceleration due to the force of gravity. We chose three round balls of different mass, size, and surface roughness to see what factors might influence their motion. These were dropped under identical conditions, their motion recorded by video, and their motion tracked with video analysis software. The resultant accelerations show that the chosen balls had accelerations that differed by more than the experimental uncertainties. This does not suggest that Newton s second law combined with the force of gravity fails. Instead, it indicates that the role of buoyancy forces and/or air resistance cannot be ignored for some of these balls. Contents: I. Introduction II. What was done (Journal) III. Data and Interpretation IV. Evaluation and Conclusions Appendix 2

I. Introduction In this lab we tackled the question, do objects fall with the acceleration due to gravity? That is, how typical is it that when you drop an object it actually accelerates with the predicted value of g=9.8 m/s 2? This is the prediction if you start with Newton s second law and throw in the fact that the force due to gravity at the surface of the Earth can be reduced to F=mg (where m is the mass). Of course we know this cannot always be true the motion is very different when an open parachute is involved, for example. However, what about simple, everyday objects? We decided to test this on three different balls, each dropped from rest in the lab. These balls had different sizes, masses, and surfaces, so there is some opportunity for them to interact differently with air. Just dropping them side- by- side was not too revealing, so instead we pulled out the web cam and video analysis tools and tried to do measurements that are accurate enough to answer the question: do these three balls fall with the acceleration of gravity? II. What was done (Methods and Materials/Journal) We selected three balls that were handy: Figure 1: Balls 1, 2, & 3 photographed against a centimeter ruler. Ball 1 SS Ball 2 BB Ball 3 Styro mass 37.9 gm 2.3 gm 1.7 gm diameter 0.75 = 18.8 mm 36 mm ~46 mm composition Stainless steel Hollow plastic Solid styrofoam Table 1: Physical parameters for Balls 1, 2, and 3. In the lab room (PHYS 154) we set up a location next to a table where each ball could be dropped from a height of about 2 meters above the floor, and observed for most of that drop by a (LogiTech) web cam attached to the lab table computer monitor. A meter stick 3

was propped up vertically at the drop location to permit calibration of the video images. The distance from the camera to the drop site was ~2.5 m. We placed dark panels on the wall behind the drop site to make it easier to see the moving balls in the video. The web cam, operated by the VirtualDub program on the lab PC, was set to operate at 30 frames per second. A higher frame rate would have been useful, but we could not get it above 30. At first we thought we should have a nice bright image, so under the Capture Filter feature (under the Video tab), we set the exposure time to a high setting. This does give a brighter image, but it turns out it does so by increasing the effective shutter opening time. This means that when video was taken of a falling ball, each frame showed a streak of multiple ball images that lengthened as the speed increased. It did prove possible to extract good data by carefully estimating the center of each streak, but we decided this was not optimal. We went back to Capture Filter and reduced Exposure to the minimum value, and made up for the poor brightness by increasing Gain to its maximum value. This led to very noticeable pixel noise, but the ball position was very sharp at even the highest speeds. We concluded that this was the better configuration. We recorded one video for each of the three balls at high Exposure setting, and repeated this for all three balls at the low Exposure setting. These videos were imported into ImageJ, and the trajectories tracked using the Manual Tracking plugin. First we calibrated the videos by identifying the pixel numbers at the top and the bottom of the meter stick, which gave ~550 pixels per meter. This calibration led to an erroneous value of g, however, which is discussed in a later section. The Manual Tracking input calibration values were 1 pixel = 1818 microns, and one frame = 0.0333 seconds (from 30 fps). Manual Tracking produced an output file with a line of text for each click on the ball per frame. The program records the X and Y values for each clicked position, and calculates successive positions (in microns) and speeds (in microns per second). There was a slight change in the horizontal position for each falling ball which slightly increases the calculated speeds, but this was so small that we ignored it, treating the calculated speeds as the vertical- only speeds. Each video led to its own output file (e.g. test2ss.xls) that was subsequently opened by Excel (and saved in the full.xlsx format to save charts etc.). The speed data was converted in a new column to units of m/s, instead of microns/s. The speed was plotted versus time (in seconds). Using Excel s built- in analysis function, a Trendline was fit to the data. It was important, however, that the data was limited to the time in free fall, since data points before free fall would be included in a Trendline and skew the results. The Trendline formula specifies the slope of the best fit speed versus time, which is the acceleration. These values are the principal results of this lab experiment. 4

