EXPERIMENT 2: FREE FALL and PROJECTILE MOTION

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1 TA name Lab section Date TA Initials (on completion) Name UW Student ID # Lab Partner(s) EXPERIMENT 2: FREE FALL and PROJECTILE MOTION ONE AND TWO-DIMENSIONAL KINEMATICS WITH GRAVITY 117 Textbook Reference: Walker, Chapter 2-7, Chapter 4 SYNOPSIS In this lab, you will study the one-dimensional motion of a ball that has been dropped (Free Fall) and the two-dimensional motion of a ball that has been bounced (Projectile Motion). You will measure the position of the ball at successive times using a computer-interfaced video camera. After completing this lab, you should be able to: construct a graph of velocity versus time, v(t), from successive position values, y(t), determine the instantaneous acceleration, a(t), from the v(t) graph. verify that the x and y components of projectile motion are independent; show that the x(t) motion is the same zero-acceleration, constant-velocity motion that you studied in Lab 1, show that the y(t) motion is the same constant-acceleration motion that you have studied in Lab 1, and construct two-dimensional velocity vectors for each point on the two-dimensional graph of the motion of the ball. APPARATUS For this experiment, we use time-lapse images of several trajectories of a ball obtained with a video camera connected to a computer. You will download the resulting image file, and will use the VideoPoint software to analyze the images and extract a table of values representing the motion of the ball. Instructions for the operation of the VideoPoint software follow: VideoPoint 2.5 Software Directions (UsethesedirectionsafteryouseVideoPointunder Procedure, on the next page) 1. If the lab software is not already running, double-click on VideoPoint2.5 on the Windows desktop.evenifitisruning,youmaywishtorestarthesoftwaretobesureno settings have been altered. 2. After the AboutVideoPoint screen appears, click to close it. 3. Click on OpenMovie.Double click on the directory with your Lab 4 file. In the file selection list, double click on the appropriate data file. 4. Check that the number of objects to be tracked is 1, then click OK 5. Maximize the screen. 6. Click on the ruler icon (6 th from the top) on the left tool bar. On the Scale Movie screen that appears, you should see 1.00 m, <Origin 1> and Fixed selected. Click Continue. Physics 117 Copyright 2007, Department of Physics, University of Washington Autumn 2007

2 7. Click the target cursor carefully on both ends of the meter stick in the video. 8. Click on the ball in every frame, clicking until motion ends. The image will blur as the velocity of the ball increases. Click on a consistent part of the image. 9. Click on the datatable (7 th from the top) on the left tool bar. This concludes the data taking required for the dropped ball. For bounced ball, Part B of this lab later on, choose open from the file menu and then repeat the procedure through Clickonthe plot icon(8thfromthetop)ontheleftoolbar. In the window that follows, select x coordinate and position, then y coordinate and position. Plot x and y (vertical) vs.t (horizontal). Get a meaningful v and a and give your plot a name. PROCEDURE Opentheprogramentitled VideoPoint2.5 inthe 117/121Z folder. A. Free-Fall For this part of the experiment, two balls of different mass are dropped and their positions recorded as stroboscopic images of position as a function of time. You will need the meter stick to be in the picture, without anybody standing in front of it. The class should divide in half with one half using the data for one mass and the other half the data for the other mass. The TA will demonstrate the use of the camcorder and, when your group has acquired a good set of data, the data file will be saved on a server. You should download this file to your computer following steps 1 to 3 above. 1. Determine the mass of the ball and its uncertainty and record them below. mass = ± g 2. The trajectory of the ball can be digitized by centering the cursor on the image of the ball and clicking. Position the cursor carefully. Clicking will advance the frame to the next picture. As the ball speeds up its image will be blurred. Adopt a consistent strategy for placing the cursor on the blurred image. After you have digitized the motion of the ball from the image file, print the data table from the computer for both partners. 3. On the computer printout of the data table for the y component of position vs time, draw y horizontal lines every four frames and add new columns labeled y, v y v y and t ave. Calculate and enter the change y in y over four frames, the average velocity over four 1 frames, v y, and the average time (t ave t over four frames. Do this for 4 groups beginning with t = and ending with the last complete set of four. On the coordinate axes below, make a graph of v y vs. t ave. Put the origin at the upper left corner. Label the axes. Pick scales for your time and velocity graph so that your data fill the graph as completely as possible, but also give values for the grid lines that make your data easy to plot. Physics

3 4. On your v y vs. t ave graph,drawthe bestfit lineandcalculatetheslopeofthislineandits uncertainty. Extend the line across the graph for the most accurate determination of the slope of the line you have drawn. To determine the uncertainty, proceed as you did in Lab 1 and draw the lines with the greatest and least slopes that still fit the data. Show your work. calculated slope = ± ( ) 5. Compare the calculated slope with the value of g = 9.80 ±0.01 m/s 2. Physics

4 6. If air resistance can be neglected, the acceleration of the ball should be constant. If air resistance had not been ignored, the acceleration would not have been constant. What might your velocity graph have looked like in that case? Sketch a possible v(t) below. Label the axes as you did in 3 and include your best-fit line from 3. Explain your reasoning. 7. If the time-lapse interval between position pictures were increased, how (if at all) would you expect such a change to affect your measurement of the acceleration of the ball? Explain. Projectile Motion In this part of the activity, you will analyze a stroboscopic image of a ball that has bounced off the floor and taken a parabolic "projectile motion" trajectory. Analyzing the image will yield a data table for the horizontal position x, the vertical position y, and the time t. Physics

