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Dec 6, 2023

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Physics 1107 Lab Report Lab 2 “One-dimensional Motion with Constant Acceleration” Peter Border Aug 31, 2006 Updated Sept 19, 2022 Note: This analysis uses the “example data” on the 1107 website, and the story of the data-taking is made up. Otherwise it is an example of a good lab report. Text in red is comments from the editor. Summary The summary section is very short description of what you were trying to do and how it turned out. I followed the procedure for Lab 2, and succeeded in taking data showing how one of the blue cars accelerates as it rolls down an incline. I measured the time at which the car passed four different, measured positions and calculated the average velocity of the car between each pair of positions. From the velocity measurements I was able to find the average acceleration of the car at two points. I found results that were roughly consistent with the theoretical values, but somewhat lower. A longer track would have been beneficial, but I did not have a longer piece of glass. I believe the difference is due to friction in the car bearings, since I can see that the car comes to a halt on a flat surface (proving that the friction may be low but is not negligible). Introduction The introduction just explains what the lab is about, without getting into technical details. What are you trying to do with this experiment? Lab 2 is about one-dimensional motion with constant acceleration. The point of the lab is to observe constant-acceleration motion by watching a small car roll down an incline, which will make it accelerate a constant rate. The assignment is to measure the velocity and acceleration, graph them against time, and compare them to theoretical values. Procedure The procedure section is about technical details of what you're doing. Put all measurements, coordinate systems, and setup data in this section. Include enough detail so you could reconstruct your experiment a year from now. The procedure was to measure the time at which a car passes measured distances as it rolls down an incline, then use that data to find the velocity and acceleration of the car as it moves. The inclined track was made of a piece of glass 18” long (covering a photo of my kids), propped up on one side by 4 CD cases. I measured the height of the cases to be 0.8 inches, which gives an angle of 2.5 degrees. The glass makes a nice track because it is both flat and smooth, as well as being easy to clean and available.

I put a piece of tape on the glass so I could make marks on it and consistently put the clips in the same places. I spaced the clips out one clip every 10 cm, which was far enough apart that they didn't hit each other as they tipped over (it took a little experimenting to find this value). Quantitative Experimentation Each lab has a quantitative part, or hands-on “playing” with the apparatus. The idea is to get you to look at the apparatus in detail and explore how it works without actually doing any measurements. Just watch it go and make sure you understand what it does. I did the quantitative part of the lab and rolled the car down the incline, listening to the clips fall. It was hard to tell with only four clips, but I could hear that the last “clicks” wer closer together than the first ones. I tried changing the angle a little (reducing it to 2 CD cases), which made the clicks slower. Using one CD case did not work as the car wouldn't start rolling by itself. Adding a few more cases (6) made the clicks perceptibly faster, and sounded much more urgent. Prediction and Method Questions Put your answers to the P+M questions here. I am leaving them out so you will have to figure them out by yourself for this lab! Data-taking The data-taking section describes what happened when you actually started to take data. Be sure to include mention of what went wrong and how you fixed it. Finally I plugged in my microphone into my computer and started up Audacity. I adjusted the microphone position and volume until the clicks were clearly visible in the Audacity display. There was a loud “crash” when the car hit the end of the frame, but it was easy to tell the “crash” from the “clicks”, as it were. So I ignored the crash, though I could have put some sort of soft bumper in to stop it. I measured the times between “clicks” with the microphone and Audacity. This data makes a set of x-t pairs which I analyzed with Excel. I used Excel to find the average velocities and accelerations, as explained in the lab manual. Finally I graphed my data with Excel. The data-taking went smoothly once the microphone positions and volumes were figured out. These are my x-t raw data pairs: Phys 1107 Lab 1 Data n x t 0 0 0.242468 1 10 0.603965 2 20 0.996322 3 30 1.445990 Data Analysis This section should describe how you did your analysis. You do not have to include things from the Excel file, but please explain everything in that file here. I used Excel to do my data analysis, as described in lab manual. The data and graphs can

all be seen in the attached Excel file. The “theoretical” columns are from a formula I concocted, based on an analysis of the kinematics. I believe that the car will accelerate at a th = g sin( q ) since it is on an inclined track. This leads to formulas for velocity and position of v th (t) = a th t x th (t) = x 0 + ½ a th t 2 Include a section on problems with the analysis, and where you think the problems may have come from. Explain your reasoning. The graphs show the measured values. The general form of the curves is similar, but the “measured” acceleration is not smooth. (Note: have a look at the graphs in attached Excel, and compare them to ones in the original “sample data” file. I have done some reformatting which makes the graphs much clearer. ) I believe that the measured acceleration depends on the car's friction which is small, but not 0. Certainly frictional effects will reduce the acceleration, and I know that the friction on the car is not 0, because they do eventually stop if I roll them on the table. Conclusions The conclusions section summarizes what you did, and what conclusions you reached. Include a paragraph about problems, if you found any, and whatever ideas you may have to make the experiment better. I have observed acceleration with my car rolling down an incline and knocking over binder clips. I have used Audacity and a microphone to measure the time between knocking over clips, and then used Excel to find the velocity and acceleration of the car as it rolls down the incline. The measured value of the acceleration agrees qualitatively with my theoretical estimate, but not quantitatively. The experiment would have been much more accurate if I had a longer piece of glass, so could use more data points.

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