# 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 given a velocity vs. time graph.
• Be able to set up the Pasco Motion sensor and DataStudio interface to record motions.

## Equipment:

 Motion sensor and Pasco 500 interface masking tape DataStudio software meter stick

## 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 sensor" interfaced 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 of position vs. time and velocity vs. time and the motions they represent.

It will help to understand what's going on. "Motion detectors" don't actually detect motion. They work by sending out a high-frequency sound pulse which strikes an object (you, in this lab) and reflects back to the sensor. 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 sensor. 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 sensor 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 sensor at 1.55 seconds, and 3.0 meters from the sensor at 1.60 seconds, your velocity would be calculated as:

## Setup:

One of the major objectives of this activity is to familiarize you with some of the features of the motion sensor and the DataStudio interface so that you will be able to set up your own labs in the future. One thing to note - the DataStudio software is one of the few software packages (in my opinion) that has a truly useful help feature. If you don't know what to do, and there's no one to ask, go to the Help menu. This is also a good way to learn some advanced features of the interface, by the way.

 Before opening the software, connect the power supply for the DataStudio interface to a wall outlet, and connect the interface cable to a USB port on the computer (some computers will require a USB interface). Set the on/off switch (on the back of the interface) to "on". Be sure that the green LED on the front of the interface is lit. Be sure that the switch on top of the motion sensor is set to wide angle/long range. The motion sensor should be positioned at abdomen/chest height, and there should be no obstructions that will cause unwanted reflections within the range of the sensor. When you open the DataStudio software, you get this introductory screen. To open a pre-made activity, select "Open Activity" and choose the file to open. Since you will be creating your own experiment, select "Create Experiment." Scroll through the list of sensors to "Motion Sensor" and double-click it. The picture at right shows how the sensor is connected to the DataStudio interface. In the upper-left portion of the screen, you will see the Data window. It displays all of the measurements that the interface will currently make, when you press the button. Note: The motion sensor measures position as described above. The interface then calculates velocity based on the position measurement, which means that any lack of precision in the position data is magnified in the velocity data - so don't expect really good velocity vs. time data in many situations. Acceleration is calculated from velocity, which magnifies precision problems again, so acceleration data is often too "noisy" to be useful. If you already pressed , you noticed that nothing much happened. That is because you haven't selected a display for the data. The Displays window is located in the lower-left corner of the screen. It shows the various methods that the DataStudio interface can use to display your data. Since you want a position vs. time graph, drag the "Position, Ch 1 & 2 (m)" data from the Data window and drop it on the "Graph" icon in the Displays window. A new graph window is created, and "Graph 1" appears under the Graph icon. Now you can press and get a position vs. time graph for a motion. It is often convenient to have the motion sensor delay its start and/or shut off automatically. You can set this up by pressing the button (in the Experiment Setup window's toolbar), which opens the Sampling Options dialog, shown at right. If you click the button (in the Experiment Setup window's toolbar), you can change various properties of the motion sensor. The picture at right shows how you can change the trigger rate of the sensor, which might be useful. Calibration of the sensor isn't necessary for this activity, but you can try it if you like.

## 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 sensor or moving nearby objects out of the way. It may help to hold a large piece of cardboard in front of you to reflect the waves better.

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...). It might help to turn off the "connect the dots" line that the computer automatically draws (press the Graph Options button - - in the Graph window toolbar, and select from the dialog.), and draw your own "best smooth curve" on a printout of the graph.

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.

If the "noisy" graphs really bother you, investigate the "smooth(" function. Call up the Help system, and search for "smooth."

Keep in mind that the motion sensor will not work well for objects closer than about 20 cm or farther than 4-6 meters.

Don't feel that you have to keep all of the data you collect in this activity. Your goal is to get used to the equipment and to obtain some reasonably-good graphs. You can delete bad or old data runs in the Experment menu.

For easy reference as you move, put small strips of masking tape on the floor at 1 meter, 2 meters, 3 meters, and 4 meters from the sensor. Don't forget to remove this tape when you are finished!

## Procedure:

1. Decide on a simple motion. Some suggestions:
1. Stand perfectly still.
2. Move slowly toward or away from the sensor.
3. Move slowly, then faster.
4. Move one direction, stop briefly, move back.
5. etc.
2. Have someone execute this motion in front of the motion sensor. You want both position vs. time and velocity vs. time graphs for each motion. (You can get them both at the same time.) When you are satisfied with your graphs, print them.
3. Do it again. Each person in your lab group will need several graphs (see the objectives above).

## Results:

For each graph, indicate "what was going on" during each phase of the motion. For example "standing still 2 m from the sensor" or "moving quickly toward the sensor."

last update January 1, 2009 by JL Stanbrough