Physics I Lab Report 1

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New York University *

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4001

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Mechanical Engineering

Date

Dec 6, 2023

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pdf

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Uploaded by GeneralMask16565

Objective This lab aimed to familiarize students with motion detection while using Capstone and MatchGraph software to analyze and calculate position, velocity, and acceleration. Capstone and MatchGraph utilize

motion sensor detectors to determine the position of a moving object in its respective field. This allowed students to create and interpret motion graphs, such as position-time and velocity-time graphs. Description This lab required the use of two software and two motion sensors. Both sensors were set to a default sample rate of 20 Hz. In part one of the experiment, a black motion sensor was mounted 30 cm above the lab bench. Capstone technology was then used such that the black motion sensor could transmit signals to measure ping echo time and calculate velocity, acceleration, and position. In part two, a blue motion sensor was acquired using the MatchGraph software. The sensor was mounted to the edge of the bench and switched to the people setting, which allowed for a wider angle of motion detection. Theory Motion sensors, in association with Capstone and MatchGraph, use waves to detect the distance an object travels. It is done by measuring sound, a pressure wave that travels at a certain speed depending on the type and temperature of the gas it is traveling in. Relative to this experiment, the speed of sound is approximately 343.6 m/s and can be used in calculations. The equation t = 2d/V is used to represent the relationship between position, velocity, and time. An understanding of derivatives is essential to determine accurate data. For example, the derivative of velocity vs. time is equal to the graph of acceleration vs. time. Procedure The lab begins with the opening of the Capstone program and ensuring the height of the sensor from the bench is 30 cm. After gaining some understanding of the software and confirming the motion sensor is correctly positioned, the experiment can proceed to parts one and two. Part One : We begin part one with the programming of Capstone . The black motion sensor must be plugged into Channel 1 of the Pasco Interface. Position, Velocity, Acceleration, and Ping Echo Time must be all checked off in the Motion Sensor II platform. Opening digit displays can portray what will be measured. We continue to measure position . As someone presses the record button, another must hold a flat surface object in their hands. The position digit display will show a number and will be labeled Run #1 and so forth. Checking on capstone allows for the assurance of the equipment working well. We can use a stationary reflector in front of the motion sensor, which would allow for the measurement of Ping Echo Time. We can finally measure velocity by moving a notebook toward and away from the sensor. This can determine velocity statistics for who has the steadier hand by selecting Standard Deviation for position.

Part Two: A blue motion sensor is set up by plugging it into Channel 1, now replacing the black motion sensor. The sensor is switched to the wide-angle “people” setting. This setting allows the motion sensor to detect a person’s movement rather than smaller objects. We mimic and analyze graphs from Position 2 and Position 3. By doing so, we should be able to explain what is happening with regard to position, velocity, and acceleration. Data Lab Manual Questions 3.1 - Programming Capstone a. What are all the units of measurements and dimensions for position, velocity, acceleration, and time? - The unit for position is meters (m). The unit for velocity is meters per second (m/s). The unit for acceleration is meters per second squared ( . The unit for Ping Echo Time is 𝑚/𝑠 2 ) seconds (sec). b. What is the speed of sound? - The speed of sound is 343.6 m/s. c. Can you think of why it might vary from day to day? - It varies from day to day because it depends on the density and temperature of the medium through which it is traveling. 3.2 - Measuring Position a. How many significant figures do you need? You’re the experimenter explain your logic. - We need 3 significant figures because this is what contributes to the degree of accuracy of the value. Velocity was measured up to the thousandth place on the Capstone Digit Display, hence 3 significant figures were the most precise to use.

