"Matching" Kinematics Graphs

Purpose:

When you finish this activity, you should be able to:

• Sketch a position vs. time graph for a described one-dimensional motion.
• Describe a one-dimensional motion given a position vs. time graph.
• Sketch a velocity vs. time graph for a described one-dimensional motion.
• Describe a one-dimensional motion give a velocity vs. time graph.

Equipment:

 Motion Detector and Pasco 500 interface DataStudioTM software graph matching activity files

Description:

A graph of position vs. time and/or velocity vs. time is one of the most effective ways to describe motion. In this lab, you will use a "motion detector" linked to a computer to automatically draw kinematics graphs in real time for your one-dimensional motions. This makes it easy and natural for you to connect kinematics graphs and the motions the represent.

This activity is divided into two parts. In the first part, you will try to "match" a pre-drawn position vs. time graph - that is, you will try to duplicate the graph by executing the required motion. In the second part, you will try to "match" a velocity vs. time graph in the same way.

It will help to understand what's going on. "Motion detectors" don't actually detect motion. They work by sending out an ultrasonic sound pulse which strikes an object (you, in this lab) and reflects back to the detector. By precisely measuring the time for the pulse to return, the software can determine the distance to the reflecting object.

For example, suppose that it takes a signal 0.017 seconds to travel to you and reflect back to the detector. Knowing that the speed of sound is about 340 m/s, the distance traveled by the pulse is easy to calculate:

total distance traveled = (average velocity)(time) = (340 m/s)(0.017 s)

total distance traveled = 5.8 m

The distance from the detector to you is half of the total distance = 5.8 m/2 = 2.9 m

Knowing the time and distance to the object it is pretty straightforward to draw the graph, and the software can construct the graph in "real time", so you can watch the graph being drawn as you move.

The software calculates your velocity from the distance and time data that it collects. For example, if you were detected 2.9 meters from the detector at 1.55 seconds, and 3.0 meters from the detector at 1.60 seconds, your velocity would be calculated as:

Hints:

Right now you are probably saying "Wow! This lab is computerized! What could possibly go wrong?" Well...

The reflection of the sound waves is not entirely reliable. Be sure that you are performing your motion in a clear area - no nearby walls, all furniture and extra people out of the way. If you can't get a good graph, try re-aiming the detector or moving nearby objects out of the way. It may help to hold a large piece of cardboard or a book in front of you to reflect the pulses more reliably.

In any case, your graph won't be perfectly "clean" and smooth. You will need to ignore the "glitches" in the graph, if possible (unless you really are jumping several meters and back in a hundredth of a second...). Keep in mind that since velocity is calculated from position, any slight problems in the position vs. time graph will be magnified in the velocity vs. time graph. Since accelerations are calculated from velocities in this software, acceleration vs. time graphs are pretty much impossible, but you can try them if you have time. If your software allows "smoothing" of your graphs, take advantage of it.

Keep in mind that the motion detector will not work well for objects closer than about 40 cm or farther than about 4 meters.

Safety Notes:

• Be sure that you have a clear area - no desks, chairs, book bags, people - at least 4 meters long and 2 meters wide in front of the motion detector.
• Don't try to walk backwards too fast! If you know you have balance problems walking backwards, then don't do it!

1. The interface will be connected to the computer and the motion detector when you arrive at the lab station. Position the motion detector so that it is abdomen/chest high, with a clear area at least 4 meters long and 2 meters wide in front of it.
2. There is a small on/off switch on the back of the interface box. When the interface is on, a small green LED should be lit on the front of the interface.
1. Select "Open Activity" from the initial dialog.
2. Open the folder "Local".
3. Open the folder "x vs. t graph matching".
4. Select the file "Graph Matching 1"
4. Decide what needs to be done in order to "match" the motion shown on the position vs. time graph shown. (You will get better at this with practice.) One person in the group will then operate the computer, one person will perform the motion, and the other two will act as "safety officers".
5. To start the detector, just press the button.
6. You can do multiple "runs" for practice if you aren't satisfied with your first attempt, just press "Start" again. If the graph gets too crowded, reload the activity and start over.
7. When you get a good "match", press the and then click on your graph. A dialog will open in which the person who performed the motion can type their name. Press return when finished. You can move or resize the text box with the mouse if it turns out to be in an inconvenient place.
8. Go to "Print Setup..." and choose landscape format, then print your graph.
9. Open another position vs. time graph matching file. There are 7 to choose from. Each person in the group should perform and print 2 position vs. time graphs - not all the same one, by the way.
10. When each person in the group has created 2 position vs. time graphs, repeat for 2 velocity vs. time graphs.

 This is an image of the "Graph Match 1" activity for position vs. time. The graph in red is the one that you need to duplicate. To start the motion detector, press The screen shot at left shows a "real" position vs. time graph - the blue line, with the student's name on the graph. Each student should have 4 graphs - 2 position vs. time and 2 velocity vs. time for motions that they have executed. The "glitch" at the upper right is caused by the student being almost out of range of the detector.

Analysis:

For each of your 4 graphs, describe each phase of the motion verbally - "Here I was at rest 1 meter from the detector", for instance - on the graph. You can write this on the printout, or if you have time you can use the text note feature () of the DataStudioTM graph (notice the pointer attached to the note) to annotate the graph before you print it out.

Each person should turn in their 4 annotated graphs.

Finishing Up:

1. Turn off the interface box with the small switch on the back. The green light on the front should go out.
2. Leave the interface box and motion detector connected to the computer.
3. Replace any furniture that you moved to its original location.

last update October 13, 2000 by JL Stanbrough