\documentclass[12pt]{book} \usepackage{epsfig} \input{iliheader} \begin{document} {\large Names:} \bigskip \centerline{\bf \Large Projectile Motion Lab} \bigskip \begin{enumerate} \item {Purpose} Projectile Motion - the motion of an object moving in the air near the surface of the earth - is one motion that has numerous applications in everyday life. In this lab we will measure the position of a ball thrown in the air, let the computer calculate (using an approximate scheme) the velocity and acceleration. Then we will model the position, velocity and acceleration using mathematical formulas, and interpret the parameters in the models. \item {Setup the experiment: } \begin{enumerate} \item Turn on the computer and launch Videopoint. \item Open the movie Pasco 104. \item On the next screen you need to tell the program how many objects to follow. For movie 104 you have only one point; enter the number $1$ and click okay. \item Enlarge the movie by clicking on the leftmost button in the upper right corner of the movie window. \end{enumerate} \item {Expectations:} Let's assume for a moment that the whole is the sum of the parts. With that theory in mind, answer the following questions. \begin{enumerate} \item What acceleration do you expect in the x-direction? What value is it? Does it change with time or is it constant? \vfill \item What acceleration do you expect in the y-direction? What value is it? Does it change with time or is it constant? \vfill \clearpage \item Given the accelerations in the last two questions, how do you expect each velocity to change with time? (e.g is it constant, linear, quadratic? Cubic? (Use calculus and antiderivatives!) \vfill \item Given the accelerations in the last two questions, how do you expect each location to change with time? (e.g is it constant, linear, quadratic? Cubic? \vfill \end{enumerate} \item {Run the ``experiment'' and take data:} \begin{enumerate} \item Run the movie by clicking on the button on the lower left next to the scroll bar. Note that you can step through the movie using the buttons to the right of the scroll bar. \item Place the movie at the beginning by dragging the scrollbar all the way to left. \item On each frame, place and click the cursor directly over the middle of the launched ball. This places the location information in a table. Be sure to click on the same place on the object in each frame. After you have done this for each frame in the movie, you can go back to any frame and adjust the location of the cursor by dragging it with your mouse, or by using the ``nudge'' tool (the set of four arrows) to move small amounts in any direction. \clearpage \item Before the data can be analyzed, we need to set the scale for the data by letting it know how many pixels are a meter for this movie. You can do the scaling in the following steps. \begin{enumerate} \item Under the "Movie" menu, select "scale movie". \item The first dialog box should have the known length to be $1$ meter, and the scale ``fixed''. \item You will then be instructed to click on one end of a known length: use your cursor to click on one edge of the meter stick in the lower portion of the movie frame. \item Now you need to click on the other end of the length: click on the other end of the meter stick. Now the computer knows the conversion from pixels to meters and the data is automatically converted. \end{enumerate} \end{enumerate} \item {Graph and model the data:} \begin{enumerate} \item Click on the graph icon on the left of the screen (or choose "new graph" under the "view" menu). \item The first coordinate is time. Keep it as time. \item The second coordinate is $x$. Select position, velocity and acceleration underneath and then click "okay". The plot should pop up. Verify that the units are in meters and seconds. \item Next you should fit the data. First, click on the $x(t)$ plot to select it, then under the {\tt Graph} menu, chose {\tt Add/Edit Fit}. Fit $x(t)$ to appropriate function that you choose above in the expectations section. Repeat for $v(t)$ and $a(t)$ plots. If the equations don't model the data well, stop and think again about what functional form you expected for each quantity. \item Repeat the above steps for the motion in the y-direction. \item Print out your plots. \end{enumerate} \clearpage \item {Analyze the data:} \begin{enumerate} \item As we did in a previous class, the first thing we need to do is made sense of the coefficients obtained in the fit. For each of your six fits do the following: \begin{enumerate} \item What are the units of each of the coefficients (is it an acceleration, a velocity or a location or time) \vfill \item Since locations and velocities vary with time, state for locations and velocities the time corresponding to the location and velocity (e.g. initial? Final?). Be sure to check from your data that these are indeed close to correct. \vfill \end{enumerate} \item From your data, does the motion in the x-direction alter the acceleration in the y-direction? Does the motion in the y-direction alter motion in the x-direction? Explain. \vfill \end{enumerate} \end{enumerate} \end{document} \item {Effects of changing coordinate systems} (if there is time). a) Predict below how all of the plots will change if you move the origin of the coordinate system. Explain. Move the origin. Do the changes agree with your predictions? b) Predict below how all of the plots will change if you rotate the origin of the coordinate system by 180 degrees. Explain. Rotate the origin by 180 degrees (double click on the origin and fill in the rotation angle near the bottom). Do the changes agree with your predictions? c) Predict below how all of the plots will change if you rotate the origin of the coordinate system by 90 degrees. Explain. Rotate the origin by 90 degrees (double click on the origin and fill in the rotation angle near the bottom). Do the changes agree with your predictions? d) Predict below how all of the plots will change if you rotate the origin of the coordinate system by 45 degrees. Explain. Rotate the origin by 45 degrees (double click on the origin and fill in the rotation angle near the bottom). Do the changes agree with your predictions? \end{document}