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3.3 - Checking on Capstone a. When compared to the meter stick how off are your values? What the motion sensor actually measures is the round-trip pulse time. - Our values were only slightly off by -0.2/+0.2 decimals. This could have been due to lags or delays in the measurement system. b. Does Capstone calculate the distance accurately? - The experiment value was not that off from the meter stick as Capstone calculates distance accurately. 3.4 - Measuring Velocity a. In the digits display what does a minus sign signify? - A minus sign indicates that an object is moving towards the motion sensor because it is producing a negative velocity. b. If a minus sign is missing then what is occurring to the motion? - If there isn’t a minus sign, the object has a positive velocity therefore moving away from the motion sensor. 3.5 - Doing Statistics on Velocity a. Explain why we use standard deviation. - We use standard deviation to determine the data and its precision. It is particularly important to this experiment because a negative standard deviation would not account for a correct velocity or position. Since vectors have magnitude and direction, using a mean would be inaccurate because the positive and negative values would contradict and cancel each other out. b. Between you and your partner, whose pulse is steadier? - My lab partner’s pulse was steadier due to her standard deviation being closer to 0 (0.0834), as hers was less than mine (0.847). c. Why would a sample rate of 20 Hz work for this part of the experiment? - A sample rate of 20 Hz works for this part of the experiment because a lower sample rate would not be able to give an accurate measure of pulse changes during the time interval between signals. This would make it harder for the motion sensor to discriminate between the pulses. 4.2 - Additional Assignment a. Initial will your direction be positive or negative? - The direction would be positive.

b. Maximum absolute value of speed you're able to obtain? - The maximum absolute value of speed we were able to obtain was +0.2 m/s and -0.2 m/s. c. Was it positive, negative, or both? - Both. d. Total time to run the motion? - The total time to run the motion was 10 seconds. Analysis Questions Position Plots 1. What does a horizontal line mean? - A horizontal line means the position remains constant and the velocity is 0. 2. What is the difference between the parts of the plot with positive slope and the parts with negative slope? - A positive slope indicates that the position is increasing over time which means an object is moving away from the sensor. A negative slope indicates that the position is decreasing over time, meaning an object is moving towards the sensor. 3. On the Position 3 plot, what is happening between 5 and 10 seconds? - Between 5 and 10 seconds, the position changes from 2.0 m away from the sensor to 1.0 m away from the sensor. This movement is exponential. 4. What parts of the plot were easier to match? What parts of the plot were the hardest to match? Why? - It was easiest to match the constant and linear positions because it is easier to move our bodies in such ways. It was harder to match exponential/curved parts due to having to move our bodies at a quick pace at the right position and timing. Velocity Plots 5. What does a horizontal line mean? - A horizontal line means the velocity remains constant and acceleration is 0. 6. What is the difference between the parts of the plot with positive slope and the parts with negative slope? - A positive slope means that the position of the plot increases over time in a positive direction, which is away from the sensor. A negative slope indicates that the velocity is decreasing over time in a negative direction, which is toward the sensor. 7. Consider the Velocity 2 plot. What is the difference between places where the slope is large and places where it is near zero?

- Velocity is changing at a fast pace where the slope is large, with its acceleration being high as well. Velocity is always constant where the slope is 0, as well as its acceleration being 0. 8. Consider the Velocity 2 plot. Where is acceleration the largest? What is the speed at that point? - Acceleration is largest at zero seconds, 5 seconds, and 10 seconds due to the slope having the greatest magnitude at these time intervals. At each of these points, the speed is 0. 9. Which of the four Velocity plots could qualitatively describe the vertical speed of a ball thrown vertically upward? - Velocity 4 could qualitatively describe the vertical speed of a ball thrown vertically upward. Error Analysis There are multiple possible sources of error in this experiment. The first could have involved systematic errors with the calibration of the motion sensors used. This can be due to a second error, which is the temperature and density of the room we conducted the experiment. We automatically accounted for the motion sensor to know the temperature of the room, which we assumed to have been 20 degrees Celsius. The motion sensor could have not picked this up, leading to possible incorrect measurements and calculations. Another error is of course human error. Our natural human reaction time could have caused inconsistent data to be recorded and consequently caused inaccurate data. Conclusion With errors and calculations taken into account, the experiment was successful. Our expected results were obtained and matched closely with Position 2 and Position 3. My lab partner and I were able to measure position, velocity, and acceleration properly with enough practice and with the use of Capstone and MatchGraph. Overall, conducting this experiment led to an understanding of the impact of motion and the relationship between velocity, time, position, and acceleration.

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