5 As you bounce the ball, observe the plane of its trajectory. It is important that the plane of the bal smotionbeaproximatelyperpendiculartotheaxisofthevideo camera. This will avoid an error in the x component of the velocity since the computer assumes you have calibrated the distance scale in the plane in which your ball bounces. As with the dropped balls, the class should divide in half to take the data. Not all will finish the analysis of the dropped ball at the same time. When the first partners have finished, their half of the class should take a break from analysis and participate in obtaining the bouncing-ball data. The edited movie should be given a filename for your group and saved on the server. When partners have finished analyzing the dropped-ball data, they should download the bounced-ball data and begin the analysis of this data. 8. Print the data table for each partner. It will be too long to fit on one page, so after the first page is printed, scroll until the next portion you wish to print shows on the screen. 9. Use VideoPoint to make a plot of the trajectory. (X and Y positions) Click on the plot icon (8 th from the top) in the left toolbar. In the window that appears under Horizontal Axis, select Point S1 and x component and under that select Position. Under Vertical Axis select Point S1 and y component and under that select Position. Clicking OK will produce a plot of the trajectory. Before printing it, examine the plot for any points that seem to be far off from a reasonable position. These should be removed. Note their position, then under the Edit menu select Edit Selected Series and click OK. In the data table window, select the x and y values for a bad point and hit the DELETE key. When the bad points have been removed, click the plot icon and regenerate the trajectory plot. Print a copy of the plot for both partners. CAUTION: Do not close any of the windows you have created or you risk having to re-click positions for the whole movie. 10. Use the plot to calculate the velocity, v(t 1 ), at some time t 1 between t = 0 and the time the ball is at the top of its trajectory. Draw the vector v(t 1 ) on your plot. Show your work on the plot. Assume a 10% uncertainty in v. t 1 = s v = ± m/s 11. Click on the plot icon and produce a graph of x(t). Before printing the graph, use VideoPoint to fit a straight line to the data. Under the Graph menu, select Add/Edit/Fit, or pick F on the graph. The window that appears should give Linear as the type of fit. Click Apply. The equationofthe bestfit lineandaquantityr 2 that indicates the goodness of the fit (R 2 = 1.00 is a perfect fit. Any value of R 2 > 0.9 indicates a good fit) appears just above the plot. Record the equation and R 2 below. Print the plot for both partners. equation of best fit line R 2 = 12. From the plot and the equation determine v x and v. What do you infer from the plot about x the constancy of v x? Explain. v x = ± m/s Physics

6 13. Generate and print a plot of y(t) for both partners. This will appear to be very similar to the plot of y(x). Explain. 14. Generate a plot of v y (t). Use VideoPoint to fit a straight line to the data. Print a copy for both partners. Record the equation of the fit line and R 2 below. equation of best fit line R 2 = 15. Find the y component of the acceleration a y and its uncertainty. Explain, based on your measurements, why you think, or do not think, that a y is a constant independent of time. a y (t) = ± m/s Determine a value for the x component of the acceleration a x from your results in 12. Explain. a x (t) = ± m/s Choose five different times in the motion for which you will explicitly determine the velocity vectors, one at the top of the trajectory and two on each side. One of the times should be t 1 from 10. The points x 1,y 1 and x 2,y 2 should be chosen so that you can use them to make a reasonable approximation of the velocity at time t. time t x 1 y 1 x 2 y 2 x y v x v y Physics

7 18. From your data in 17, calculate v(t 1 ). Use this value and the length of the velocity vector you drew in 10 to establish a scale for your velocity vectors. At points corresponding to the times given in the table above, draw the horizontal and vertical components of each velocity vector on your y(x) graph,. Then draw the velocity vectors themselves. Show your work. v(t 1 ) = m/s SUMMARY Simplicio: Oh, that I do not believe, nor does Aristotle believe it either; for he writes that the speeds of falling heavy bodies have among themselves the same proportions as their weights Salviati: Since you want to admit this, Simplicio, you must also believe that a hundred-pound ball and a one-pound ball of the same material being dropped at the same moment from a height of one hundred yards, the larger will reach the ground before the smaller has fallen a single yard. Now try, if you can, to picture in your mind the large ball striking the ground while the small one is less than a yard from the top of the tower. from Two New Sciences by Galileo Galilei (1638) We are taught very early on that Galileo was right and Aristotle was wrong: heavier bodies do not fall with velocities proportional to their masses: all bodies, large or small, heavy or light, accelerate at exactly the same rate if subject only to a gravitational force. Aristotle believed that falling bodies veryquicklyreachedtheir naturalvelocity'' and that this natural velocity was proportional to the mass; so a mass one hundred times heavier should fall one hundred times faster. In their times, it was not easy to remove all the extraneous forces (particularly air resistance) and to make sufficiently precise measurements to convincingly demonstrate either position. 19.Rather than repeating the measurements with a ball of different mass, obtain the value of g from part 4 that was acquired by the other half of the class. Write their value of the mass and g below. m = ± ( ) g = ± ( ) 20. Based on your value and theirs, with whom do you agree, Aristotle, Galileo or neither of them? Explain (You must compare and comment.) Physics