Aug 26 1996

A) Setting up

--If your computer has a hard drive (i.e., either a 386 or 486):

1) From the MAIN menu, access the PHYSICS menu

2) From the PHYSICS menu, access the MOTION PLOTTER software

--If your computer does NOT have a hard drive:

The appropriate software diskette is MPX. It should be in drive A. Turn the computer on. The computer should then boot and run the MOTION PLOTTER software.

---Plug the sonic ranger probe into slot A of the blue box labeled MultiPurpose Lab Interface. When you are finished using the computer at the end of the period, please remove the sonic ranger. DO NOT PULL ON THE CORD. Grasp the plug and pull it out.

B) The Range of the Motion Detector

After the Motion Plotter logo appears on the screen, press <Enter> to access the main menu, and then choose L to determine the approximate minimum and maximum distances that the sonic ranger can measure. You'll need a meter stick also. Record results in your lab journal. Check with the instructor to see if your answers are reasonable. After your finished with the determination of the workable range, press <Enter> to return to the Main Menu of Motion Plotter.

C) Position, time, & velocity

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general instructions for acquiring a graph using the motion detector

A) Select M to have the sonic ranger graphically display an object's motion.

B) From the Graph Style Options menu, select M (read instructions at the bottom of the screen for turning options on/off).

C) From the Select Options menu, turn Store Data in Memory ON

D) From Real-Time Graphing - Scaling, turn the Distance graph (they should have called it the "Position" graph as Giancoli does) On and all the other graphs Off.

E) Select G for graph and then <Enter>; follow the instructions on the screen.

F) When you are finished with a graph, press <Enter>. A menu will appear; press R to keep the same graphing options; otherwise press X to return to the menu which allows you to change the graphs displayed.

If you occasionally get spikes (exceptionally high points) on the graph, this is due to the failure of the ranger to detect your reflected signal. It sometimes helps to hold a reflector in front of the ranger as you walking. This could be a book or other hard, flat surface.

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1) (While standing still), aim the sonic ranger at a wall. Before asking the software to produce a graph of the wall's position vs time, predict what you think that graph will look like by making a sketch in your lab journal at the top of a new page; use the whole top half of the page for this prediction and reserve the bottom half for the velocity-vs-time graph that will come later.. Label your axes: position and time.

2) Once you've predicted the shape of the graph, get the software to plot it. Does your prediction agree with the plot?

3) You probably have some familiarity with the term velocity. What is the velocity of the wall (with respect to the sonic ranger) for the situation described in #1 above? What would the velocity-vs-time graph for the wall look like? Make a prediction and sketch it in your lab book right below the position-vs-time graph.

4) Hopefully, you answered zero (or some equivalent) to the previous question. Now go back to the computer and check your prediction. Here's the general instructions for turning graphs on and off:

Go back to the main menu (if you hit <ESC> you'll eventually get there)

Select M

Keep hitting return till you get to the Real Time Graphing menu

Select which graphs you want On and which Off

hit <ESC> enough times till you get to the main menu

Select P for Plot & hit return enough times till you get the graphs

Look back at the position-vs-time graph for th wall that you predicted and the computer plotted...is there anything zero about the graph? Talk it over with your partner.

5) We trust that your answer to the previous question, without looking ahead, was something like "the slope of the line or graph is zero." Now, is it a coincidence that both the velocity and the slope of the line are zero? In your lab journal, write a general definition of the slope of a line. Do not use the symbols x and/or y in your answer, but you may use words like horizontal, vertical, rise, and run. (This is the last we'll remind you to write something in your lab journal. In the future, we expect you to do this automatically.)

6) If we now apply your definition of slope specifically to a position-vs-time graph, we see that the slope of the graph is the change in position divided by the change in time. And this is exactly the definition of velocity.

7) Now let's try something that moves. One person will walk away from the sonic ranger at a fairly slow constant rate. But before you try this, sketch a prediction of the position-vs-time graph for the slow-walking person. Again, label the axes (but don't worry about numbers). Compare your prediction to your partner's.

Now collect data. The person who walks should begin at a distance from the sonic ranger that is roughly equal to the minimum distance for which the ranger works; you might also want to set the time of run on the graph menu to 3 seconds and the maximum distance to about 3 meters. Record the computer-generated graph.

8) Did your prediction match reality? Check with the instructor if you're not sure. Estimate the slope of the position-vs-time graph by reading two (time, position) coordinates off the line and calculating the slope. Show your work, and include units (m, s, m/s) whenever you write a position, time, or velocity.

9) Now for a new prediction. What would the velocity-vs-time graph look like for the walk done above? Sketch your prediction. [Hint: Was the velocity of the walker constant? How could you tell from the position-vs-time graph?]

10) After you have sketched your velocity-vs-time graph prediction in your lab book, go back to the computer and turn the velocity-vs-time graph on. Leave the position-vs-time graph on.

