PHYS 2010 Lecture 06 (Laboratory) Acceleration Due to Gravity

PHYS 2010 Lecture 06 (Laboratory) Acceleration Due to Gravity We’ve talked about motion from the perspective that position, velocity, and acceleration are all interrelated. A lot of the time, it makes a fair amount of sense. However, there are some accelerations that seem to just…happen… While there are definitely reasons why they happen, we haven’t really introduced that level of understanding yet. The purpose of this activity is to explore the accelerations involved from dropping something. Materials: Tracker software (free; download from course module or https://physlets.org/tracker/) BallDrop.mov video from course module BallTossUp.mov video from course module Background Over twenty-two centuries ago, a Greek philosopher and scientist named Aristotle proposed that it was a natural behavior for objects to fall to the ground. However, there was a flaw in this understanding, as it implied that heavier objects fell faster. About 1700 years later, the scientific method had developed to a point where Galileo was able to prove that two objects of identical size but different weights fell with the same behavior, thus disproving Aristotle’s ideas but taking a closer step to what happens in that case; and laying the groundwork for those to follow. When an object is in “free fall”, it moves through the air without being touched. So while the object is touching your hand or held up by something, it’s not in free fall; same for the moment when the object hits the ground. It’s only a matter of instants that are often too small to measure, but the difference is conceptually important. Free fall happens after you let an object go, but before it hits the ground. Video Tools Ordinarily, this is the sort of lab you would accomplish in a more academic setting, with appropriate equipment and partners. However, as it’s an online lab activity, we’re going to be using tools that allow you to interpret pre-recorded video, or video you make yourself. A video is basically a set of images recorded typically at a rate of 30 frames per second, or in other words a timeinterval of 1/30 s between frames. To measure an object’s position in a video, you need to: 1. define a coordinate system including an origin and x,y axes. 2. define a scale; in other words define a standard length, perhaps 1 m, in the video. For this, it helps to have a reference object of known length, such as a meterstick/tile/wall, in the video. This is called a calibration. It’s very important that the reference object is in the same plane as the object’smotion. If the reference is significantly closer to the camera or further from the camera than the object you are studying,then your measurement of position will be inaccurate. Together, these two pieces of information (scale and time) allow us to make measurements of position, velocity, and acceleration. Video analysis software makes it easy to measure position coordinates (both x- and y-) and time for an object. After defining the scale and the coordinate system, you click on the object. The software shows a dot where you clicked and advances the video to the next frame. The software measures the position of where you clicked in units of pixels and then uses the calibration and your definition of the coordinate system to convert this position in pixels to a position in meters (or whatever units are used in the calibration). The software also measures time because it knows that the video is recorded at 30 frames per second (or perhaps higher for high-speed video). Thus, whenever you advance the video by a single frame, time advances by 1/30 s. With time and position measured by the software, you can calculate velocity by calculating how much the position changed during the time in which it changed. Other quantities can also be calculated and/or graphed. All of these calculations can be done by the software. Activity 1: Dropped Ball 1. If you haven’t already, download the Tracker software from our course shell (or from https://physlets.org/tracker/), and install. 2. Download the first video for today, “BallDrop.mov” 3. Open the Tracker software on your computer. 4. Use the menu items Video→Import…to import your video, as shown below. Video→Import menu 5. To zoom in or out on the video, click on the toolbar’s magnifying glass icon that is shown below. When it appears with a , then clicking once on the video will zoom in (thus making it larger).Clicking the magnifying glass again will make it ; then clicking on the video will zoom out (thus making it smaller). Zoom in and out on the video to see how it works. The icon used for magnifying the video. 6. At this point, it’s nice to lay out the video and graphs so that you can clearly see everything. The middle border between panes can be dragged left and right to make the video pane smaller and graphs larger. The same is true of any other bar that separates panes in the window. Drag the vertical or horizontal bars to make panes larger or smaller. 