Lab01_1D Kinematics_Capstone

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Pennsylvania State University *

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211

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Physics

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Apr 3, 2024

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Motion in One Dimension (1D Kinematics) (Type in this document and upload these pages at the end of the laboratory) N otes: • A maximum of three students will be allowed per group. o In the event that a group of four students must be formed, you need to check with your laboratory instructor before starting to work on the activity. • Grading is based on ▪ Physics –Correct reasoning, explanations, units and numeric answers ▪ Communication- Complete sentences, clear answers, correct units, vectors, labels ▪ Participation– active engagement and contribution. • Students arriving 10 minutes or more past start will not be admitted. • This activity must be uploaded at the end of lab. A student not present at this time may not get credit for the activity. o Writing the name of a person not present is not permissible and will result in an academic integrity violation being processed. • Keep a copy of the original activity even if you are not the Recorder. • You are responsible for checking your grade (in the course website) and report any mistakes to your TA within two weeks after the activity. Date: ________________ Enter your name as it appears in your PSU registration, no nicknames please. N ame: Section # N ame: Section # N ame: Section # Clean Up Check: After you finish working and completing the lab report, you need to clean and organize your working area. Then call one of your laboratory instructors who will check your area, initialize below and take the lab report. All the members of the group must be present at that time. If you leave the lab before your laboratory instructor performs the check up, you will be deducted 5 points from your score for this lab report. Laboratory Instructor Initials: _______ 1

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) Clearly 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 relevant 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. (5) Communication: correct units, graph labels, and complete sentences. Equipment List: 1.2 meter Low Friction Track (end bracket on left of track) Dynamics Cart with plunger at one end Ultrasonic Motion Detector 3/4”-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 acceleration. ( If you need to draw something,use Draw functions in Word.) x v a x(t): v(t): 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? 2. What direction does the motion sensor call positive – towards or away from the motion sensor? 3. Is positive velocity moving towards or away from the motion sensor? 3

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4. Is there a minimum distance away from the motion sensor it can measure effectively? If so, approximately what is it? 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 t x t v

Activity 2. Testing the constant acceleration model. 6. Before you take any data, predict what the position, velocity, and acceleration graphs will look like if you launched the cart up the track at an angle, starting at the bottom, and it eventually returns back to its release point ( without hitting the motion sensor at the top of the track !) Start your graph when you would let go of the cart ( If you need to draw something use Draw functions in Word) Now, Do the experiment! 1) For the rest of this lab, you will be using the carts on the track so if necessary attach the motion sensor to the right end of the track. Your #1 rule for using this equipment is: Never crash the cart into the Motion Sensor! 2) Tilt the track at a small angle (about 1 degree) by placing a block of wood under the track’s legs near the motion sensor (the motion sensor should be at the top of the track). 3) Point the plunger away from the motion sensor so that you get a soft landing when the cart bumps the lower end of the track. 4) Change the sampling rate to 25 Hz (why might we want a faster sampling rate?). This can be done at the bottom center of the Capstone interface. 5) Add the acceleration a(t) graph to your existing position and velocity graphs (use the icon with the arrow and green star called “Add new graph to active plot area) . 5 t x t v t a

7. Highlight just the data requested above (the initial rise, initial fall, and two bounces from the end) and zoom the graph on that data. Be sure to highlight the same time interval for all three graphs. Save your three graphs and include in your report. (You can save all three separately or do a screenshot with all three in view.) [You can either copy the window in Capstone and then Paste-Special (Bitmap) into Word or use the Snipping tool available in Windows 7.] 8. As a group, you are discussing when you can reasonably apply the constant acceleration motion model to the cart as it goes up, back down, bounces off the bottom end, goes back up, and falls down a second time. Partner A says, “Since it’s accelerating the entire time, we can use the constant acceleration model for the entire time interval.” Partner B says, “We should consider at least two separate intervals within which we can use the constant acceleration model: (1) the first trip up and down, but before it hits the end of the track, and (2) the second trip back up and down again. I’m not sure if acceleration is constant when the plunger of the cart hits the end of the track, but if so, then that would be a third constant acceleration interval.” Partner C says, “Since sometimes its velocity is upwards and sometimes downwards, we need to use four separate intervals within which we can use the constant acceleration model: (1) going up, (2) falling down, (3) going back up, and (4) falling back down the second time.” With which partner, if any, do you agree? Use evidence from your graphs to justify your position in your response to your partners (write down this evidence in clear sentences) For this next section, use only the position, velocity, and acceleration data associated with the cart’s motion after it was released but before it hit the bottom end (i.e., the first trip up and down). 9. Consider the direction of the acceleration and the velocity during the cart’s motion. Part of this time the velocity is in the same direction as the acceleration; part of the time the velocity is in the opposite direction as the acceleration. How does the relative direction of velocity and acceleration determine what happens to the speed |v| of the cart? 6

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10. What is the velocity at the instant the cart reaches its highest point on the ramp (the “turning point”)? Should the acceleration be zero at that point? 13. What type of function – linear or quadratic – would best fit the velocity v(t) ? See the guide to using Capstone (2 nd page) on the course website for directions on using the Fit feature of Capstone to fit the appropriate function to the velocity data. 13a. Linear or Quadratic? ______________________________ 13b. According to the Capstone guide, what is the function for this type of fit? (Type it below). Explain what each variable in the fit function corresponds to in the V equation. 13c. What acceleration did you get from this fit to the v(t) graph and how does it compare to the average value during this interval you got from the acceleration graph? Don’t forget units. 14. What type of function – linear or quadratic – would best fit the position x(t) ? See the guide to using Capstone (2 nd page) on the course website for directions on using the Fit feature of Capstone to fit the appropriate function to the position data. 14a. Linear or Quadratic? ______________________________ 14b. According to the Capstone guide, what is the function for this type of fit? (Type it below). Explain what each variable in the fit function corresponds to in the X equation. 14c. What acceleration did you get from this fit to the x(t) graph and how does it compare to the average value during this interval you got from the acceleration graph? Explain your thoughts clearly. 7

15. Is the cart’s motion well described by the constant acceleration model during this first trip up and down the ramp? Justify your statement based on your data (explain your data below). 16. If you started the cart at a different location on the ramp and with a different initial speed, how would that affect the acceleration values on your acceleration graph? 17. Bouncing off the end of the track. What is the average acceleration of the cart during the bounce off the end at the bottom of the track? (You may only have a couple data points in this interval.) 18. Use Capstone to make a position vs. velocity graph (position on the y axis, velocity on the x axis) for a data run with only one trip up and down the ramp (no bounce). Include this graph (and its fit function) in your report. 18a. What kind of function (linear or quadratic) fits how position changes with velocity for this motion? Write down your best fit equation. 18b. Using one of the constant acceleration equations (you may have to rearrange the equation to get it in a form that matches well) describe what each variable in your fit equation corresponds to. Can you find the acceleration from this data? Compare this to your previous values of acceleration. 8

Lab01_1D Kinematics_Capstone

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