Lab01_1D Kinematics_Capstone (2)-2-4

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Pennsylvania State University *

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211L

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Mechanical Engineering

Date

Jan 9, 2024

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3

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Conceptual Understanding Goals : By the end of this laboratory, you should be able to: (1) Articulate the relationships between position, velocity and acceleration in one- dimensional motion. (2) Draw and recognize x(t), v(t), and a(t) graphs corresponding to constant acceleration motion. (3) State the conditions on velocity and acceleration for which speed (|v|) increases or decreases. Laboratory Skill Goals: By the end of this laboratory, you should be able to: (1) Explain the function, operation, and limitation of the ultrasonic motion sensor. (2) Collect data using Capstone TM software and a motion sensor, tools that you will use for many of the laboratories in this course. (3) Visualize and analyze data within Capstone TM – e.g., create graphs, select regions of data, find slopes, and do linear and quadratic fits to data. (4) Draw reasonable conclusions about the motion of an object based upon data. Equipment List: 1.2 meter Low Friction Track (end bracket on left of track) Dynamics Cart with plunger at one end Ultrasonic Motion Detector ¾”-Thick Wooden Block (to fit under legs of track) Computer with Capstone TM and PASCO® 550 Universal Interface Angle Measuring Device (near right end of the track) You will be doing four activities: Warm up. Stating the relationships between the kinematics variables Activity 1. Learning to use the Motion Sensor and Capstone software Activity 2. Exploring your own motion Activity 3. Testing the constant acceleration model Warm-up: Show the relationships between x, v, and a; also, list the x(t) and v(t) eqns for constant a x v a ∫ 𝑣 𝑑? 𝑑? 𝑑𝑣 𝑑? x(t): v(t): ∆? = 𝑣 0 ? + 1 2 𝑎? 2 𝑣 0 + 𝑎? 2
Activity 1. Exploring the operation of the Motion Sensor and Capstone TM This first activity is to familiarize yourself with the motion sensor and Capstone software so that you are able to design experiments in subsequent laboratories using this equipment. Many of the laboratories in this course will use this equipment so what you learn here will aid you the entire semester. Understanding a piece of equipment also requires understanding its limitations and what settings are best for a given context. Set up the Motion Sensor and Capstone software as specified in the supplemental document on the course website laboratory page and then explore how the motion sensor and software works so that you can give complete answers to these guiding questions. Set up and collect some data with the motion sensor before trying to answer the questions! For Activity 1 you will need: the position graph, velocity graph, and you can use the default sampling rate of 10 Hz. (Your instructor can show you how to put both graphs in the same window.) Never crash the cart into the Motion Sensor! To avoid crashing the cart into the Motion Sensor, you can either: use low speeds or put a low bumper (e.g. your finger) across the track a few centimeters away from the Motion Sensor. Briefly answer the questions below (based on the guiding questions) as you explore this equipment. Each of these questions should take only a minute or two to answer. 1. What is the origin of the coordinate system ( x = 0) for the motion sensor? The origin of the coordinate system is the motion sensor. 2. What direction does the motion sensor call positive – towards or away from the motion sensor? The positive direction is away from the motion sensor to the left. 3. Is positive velocity moving towards or away from the motion sensor? Positive velocity is moving away from the motion sensor. 4. Is there a minimum distance away from the motion sensor it can measure effectively? If so, approximately what is it? There is a minimum distance which is approximately 10 centimeters. 3
5. Your cart is at rest on the track, but yet you see a sudden spike in your position data (e.g., values of 1.0 m, 1.0 m, 1.0 m, 3.1 m, 1.0 m, 1.0 m, 1.0 m) because the sensor failed to hear one of the “echoes” from the cart. What would the velocity graph look like because of this spike in the position data? Check with an instructor at this point (show off your graph!) 4
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