Table of Contents

Chapter 3: Mechanics Experiments

Familiarization with Position, Velocity, and Acceleration Measurement

References

Crummett and Western, Physics: Models and Applications, Sections 3-1, 3-2, 3-5
Halliday and Resnick, Fundamentals of Physics (4th ed.), Sections 2-2 to 2-5
Tipler, Physics for Scientists and Engineers (3rd ed.), Chapter 2

This orientation is designed just to familiarize you with the apparatus that you'll use throughout this laboratory.

Introduction

Much of the data that you take in this laboratory will be acquired using your laptop computer in conjunction with some simple external devices controlled by homemade software:

In this exercise you will use your laptop computer, the BIB box, and the sonic ranger to gain some familiarity with the software and equipment as well as obtain position, velocity, and acceleration measurements. As you go through this exercise, keep notes in your laboratory notebook of what you do and what you observe, record all your results, etc. Your instructor may want to collect your notebooks and look over your work, but probably will not grade it. OK, let's get started.

Data Acquisition Software

The first thing you need to do is get a copy of the data acquisition software. There are two ways to do this. You may either (1) transfer the software to your computer over the Internet, or (2) your instructor may provide the software on a floppy disk. If you wish to transfer the software over the net, log on to the network and bring up Netscape. Go to the site

http://www.Rose-Hulman.edu/~hatten/index.html

From this page you will be able to call down the physics lab software in the form of a "zip" file called "physics_lab_software.zip". A zip file is a compressed data file written by the WinZip program. A zip file may contain many files compressed into one. Save this zip file to your hard drive. It might be a good idea to make a new directory to hold it. Then double click on the zip filename in the Windows Explorer. The WinZip window (shown at right) will open up. Click on the Extract button, and give the path to where you want the files. Once the files are extracted, you may delete the "physics_lab_software.zip" file to save hard drive space.

If your instructor wishes, or if the network is down, the physics_lab_software.zip file will be available on floppy disk. Copy the zip file to a directory on your hard disk, and extract the software in the same manner as described above.

Data Acquisition Hardware

Figure 2

Figure 3

Now that you have the software, let's move on to the hardware. The various data acquisition devices we will use all go through the BIB Box (See Figure 2) to talk to your computer. Plug the BIB Box's A/C adapter into one of the power outlets on your lab table. Plug the adapter cable into the BIB Box. Connect the BIB Box data cable to the printer port on the back of your laptop. The first device we will be using is the sonic ranger (See Figure 3). Plug the cable from the sonic ranger into the BIB Box. You will need a short adapter cable (~ 5 inches) to make this connection.

Now run the program called "Lab Startup.exe." This program is the shell program which allows you to select the instrument that you will be using. Select the Sonic Ranger Software option and click OK. The sonic ranger program will come up (See Figure 4). Note that the program has both a button bar and pull-down menus. The button bar gives you fast access to frequently-used commands. All of these commands may also be accessed through the pull-down menus. In addition, the pull-down menus have additional commands not found on the button bar. The software uses the standard Windows 95 file manipulation commands and windows. Move the mouse over the items on the button bar. The title of the command will pop up under each button as the mouse passes over it. Browse through the pull down menus and familiarize yourself with which commands are where. Some of them may not yet make sense to you, but they will soon.

Now let's take some data with the sonic ranger. Click on the "set parameters" button on the button bar to set your data acquisition parameters. The parameters window will open up allowing you to input the room temperature, set the frequency with which the ranger sends out pulses, and set the total number of data points taken. The room temperature is available from the thermometer on the wall in the front of the room in the labs. Set the ping rate at 75 Hz and the number of data points at 200. Then click on OK. You are now ready to take position vs. time data with the ranger. Hold your hand in front of the ranger (at least 40 cm away from it). Click on the "take data" button, and move your hand back and forth. A position vs. Time graph will appear on the screen with a plot of your hand's position on it. The plot should look something like Figure 5. The software allows you to do numerous things with this plot such as zoom in on a particular range, fit a line or parabola to sections of the plot, remove bad data points, extract the coordinates of a point on the plot, or dump the plot to a printer.

Let's try a few of these. Click on the "zoom" button on the button bar. This enables the zooming function. Move the mouse to the upper left hand corner of a region you would like to zoom in on. Left click and drag the mouse down and to the right. An expanding rectangular box will appear indicating the region you have selected to zoom in on. When you have selected the region you want, release the mouse button. You should now be looking at an expanded plot of the selected region. If you are unhappy with the region you selected, you can click on the "zoom out" button and start over. Now let's try a parabola fit of the zoomed region. Click on the "plot quadratic" button.

The program is now ready to let you do an eyeball fit of a parabola (quadratic) to the data. Since three points determine the equation of a parabola uniquely, you will left click at three points on your plot where you envision a parabola passing through. (You don't have to click on actual data points.) After you have clicked three times, a parabola and its equation will appear on the graph. Continued left-clicking will re-adjust the positions of the first, second, and third points in a revolving sequence. Try it and see if you follow what's going on. Your eye is a pretty good judge of whether you have the curve in the right place. Readjust the coordinates of the three points until you think you have the best fit of your data. Then ask your instructor or lab assistant to take a look at it (See Figure 6). If you wish to start all over on your fit, you can click on the "clear points" button which will remove the three marked points, the parabola, and its equation. You may now start over again by clicking on the "plot quadratic" button. Do this and let your partner re-do the fit. When you are done with the fit, you can view the entire plot again by clicking on the "zoom out" button. Do so now. You should be looking at the entire plot once more.