You might also set the minimum velocity equal to zero and the maximum velocity equal to 2 m/s. Was your velocity-vs-time graph prediction correct?

11) The other partner will now try a faster walk away from the sonic ranger. Before this happens, however, make a prediction of the position-vs-time graph on the same axes as your previous prediction for the slow walk). Label the first prediction SLOW and the second one FAST. Also predict the velocity-vs-time graph (don't worry about numbers here) for the FAST walk and record it on the same velocity graph for the slow walk). Label both lines.

12) After predicting both position-vs-time and velocity-vs-time graphs for the fast walk, collect data for the faster walk, remembering to start at about the minimum working distance of the sonic ranger. Did your predictions match expectations?

13) Summarize what you have learned so far about how velocity information shows up on an object's position-vs-time graph.

D) Changing directions

Use a dynamics cart, loaded with weights, for these activities. Set the ranger on the floor, aimed at the cardboard reflector taped to the back of the cart. Change the software settings to give you a position-vs-time graph only. A maximum position of 3 meters and time of 3 seconds should be fine.

1) In this part you will give the cart a push away from the ranger. Try it first without the sonic ranger recording data (just turn the ranger face down on the floor temporarily). Then predict & obtain the position-vs-time graph. If the cart slows down as it moves, how is that seen on the graph? Did it slow down?

2) Based on your position-vs-time graph, predict what the velocity-vs-time graph of the same motion would look like. [Hint: As the slope of the position-vs-time graph changes, how does the velocity-vs-time graph change?]

3) Turn on the velocity-vs-time graph and check your prediction in 2). Sketch the graph you obtain. Were you correct?

When you compare the actual velocity-vs-time graph to your prediction, you may find that the former has more irregularities than you might expect. This is due to the fact that the velocities are not measured directly by the ranger but instead are calculated by dividing the differences in position between successive data points by the corresponding time differences. Since the differences are quite small, substantial error is introduced into the calculated result. These errors show up as bumps and valleys in the graph. You should be looking for overall trends in the graph.

4) Next you'll look at a collision. If you push the cart so that the plunger end strikes a wall, the cart will push back off again and return. Set up the ranger facing the wall and about 2 m away. Put the cart about a half meter from the ranger, ready to be pushed toward the wall. But wait! That's right, make your predictions of the position-vs-time and velocity-vs-time graphs. You can, however, try the experiment without having the sonic ranger recording if that will help you visualize the position and velocity graphs. Once you've recorded them, push the cart and record the results.

5) When the cart turned around at the wall, how did the position-vs-time graph change? Be sure to be specific in discussing the slope of the line.

How did the velocity-vs-time graph change? Again, be specific.

6) Something to note at this point is that changes of velocity are caused by the application of forces. When the moving cart slows down, that is due to frictional forces. When the cart changes direction, that is due to the push of the wall on the cart. (It may seem strange to think of a solid, immovable wall as exerting a push. However, we'll see later that walls, floors, etc., do exert forces.)

Something else to note is that there are two ways that velocity can change. One way is when the object speeds up or slows down. The other is when the object changes direction.

You probably noticed that the velocity of the cart changed faster when it bounced off the wall than when it was slowing due to friction. This rate of change of velocity, termed acceleration, is investigated in the next section.

E) Velocity, time, & acceleration

In this part, you'll look more closely at acceleration. Use the same cart as before, but allow it to roll down an inclined ramp. You'll find a variety of boards in the lab to serve as ramps. Don't incline the ramp more than about 30deg..

1) Here, you'll start the cart at the top of the ramp. Position the sonic ranger aimed down the ramp so that the cart will move away from the ranger while rolling down the ramp. Obtain position-vs-time and velocity-vs-time graphs and record them. You may need to change scales if the maximum values are too small/large.

2) Describe in words each of the graphs you just obtained. Use words like constant, increasing, decreasing, slope, positive, negative, zero.

3) How do you think you could determine the acceleration of the cart? [Hint: Think about how you found velocity from a position-vs-time graph. How can you find acceleration from a velocity-vs-time graph?]

4) Hopefully, you realized that the slope of the line on the velocity-vs-time graph is the acceleration. You can calculate a value for it by reading two (time, velocity) coordinate pairs from the graph and using the slope formula. Do that now, and be sure to carry units throughout the calculation. Note that the units of acceleration are m/s per s or m/s[[twosuperior]] for short.

5) If you would like to see a graph of acceleration-vs-time, go to the graphing menu to turn the acceleration graph on. You should expect to see a lot of bumps in this graph, because the process of calculating accelerations from the velocity-time data introduces error in addition to that introduced in calculating velocities from the position-time data.

6) Unlike the accelerations discussed in section C, the acceleration of the cart on the board should be fairly constant.