Physics I - Motion I Lab

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Physics I - Motion 1 Lab Student: Havana Perez Partner: Medha Namala Section 024 Lab Date: 09/21/23 Due date: 09/28/23
Objective: What are you trying to accomplish, observe, or verify by doing this experiment? The objective of this experiment is to measure one-dimensional motion using the motion sensor and analyze the relationship between the position, velocity, and acceleration of an object moving in one dimension. Another aim is to successfully learn how to utilize Capstone for the motion sensor and how to properly run MatchGraph to analyze position vs. time and velocity vs. time graphs. Description. What does the apparatus look like and what happens? A diagram might be illuminating. The motion sensor apparatus is set up on a metal rod that is clamped onto a table. This sensor detects the distance an object is from the motion sensor by using sound waves. The sensor sends out short pulses traveling at the speed of sound with a sample rate of 20 Hz, meaning that 20 snapshots of the object’s position are taken per second. It also detects the sound wave reflections and measures the time it takes for each pulse to be reflected. In addition to the motion sensor, two PASCO software programs, Capstone and MatchGraph, are utilized to further analyze the one-dimensional motion of the object, which in this experiment is a notebook. The Capstone digits are utilized to measure the ping echo time and calculate the distance, velocity, and acceleration of the notebook while the MatchGraph software compares the experimenter’s motion to a set graph to test the accuracy of the match in terms of position, velocity, and acceleration.
Theory. The guiding principles of mathematics are pertinent to the experiment. An object’s motion can be described by its position relative to a reference point, the speed and direction with which it is traveling, and the changes to its rate of motion. In other words, the position, velocity, and acceleration of an object are necessary to accurately describe the object’s motion. To measure the position, sound waves are emitted in short pulses that are reflected when it meets the notebook and the distance at which the sound wave is reflected indicates the position of the notebook. Velocity, or the change in position over time, is measured by taking multiple snapshots of the notebook’s position per second as the notebook is moved towards and away from the motion sensor. The acceleration, or the change in velocity over time, of the notebook is calculated by the Capstone software by differentiating velocity. Once all the measurements are obtained, a motion graph describing the notebook’s motion is generated and reveals critical mathematical concepts about one-dimensional motion. For example, the slope of a position vs. time graph corresponds to the velocity of an object because the slope depicts the change in position over time which is the formal definition of velocity; similarly, acceleration corresponds to the slope of a velocity vs. time graph. The mathematical proof through motion graphs demonstrates that position, velocity, and acceleration are all critical for describing the notebook’s motion as they are dependent on each other. Procedure. In experimenting, what actions do you take? Part I 1. Set up Capstone and connected the interface to the computer 2. Spent a couple of minutes navigating the Capstone software a. My partner and I followed the instructions provided in the pre-lab description 3. Prepared the Capstone display to include the Digits box 4. Ran a trial run for measuring position and double-checked that Capstone was working properly. a. My partner and I verified that Capstone was accurately calculating the distance 5. Proceeded to measure position and velocity under various conditions (i.e., altering the motion of the notebook) 6. Tested who had the steadiest hand amongst our lab group by holding the notebook steady at 1.1 meters from the motion sensor. Part II 1. Set up the Motion Graph Matching software on PASCO Capstone. 2. Removed the black motion sensor and set up the blue motion sensor by plugging it into a passport and positioning it to have more space to perform the graph-matching experiment. 3. Matched the notebook’s motion to position graph #1 and velocity graph #1. 4. Unmounted blue sensor and remounted black motion sensor. Data And Calculations. You should include your original data sheets, but feel free to generate new tables that contain the original data sheets and new calculations.
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a. Position #1 Graph Matching \ b. Velocity #1 Graph Matching
c. Measuring Position and Ping Echo Time Distance Ping Echo Time (s) Theoretical Position (m) Actual Position (m) 0.800 0.00460 0.763 0.791 Theoretical Position: speed of sound in air @ 20°C = 343.6m/s Ping Echo Time: 0.00460s ( 343.6 m s )( 0.00460 s ) 2 = 0.763 m d. Measuring Velocity Mean Velocity: -0.0219 m/s Max: 4.77 m/s Min: -5.60 m/s Person Position(m) Standard Deviation Havana 1.1 0.0112 Medha 1.1 0.00110 Lab Questions a. What are all the units of measurement and dimensions for position, velocity, acceleration, and time? Position: meters (m), Velocity: meters/second (m/s), Acceleration: meters/second 2 (m/s 2 ), Time: seconds (s). b. What is the speed of sound? Can you think of why it might vary from day to day? The speed of sound is 343.6 m/s when the sound wave is traveling in air at 20°C. This value depends on the type of gas and the temperature through which it is traveling. As such, the speed of sound varies day to day because the temperature varies daily, and it even varies throughout the day. c. How many significant figures do you need? Three significant figures were needed because it was the most accurate reading, we could ascertain given the meter stick can only measure up to three significant figures accurately. The Capstone program also verified this as the 4 th and 5 th significant figures were unreliable and would change in value.
