Physics Lab 3

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Dec 6, 2023

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Shrivatsa Patil Jimmy Ding Ethan Periera Sean Kim Physics Lab 3 Introduction: In this experiment, we will be measuring the coefficient of kinetic friction of the IOLab device as it moves along the smooth side of a board. This will be determined with two different methods, with one method performed by two different groups. The coefficient of kinetic friction is related to the friction of an object. Specifically, kinetic friction is the friction an object experiences while it is moving. This friction opposes the motion of a moving object in an attempt to slow down and ultimately stop its motion. It can be calculated with the use of Newton’s Second Law, where the net force acting on an object is equal to the mass of the object times its acceleration. Methods: 1. Place IOLab flat down on the smooth side of a cardboard plank with the felt pads touching the board 2. Calibrate the device using IO Lab software. Connect the IO Lab Device to the computer and verify that data is being recorded with a test run of the device. 3. Align the IOLab towards one end of the board, and then give an initial push to the IOLab towards the longer side of the board (see picture on right) 4. Record acceleration (m/s 2 ) of the IOLab in the computer application for each trial 5. When the IOLab comes to a halt, stop the recording and the trail is complete 6. Repeat steps 2, 3, 4, four more times (5 trials total) 7. Use the absolute value of the acceleration data to find the friction force by multiplying with the known mass (according to Newton’s second law F=ma) of the IOLab (0.2kg) 8. Using the equation f k =μN, the friction force and Normal force (g*0.2kg) can be plugged into the equation, and then algebraically solved to find the value of μ Board IOLab Device

Results: Trial Acceleration Value Coefficient of Friction Graphs 1 -2.271 m/s 2 .2315 Graph 1 2 -2.281 m/s 2 .2325 Graph 2 3 -2.259 m/s 2 .2303 Graph 3 4 -2.160 m/s 2 .2202 Graph 4 5 -2.252 m/s 2 .2296 Graph 5 Trial 1 Trial 2

Trial 3

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Trial 4 Trial 5 Analysis(Part 1): Calculation of Coefficient of friction: U k = a/g Trial 1 -2.271 / 9.81 = -.2315 Trial 2. -2.281 / 9.81 = -.2325 Trial 3. -2.259 / 9.81 = -.2303 Trial 4. -2.160 / 9.81 = -.2202

Trial 5. -2.252 / 9.81 = -.2296 Beyond this point all frictional coefficient values have absolute value applied to them for accurate comparison of magnitude. Mean Coefficient of Friction = (.2315 + .2325 + .2303 +.2202 +.2296) /5 = .2288 Standard Deviation = (.2325 - .2202) / 2 = .0615 Standard Error = .0615 / √(5) = .0275 Our data falls within 0.2288 ± 0.0275 Information from other group: The method used by the other group was attaching a string to the IOLab device and dragging it across the plank. The plank was made to rest in a horizontal position and the string was attached to the IOLab device by tying it to the force hook. A pulley mechanism was attached to the end of the plank, with the string resting on the wheel of the pulley. A counterweight of 0.042 kg was added to the end of the pulley so that the falling mass would allow the device to slide across the plank, with the string wrapping around the wheel of the pulley. This was repeated five times for five separate trials. Other Group’s Mean coefficient of friction is -0.2056 Other Group’s Standard Deviation = -0.055 (converted to positive values to allow for proper comparison of magnitude) Their Data Falls within: 0.2056 ± 0.055 Analysis (Part 2) : t’ = |mean A - mean B| / √(std error A 2 + std error B 2 ) t’ = |0.2288 - .2056| / √(0.0275 2 + .055 2 ) = = .37728 t’ = .37728 our t’ is below 1 so our data and overall values are very close together. Revision not necessary as the t’ value is very small, < 1 Discussion: Revisions were not needed as the data between the 2 groups had a t’ value of only . 377. A t’ score of .377 means that the results are likely to happen if the parent distributions are the same, meaning both data set’s fall into the same parent distribution. This means that the data is similar enough that it can be concluded that both of the different methods worked and could properly measure the coefficient of friction of the board. The other lab group agrees with this conclusion, as the t’ value was calculated to be the same. The only difference was the sign of the t’ value as the other lab group kept their frictional coefficient values - in the final calculation, while these frictional coefficients were converted to be positive, allowing for easier comparison of magnitude.

Conclusion: By calculating and analyzing the mean of the frictional force during travel of the IO Lab device, we find that the coefficient of friction of the surface is 0.2288±0.1012 . To obtain a more reliable result of μ k , the method with a horizontal/inclined plane will help. Be careful that the surface you are gathering data on is level, to avoid discrepancies due to slopes. Additionally, try to find a smooth surface to perform the experiment on. This and how smooth the felt surfaces on the IOLab are will determine how large or small the value of kinetic friction will be. With the results of the two methods we have found, the value for kinetic friction may be more accurate when the IOLab device is dragged across the plank with the use of a pulley and counterweight. However, the difference between the two methods was very small, so either method is viable. Contributions: Shrivatsa Patil: Introduction, Results, Conclusion Jimmy Ding: Analysis, Conclusion Ethan Periera: Methods, Analysis Sean Kim: Data Collection, Analysis All: Discussion

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