Motion in two dimensions (video)

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Physics

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Dec 6, 2023

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T E M P L E U N I V E R S I T Y P H Y S I C S 1 9/15/2023 1:07 PM Motion in two dimensions Do you know what the kinematic equations of motion are? Refer to your text if you’re not sure. Then answer the following question. The kinematic equations are only applicable for analyzing the motion of an object when that object has which one of the following? a) Zero displacement b) Constant velocity c) Constant acceleration d) Increasing acceleration Learning Goals for This Lab: • Be able to determine speed and acceleration due to gravity ‘g’ from projectile motion data and graphs. • Understand that x and y motion are independent • Become familiar with the effect of constant acceleration on velocity and position • Gain experience graphing and interpreting data captured from video Apparatus: computer with PASCO Capstone software, ball, webcam, meterstick Part I. Capturing 2D motion on video We’ll use a webcam and the Capstone software to capture the 2D projectile motion of a ball. a) Place the webcam on top of the computer monitor and point it toward you. Open the Pasco Capstone software. Click the drop-down arrow next to Video Analysis and select “Capture video.” Select the Logitech camera. See image below.

2 b) For good results use these tips when capturing your video. • Make sure your ball stays the same distance from the camera throughout its trip (avoid angling the trajectory toward or away from the camera). • Make sure the area for capturing the video is well lit. • Hold a meterstick at the same distance from the camera as the ball so that you have an accurate length for distance calibration (pixels per meter). • You can repeat video capture as many times as needed until you have a good video to analyze. • To keep the file size small, plan to make the video brief by starting recording just before the ball is thrown and stopping just after it comes down. c) When you’re ready to capture your video, click record in Capstone, then toss the ball, then click stop. Repeat video capture if needed until you have a suitable video for analysis. Part II. Tracking the motion We’ll now track the motion of the ball to obtain position and velocity data. a) Click the “Enter video analysis mode” button on the toolbar at the top of the video (see figure below). This toolbar has several other useful tools that you can explore. b) Set the distance scale in your video using the yellow caliper-shaped. Match the scale tool to the meterstick in the video and enter the corresponding value in the caliper’s text box. c) As an option, you can also set the origin using the yellow x-y coordinates tool, but this is not required. d) If you like, before you start tracking the motion, make position vs. time and velocity vs. time graphs in Capstone for both x and y motion and you will be able to see the graphs being populated with data in real time as you mark the position of the ball. Video Analysis

3 e) Use the Next Frame button (see figure below) in the toolbar at the bottom left to advance the video to just before the ball is released from the person’s hand. The other video controls may also be useful for navigating to specific points in the video. f) Now track the motion of the ball by clicking on the ball once. From this point, each time you click on the ball, Capstone will mark the location and simultaneously advance the video by one frame. If the ball is small, try using the magnifying tool in the toolbar at top. Repeat clicking on the position of the ball in the movie to track its movement. (If you make a mistake or want to start over, either create a new analysis object or delete the marks you made.) Part III. Data Analysis a) If you haven’t already made the graphs, do so for both x and y motion for position, velocity, and acceleration. b) Use the graph you made and the coordinate tool (see figure below with tools indicated) to answer the following questions. Question 1. What is the time value when the ball in your video is at its maximum height? Question 2. Is the time value when the ball in your video has zero y-velocity the same as the time value for when it is at maximum height? Would you expect them to be the same? Explain why or why not. c) Fit the x and y position vs time data to an appropriate function by highlighting the data you wish to fit and then using the fitting tool to choose the function (e.g., if the data looks linear try fitting it to y = mx + b). Also refer to the kinematic equations to help you determine what function to use. To improve results, you may want to limit your fitting to only include the data around the peak where the ball is traveling slowly. Question 3. Which general kinematic equation is most like the fit equation for the x position vs time? Which kinematic equation is most like the fit equation for the y position vs time? Question 4. For the y-velocity vs time graph, how do you find the y-acceleration from the fit? What is the acceleration expected to be for such an object in free fall? Next Frame Coordinate Tool Highlighter Fitting Tool Settings. Click Movie playback to adjust framerate as needed

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4 d) Report your experimental value for the acceleration due to gravity g in the Data and Analysis section of your lab report. Calculate and report the percent difference between your value and the expected value. If your acceleration due to gravity is significantly off from 9.8 m/s 2 first check that your calibration tool is set to the correct distance. Question 5. What is the x-acceleration according to your graph and fit of the x-velocity data? What would we expect it to be in this scenario according to the assumption that we have no forces in the x-direction? e) For your lab report discuss whether the fit results from your y-velocity graph agree with how the data changes with time in your y-acceleration graph. Question 6. One source of error in this experiment is that we ignored the effect of drag. In fact, the magnitude of the drag force is proportional to the speed of the ball. In light of this fact, is it safe to assume the magnitude of the drag force on the ball is the same at all points on its trajectory? Support your answer with your reasoning.

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