7. Note the video controls at the bottom of the video pane. Go ahead and play the video, step it forward,backward, etc. in order to learn how the video controls work. Note the counter that merely shows the frame number for any frame. Also, click on each of the icons in the video control bar to see what theyare used for. Finally, use the left and right arrow keys on your keyboard, and note that they can beused to control the video as well. 8. Rewind to the first frame of the video. This is the instant that you will begin making measurements of the position of the moving object. 9. If your object moves very slowly, you can skip frames between marking the ball and thus take fewer data points. Click on the Step Size button and change the value to 5 to see the effect. Change the step size in order to skip frames and see how that works. Resetthe step size back to 1 for this exercise.. 10. You now need to define the origin of the coordinate system. In the toolbar, click the Axes icon shown in Fig. 1.6 to show the axes of the coordinate system. (By now, you have probably noticed that youcan hover the mouse over each icon to see what they do). Icon used to set the coordinate system axes. 11. Click and drag on the video to place the origin of the coordinate system at the location where you would like to define (0,0), as shown below. You can place the origin at any point you choose, but in this case, it makes sense to put the origin at the bottom of the reference marker. 12. If you click the x-axis and drag, you can rotate the coordinate system. In this case, the video camera was fairly level so it’s not necessary. However, practice a bit to make sure you are familiar with the operation. Note that the angle of the axis is displayed along the top of the video. 13. Click the Axes tool again to hide the axes from the video pane. You can click this icon at any time to show or hide the axes. 14. Now, you must calibrate distances measured in the video. In the toolbar, click on the Tape Measure icon shown below to set the scale for the video, and select a Calibration Stick. Icon used to set the scale. 15. You now will define the ends of the reference length. Move the mouse to the origin, and hold down the shift key. The cursor will change to a marker, and click on the origin to place it. Then move to the uppermost marker line on the meter stick (not coincidentally, ten divisions above the origin) and repeat. The scale will be defined in blue, and a number describing the length of the line in pixels will be shown. 16. Double-click the number, and enter the distance, 1.0 (Tracker defaults to units of m) 17. Click the tape measure icon again to hide the blue scale from the video. 18. You are ready to add markers to the video to mark the position of the ball. Let’s not show the coordinate system and scale. It’s too distracting. So, make sure you’ve clicked the Axes and Tape Measure icons in the toolbar to hide them. 19. To add markers, click on the Create button and select Point Mass as shown below. Then, mass A will be created, and a new x vs t graph will appear in a different pane. You will now be able to mark the x-position of the ball which will be referred to as mass A. You’ll notice that there’s a bit of blurring, which can happen with video (it’s an effect of interpolation in older video). Focus on the leading ball (which is the second image of the two displayed). 20. To mark the center of the ball, hold the SHIFT key down and click once on the center of the ball. You should notice that a marker appears at the position of the ball where you clicked and that the video advances one step. 21. Again, shift-click on the ball to mark its position. You should now see two marks. 22. Continue marking the position of the ball until it reaches the right end of the track. As the ball peaks through it’s arc, note that you’ll want to mark the bottom ball instead of the upper ball. 23. After marking the ball as it moves from the start to the end of the toss, your video should look something like the picture shown below. 24. Tracker uses the frame and frame rate to calculate t, and it uses the scale and coordinates of the marks to calculate x- and y-coordinates for the ball. It then works the math to calculate x-velocity and y-velocity. 25. By now, you may be thinking “this doesn’t look right”, and you’re correct. The graph is displaying the horizontal (x) position, and the ball was dropped vertically (in the ydirection). To fix that, click on the vertical axis label, and select “y: position, y component”. The graph should update to something more familiar for the motion of a tossed ball (note there wasn’t anything actually wrong before, it just wasn’t plotting the data we were wanting).. Think About It: Looking at the graph of the data pulled from the video, at what time does it become clear that the ball has been dropped, as opposed to being held? Analysis We will now analyze the y vs t graph. You can click and drag the border of the video pane to make it smaller so that you can focus on the graph. 