d. When compared to the meter stick how off are your values? What the motion sensor measures is the round-trip pulse time. Does Capstone calculate the distance accurately? Our actual value was 0.791m while the meter stick indicated 0.800m so our values were off by approximately 0.009m. Meanwhile, our theoretical position is off by 0.037 m. In this case, Capstone did calculate the distance fairly accurately but there is still some discrepancy due to the difference in distance values compared to the meter stick. However, this can be due to systematic error from the software itself, instrumentation precision issues, or calibration difficulties. e. In the digits display what does a minus sign signify? If a minus sign is missing, then what is occurring to the motion? The minus sign indicates that the distance between the notebook and the motion sensor is decreasing (the object is moving toward the sensor). Hence, if the minus sign is missing it indicates that the distance between the notebook and motion sensor is increasing (the object is moving away from the sensor). f. Explain why we use standard deviation. Standard deviation informs us on how spread out the values are in the dataset. The lower the standard deviation, the more clustered the data is around the mean, so the mean is an accurate representation of the entire data set. The opposite occurs when the standard deviation is high. g. Between you and your partner, whose pulse is steadier? My partner’s pulse was steadier as indicated by our standard deviation values. h. Why would a sample rate of 20 Hz work for this part of the experiment? Since we are moving the notebook and determining its motion, 20 snapshots per second provided more than sufficient data points to accurately determine and describe its motion. If a faster machine was being used or an object with a more frantic motion was being observed, a larger sample rate would be necessary to get an accurate conclusion related to its motion. Error Analysis . How do you arrive at the uncertainties you give to the numbers presented? When we tested the steadiness of each other, Medha had a standard deviation of 0.00110 while I had a standard deviation of 0.0112, indicating that there was variation in the velocity of the notebook as its distance changed over time. This difference in steadiness or velocity, as more accurately described, was due to how much we moved while holding the notebook. Additionally, Capstone is capable of measuring even the slightest movements which is why the difference in
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standard deviation is minimal. Lastly, there was a difference in the position at 0.800m as the meter stick indicated a value of 0.800 meters while Capstone calculated the distance to be 0.791 meters. This could be explained by calibration error, i.e., the sensors may not be properly calibrated, or calibration drift may occur especially when switching from the black to the blue sensor. Additionally, systematic error in the software may result in a different value for the Ping Echo Time and the speed of sound as these values can easily vary, particularly when extraneous environmental factors, like temperature and humidity. Conclusion(s). These can be of different forms. If your results be displayed as a number or numbers, or are they consistent (within the uncertainties) with known values? Or if you are observing a phenomenon, are you seeing what you expect to see? For the first part in which we measured position, velocity, and acceleration, we concluded that the sign of the numbers on the digits display indicated the position of the notebook; the (-) sign indicated less distance from the sensor while the (+) sign indicated more distance from the sensor. When calculating velocity, it was concluded that the slower the speed with which we moved the notebook, the less distance traveled and vice versa. These speed changes are depicted by the position vs. time graph and the steepness of the graph indicates how fast the speed was reached (i.e., the steeper the slope, the faster the change in speed and therefore position). For the Graph Matching portion of the experiment, our results for the position graph were accurate as we achieved a score of 99.0 but the velocity graph was more difficult to match, as can be seen in our final score of 86.4. It is expected to have a lower score for the velocity graph as it is more difficult to maintain a constant velocity. This demonstrates that motion is sensitive to many changes in position, velocity, and acceleration. 4.2 Additional Assignment Initially, the direction did not change until 0.5 seconds at which the object started moving in a negative direction at 0.20 m/s 2 for 1 second until reaching a velocity of -0.20 m/s. The object travels for 0.5 seconds at -0.20 m/s. It then decelerates at 0.20 m/s 2 for one second, momentarily stopping at 0m/s for 0.5 seconds. Next, the object accelerates at 8.0 m/s 2 for 1 second in the positive direction and reaches a velocity of 0.20 m/s. It immediately starts to decelerate at 0.20 m/s 2 for 1 second and stops at 0.0 m/s for 0.5 seconds. The object continues to accelerate in the negative direction at 0.40 m/s 2 for 0.5 seconds until reaching a velocity of -0.20 m/s. This velocity is maintained for 0.5 seconds, then it starts to decelerate at 0.20 m/s 2 for 1 second, ultimately reaching a velocity of 0 m/s. The object remains still for 0.5 seconds, then it accelerates at 0.40 m/s 2 for 0.5 seconds in the positive direction until reaching a velocity of 0.20 m/s. This velocity is maintained for 0.5 seconds, followed by deceleration at 0.4 m/s 2 for 1 second, reaching a velocity of 0.0 m/s. Initially, the direction was negative at a velocity of 0.20 m/s 2 for 1 second. The maximum absolute value of speed obtained from the object is 0.20 m/s; this value was both positive and negative depending on the moment the absolute value is being observed. The total time to run the motion was 10 seconds and the maximum absolute value of the speed obtained was positive.