If you wish to know the coordinates of a particular data point (or any point on the graph for that matter), you can find these using the "point coordinates" command under the "left-click" pull down menu. Then when you click somewhere on the screen, the coordinates of where you clicked appear on the screen. Try this now. This feature is very useful for measuring time and position differences from the graph.

Try several other objects as targets, as well as your hand. Move the targets toward and away from the Sonic Ranger. Try a flat target like a book, and a skinnier one, like the edge of a book. Record all your observations on this in your lab notebook. Are echoes equally smooth for all kinds of targets, or does data "jump around" more for some targets than for others? What is the best target for work in the two-to-four foot range? Lower the ping rate and try some targets in the six-foot to ten- foot range (the floor tiles are a handy way of estimating horizontal distance, once you know their dimensions).

Use one of your rocky data sets to try the "deletion" functions under the "Left-click" pull down menu. Under this submenu there are two items: (1) "delete point" which excises bad data points from the data set, and (2) "replace point" which replaces bad data points with a linearly extrapolated value based on the points immediately before it and after it in the data set. Try cleaning up some of the bad data points in your data set. When do you suppose these functions are useful?

Velocity and Acceleration Plots

Take a set of data on a moving target. A data set contains just t and x values, and the software displays a position vs. time plot by default. The software can also display the corresponding velocity vs. time and acceleration vs. time plots. This is accomplished by clicking on the velocity or acceleration plot buttons on the button bar. Give this a try. The software computes velocity and acceleration from the position data by simple difference formulas

and (1)

for the various displays. You will notice that the velocity and acceleration plots are not as "nice" and the position plot. This is an inevitable result of the use of the above difference formulas, which are approximations. Small errors get amplified when these formulas are used.

Saving and Transferring Data

The software automatically saves the position data to a default file every time you take a new data set. The default file name is "erase.me" and it is saved to the same directory where your data acquisition software is located. The purpose of this default data file is to prevent data loss in the event of computer lockup or network problems prior to intentionally saving the data. Be aware that this backup copy of your data is there in the event of a problem. Also be aware that the next time you take data, the default file will be overwritten with the new data set.

When you get a data set you wish to keep, you may save the data to a file name of your own choosing using the File|Save or File|Save As options from the pull down menu, or clicking on the file save icon on the button bar similar to any other Windows 95 program. As an exercise, create a small (50 data points) data file, and send it to your F: drive on the server.

You will notice that files are saved with a default extension of ".xls" which is normally indicative of a Microsoft Excel file. The files that the data acquisition software saves are not in the Excel format, but may be opened in Excel using the File|Open commands. The data files are formatted so that they will parse correctly into columns in Excel. Excel may then be used for more extensive analysis/graphing of the data.

Studying position, velocity, and acceleration.

(a) As a warm-up, predict what the graphs of x vs. t and v vs. t will look like for a stationary object, and make small sketches in your notebook. When that is done, take some data for a stationary object (like a wall or a chair), and check that the graphs in the computer are similar to the ones that you drew.

You have probably noticed that there is often some "jitter" in the (x-t) data, and that this produces glitches in the (v-t) graph which are sometimes fairly wicked. Some of the jitter is due to software timing, and some of the jitter is due to irregular returning echoes from the target. Another complication which will also show up is that your pinger may pick up sounds from other pingers - and this WILL mess up your data.

The velocity and acceleration points are calculated using very simple difference routines (Equations (1) above). We wind up with two fewer velocity values than positions, and fewer acceleration values than velocity values.) When data is saved to a file, only the x vs. t data is saved. The computer's (v-t) and (a-t) graphs are just to give you an idea of what's going on, with minimal processing.

(b) The graph of velocity vs. time for constant-velocity motion is a straight horizontal line. For this very simple motion, make a small sketch in your notebook of what you expect for the graph of x vs. t. Now move your hand or other target at what you think is constant velocity until you get some reasonable-looking data. Figure out a way to determine the velocity from this graph. You can use simple multiplying and dividing as a check on what the Line function gives you.

Plot the (v-t) graph on the screen. The velocity values should fall in the same general range you got before. (Do they?)

Now try making a graph that shows motion with constant velocity with a reversal of direction -- the (x-t) graph would look something like Figure 2, below. Work on this until you get the constant-velocity sections pretty straight and the reversal (the "corner") pretty sharp. Try to get about the same velocity coming and going.

For this motion, what should a graph of v(t) look like? Make a small sketch of the anticipated (v-t) graph in your lab notebook before you begin. Take data until it looks about right in x vs. t. Then see if the (v-t) graph also looks like what you expected. What do you think the acceleration vs. time graph will look like? Take a look at it! Record your observations and conclusions.

Shown in Fig. 3 is a different motion, this one on a graph of velocity vs. time. Try to generate a sonic ranger graph of v vs. t which looks like it. Before you start out, make a small sketch in your lab notebook of what you think the (x-t) graph for this case should look like. Take the minimum velocity to be zero.

(c) In this part you will try to make a target move with a small constant (1 or 2 m/s2) acceleration. Before you generate any data, make a small sketch of what you think the x vs. t, v vs. t, and a vs. t graphs will look like. Then go ahead and try your hand at it.

When you get some (x-t) data which looks reasonable to you, try to determine the value of the acceleration. Try to get a value from the (x-t) graph (helped by curve fitting), from the (v-t) graph (with or without curve fitting) and -- if possible -- the (a-t) graph. Record your observations and conclusions.

Falling Bodies

last rev 9/97 - DLH