III. Data and Interpretation. We acquired results from six measurements, three from the high Exposure mode and three from the Low exposure mode. A typical chart is shown here, for Ball 2 at low Exposure: 6 Ball 2, Low Exposure 5 y = 9.9586x - 0.3281 4 Speed (m/s) 3 2 ImageJ output Linear (ImageJ output) 1 0-1 0 0.1 0.2 0.3 0.4 0.5 0.6 time (seconds) Figure 2: Plot generated by Excel showing the calculated speed versus time from ImageJ Manual Tracking, plus a best- fit Trendline. The slope of this line should give the acceleration of this falling ball. The y- axis error bars assume an uncertainty in clicking on the correct center of the ball of about 1.5 cm. Note that the data points are quite well characterized by a straight line, so the slope of the best- fit trendline should give the acceleration. All six measured accelerations are given in the following table: Acceleration (m/s 2 ) High light exposure, Low light exposure, long shutter time Short shutter time Δ Ball 1 11.6 12.0-0.4 Ball 2 9.9 10.0 +0.1 Ball 3 8.4 8.0 +0.4 Table 2: Slopes of the best- fit trendlines for all six videos; these slope values are the nominal accelerations of the balls, although they are systematically too high. The last column gives the difference in the two measurements on each ball, a measure of the experimental uncertainty (reproducibility). 5

One problem with these results is obvious: the heavy stainless steel ball has a calculated acceleration greater that the known value of g (=9.8 m/s 2 ). This must be due to a calibration error in the ImageJ Manual Tracking process. Either the assumed time interval between frames is too small by 20%, or the distance calibration is off by 20%, or some combination of these two effects. We are unable to determine the origin of this discrepancy. We argue, however, that any reasonable error here would likely apply equally to all of the measurements, so it is permissible to rescale all of these data by a correction factor of 12.0/10.0 = 0.83 to get the true accelerations. Note the last column, where the difference between accelerations deduced from the two configurations is given. We present this as a practical estimate of the uncertainty in the measurements. Separately we could try to fit trendlines to the data taking into account the uncertainty in each data point, but the nominal error bars are rather small (see Figure 2). Either way, however, there is a clear conclusion: The acceleration of these three balls is not the same. The measured differences are outside the likely uncertainties. At least two of these balls do not satisfy the prediction that a=g. 13 Comparison of both data sets acceleration (m/s2) 12 11 10 9 8 accel (high) accel (low) 7 Ball 1 Ball 2 Ball 3 Figure 3: Acceleration data from Table 2 comparing results from the high exposure and low exposure modes. It is clear that the drop in acceleration observed with the lighter balls is much greater than would be expected from the uncertainties in the measurements, based on the good reproducibility shown in this plot. Let s assume that Ball 1 has an acceleration close to g.(that is, we assume the value of 12.0 m/s2 s would be 9.8 m/s2 if VirtualDub/ImageJ were properly calibrated.) Why would Ball 2 and Ball 3 be different? The acceleration due to gravity does not depend on mass, because Fnet=ma=mg, so a=g. But if there is a force FR like air resistance or buoyancy that does not depend on mass, then we get Fnet=ma=mg- FR, so a=g- FR/m. The new correction term caused by FR/m will be smaller when the mass is big, like with Ball 1, but becomes much more important when the mass is small, such as with Ball 2 and Ball 3. The actual cause of this force is assumed to be due to 6

the presence of air, a low density fluid. That could be due to the buoyancy force, or the friction- like resistive force caused by the rough styrofoam surface. Further studies would be required to determine the most likely origin. IV. Evaluation After hearing the presentations from the other groups, we realized that we made one big mistake in the design of this experiment. By not choosing our balls properly, we were unable to determine what caused the change in acceleration. Instead we should have focused on one variable at a time: A. Choose three balls made of the same material and having the same diameter, but with two of them being lighter (e.g. hollow). Then all three have the same frictional resistive force but different weights. Any change in acceleration would be due to the buoyancy force. B. Or choose three balls with the same diameter and the same mass but with different surface roughness. Then any change in acceleration could only be due to air resistance. If we did this experiment over again, we would choose the balls in this more systematic way in order to determine the nature of the additional force. 7

Appendix: Appendix Figure 1: These are screenshots from the videos recording the fall of the stainless steel ball (Ball 1). On the left is the video from the high exposure mode; note that the overall image is bright and sharp, except that the ball is a blurred streak due to the long shutter opening time. On the right is the video from the low exposure mode; because there is less light per frame, the individual pixels show obvious noise. (Gain was increased to the maximum setting to make the image visible.) Most important, however, is that the ball shows no evidence of blurring or streaking, making the determination of its position much more accurate. 8

High exposure results speed (m/s) 6 5 4 3 2 1 Ball 1 (ss) Ball 2 (bb) Ball 3 (styro) 0-0.2 0 0.2 0.4 0.6-1 time (seconds) 6 5 Low exposure results speed (m/s) 4 3 2 1 Ball 1 (ss) Ball 2 (bb) Ball 3 (styro) 0-0.2 0 0.2 0.4 0.6 time (seconds) Appendix Figure 2: Plots of the speed versus time values generated by Manual Tracking in ImageJ for both the high and low exposure modes. Acceleration values were derived from the slopes of these curves. 9