1. Play the video. (You can hide the marks if you wish by clicking the Show/Hide Positions icon,and you can show the path by clicking the Show/Hide Paths icon. Both of these icons are in the toolbar.) Note how the graph and video are sync’d. Each video frame data point is shown in the graph using a filled rectangle. Also, when you click on a data point on the graph, the video moves to the corresponding frame. 2. Observe the y vs t graph. Think About It: What sort of function is associated with this graph (i.e. linear, quadratic, square root, sinusoidal, etc.)? How can you tell? 3. Right-click (or ctrl-click) on the graph and select Analyze…. In the resulting window, check the checkbox for Fit, and additional input boxes will appear. What sort of data fit most cleanly fits your data? How does that compare to your thoughts in 2? 4. Close out the Analyze window for Position 5. Adjust the graph to show “vy: velocity y-component” vs t. Think About It: Looking at the graph of the data pulled from the video, at what time does it become clear that the ball has been dropped, as opposed to being held? How does this compare to your thoughts for the position-time data? Think About It: What sort of function is associated with this graph (i.e. linear, quadratic, square root, sinusoidal, etc.)? How can you tell? 6. Right-click (or ctrl-click) on the graph and select Analyze…. You may find that the resulting graph shows more than one graph (pulling your earlier work back in). To remove the position data, right click the top of the “y” data, and “cut column”. That should only leave your velocity data plotted. 7. Check the checkbox for Fit, and additional input boxes will appear. What sort of data fit most cleanly fits your data? How does that compare to your thoughts? Think About It: Your fit line should have the form “vy = At + B”. What role does A have in this formula? Based on what is being plotted on the axes, what units should go with this number? What kinematic quantity is associated with those units? 8. You can also restrict what data is involved in the Fit. Select the checkbox marked “Autofit” and using your mouse, stretch a rectangle over the data you want to use in the fit. Use the data that you associate with the ball cleanly falling through the air. If you hover your mouse over the formula parameters, you also will see the uncertainties associated with the parameter. Based on your understanding of the graph, indicate the acceleration of the ball. Acceleration = ± m/s2 Think About It: How does this acceleration compare to the accepted value for the acceleration due to gravity? Activity 2: Tossed Ball Repeat Activity 1, using the video file “BallTossUp.mov” Acceleration = ± m/s2 Think About It: Does your value for acceleration agree as before? Does it matter if the velocity is positive or negative? Is there ever a point where the acceleration is zero? Activity 3: Personal Experimentation Set up a video of your own. Make sure you include a scale reference for Tracker. Save or convert the file to a *.mov format. Repeat the analysis of Activity 1, and determine your value for the acceleration. Acceleration = ± m/s2 Think About It: Does your value for acceleration agree as before? If not, try to adjust some of the parameters of the experiment. Does the weight or size of the ball matter? Deliverables We need an informal report describing what you did and what you learned. Imagine you are talking to your parents or your boss, and describing the activities you just completed. Make sure to include any pictures and resulting understanding you have gained. Submit a copy of this report and your video file for grading. Rubric: Missing Novice Partial Proficient Video 25 (0.00%) 15 (30.00%) 20 (40.00%) 25 (50.00%) Did not submit Video is not a continuous scene, or does not include a reference object for scale. Video does not include a standard reference, or one that would need additional information to determine scale. Clear single-shot video, edited for length, includes easily definable reference whose length is readily available. Documentation 25 (0.00%) 15 (30.00%) 20 (40.00%) 25 (50.00%) Did not submit Narrative unclear, incomplete thoughts and/or sentences. Did not include sufficient information for a person to replicate the work Narrative was fairly clear, but left out something significant (i.e, meaning of the results, numbers without units or uncertainties) Ideas were expressed in a clear and organized fashion. It was easy to figure out what was going on, and how to repeat the experiment if desired. Included discussion of results compared to accepted values (with appropriate uncertainties and units) A post-lab quiz will also be required to assess your understanding of the goals for this lab, and will count for half the grade.

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