GETTING STARTED WITH THE CBR 2 SONIC MOTION DETECTOR

INCLUDING

STUDENT ACTIVITIES
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Activity 1 (Graphing Your Motion) and Activity 3 (A Speedy Slide) are used with permission from Vernier Software and Technology. These activities were adapted from Middle School Science with Calculators by Don Volz and Sandy Sapatka.

Table of contents

Introduction What is the CBR 2 Sonic Motion Detector? Getting started with the CBR 2 Sonic Motion Detector Hints for effective data collection Activities with teacher notes and student activity sheets 6
Activity 1 Graphing your motion Activity 2 Match the graph Activity 3 A Speedy slide Activity 4 Bouncing ball Activity 5 Rolling ball
Teacher information Technical information Sonic motion detector data is stored in lists EasyData settings
linear linear parabolic parabolic parabolic
Using a CBR 2 Sonic Motion Detector with a CBL 2 System or with CBL 2 System programs Service information Batteries In case of difficulty EasyData menu map TI service and warranty
2004 TEXAS INSTRUMENTS INCORPORATED
What is the CBR 2 Sonic Motion Detector?
CBR 2 (Calculator-Based Ranger) (CalculatorCalculator Ranger)
sonic motion detector use with TI-83 Plus, TI-83 Plus Silver Edition, TI-84 Plus, and TI-84 Plus Silver Edition bring real-world data collection and analysis into the classroom easy-to-use
What does the CBR 2 sonic motion detector do?
With the CBR 2 motion detector and a TI graphing calculator, students can collect, view, and analyze motion data without tedious measurements and manual plotting. The CBR 2 motion detector lets students explore the mathematical and scientific relationships between distance, velocity, acceleration, and time using data collected from activities they perform. Students can explore math and science concepts such as:

When setting up activities, ensure that the CBR 2 motion detector is securely anchored and that the cord cannot be tripped over. Always exit the EasyData App using the Quit option. The EasyData App performs a proper shutdown of the CBR 2 motion detector when you choose Quit. This ensures that the CBR 2 motion detector is properly initialized for the next time you use it. Always disconnect the CBR 2 motion detector from the calculator before storing it. EasyData is launched automatically when the unit-to-CBR 2 cable is connected from a TI-84 Plus or TI-84 Plus Silver Edition graphing calculator to a CBR 2 motion detector.
Hints for effective data collection

Getting better samples

How does the CBR 2 sonic motion detector work?
Understanding how a sonic motion detector works can help you get better data plots. The motion detector sends out an ultrasonic pulse and then measures how long it takes for that pulse to return after bouncing off the closest object. The CBR 2 motion detector, like any sonic motion detector, measures the time interval between transmitting the ultrasonic pulse and the first returned echo, but the CBR 2 motion detector has a built-in microprocessor that does much more. When the data is collected, the CBR 2 motion detector calculates the distance of the object from the CBR 2 motion detector using a speed-of-sound calculation. Then it computes the first and second derivatives of the distance data with respect to time to obtain velocity and acceleration data. It stores these measurements in lists.

Object size

Using a small object at a far distance from the CBR 2 motion detector decreases the chances of an accurate reading. For example, at 5 meters, you are much more likely to detect a soccer ball than a ping-pong ball.

Minimum range

When the CBR 2 motion detector sends out a pulse, the pulse hits the object, bounces back, and is received by the CBR 2 motion detector. If an object is closer than 15 centimeters (about six inches), consecutive pulses may overlap and be misidentified by the CBR 2 motion detector. The plot would be inaccurate, so position the CBR 2 motion detector at least 15 centimeters away from the object.

Maximum range

As the pulse travels through the air, it loses its strength. After about 12 meters (6 meters on the trip to the object and 6 meters on the trip back to the CBR 2 motion detector), the return echo may be too weak to be reliably detected by the CBR 2 motion detector. This limits the typical reliably effective distance from the CBR 2 motion detector to the object to less than 6 meters (about 20 feet).

Sensitivity switch

The sensitivity switch has two modesTrack and Normal. The Track mode is intended for activities using dynamics tracks and carts; the Normal mode is intended for all other activities, such as, walking, ball toss, bouncing ball, pendulum, etc.

Track Normal

If you are getting lots of extra noise in your data, the sensitivity switch may be in the Normal mode. Moving the sensitivity switch to the Track position, will reduce the sensitivity of the sensor and may produce better data.

The clear zone

(cont.)
The path of the CBR 2 motion detector beam is not a narrow, pencil-like beam, but fans out in all directions up to 15 from center in a 30 cone-shaped beam. To avoid interference from other objects in the vicinity, try to establish a clear zone in the path of the CBR 2 motion detector beam. This helps ensure that objects other than the target do not get recorded by the CBR 2 motion detector. The CBR 2 motion detector records the closest object in the clear zone.

15 centimeters

Reflective surfaces
Some surfaces reflect pulses better than others. For example, you might see better results with a relatively hard, smooth surfaced ball than with a tennis ball. Conversely, samples taken in a room filled with hard, reflective surfaces are more likely to show stray data points. Measurements of irregular surfaces (such as a toy car or a student holding a calculator while walking) may appear uneven. A Distance-Time plot of a nonmoving object may have small differences in the calculated distance values. If any of these values map to a different pixel, the expected flat line may show occasional blips. The Velocity-Time plot may appear even more jagged, because the change in distance between any two points over time is, by definition, velocity.

EasyData settings

Setup data collection for Time Graph
Experiment length is the total time in seconds to complete all sampling. Its determined by the number of samples multiplied by the sample interval. Enter a number between 0.05 (for very fast moving objects) and 0.5 seconds (for very slow moving objects). Note: See To set up the calculator for data collection on page 12 for detailed information about how to change settings.

Menu name Description

Measures time between samples in seconds. Total number of samples to collect. Length of the experiment in seconds.

Using the CBR 2 sonic motion detector without the EasyData application
You can use the CBR 2 unit as a sonic motion detector with a CBL 2 system or with programs other than EasyData. Using the I/O unit-to-unit cable, the CBR 2 motion detector can be used with graphing calculators that do not have the EasyData App installed but do have the CBL/CBR App and/or the RANGER program. The CBR 2 motion detector will provide the same functionality as a CBR motion detector when sample data is collected using the CBL/CBR App and/or the RANGER program. The CBL/CBR App can be used on most older TI-83 Plus calculators. The CBL/CBR App is available for downloading at education.ti.com and allows you to collect motion data using the I/O unit-to-unit cable on the CBR 2 motion detector. The RANGER program, which is part of the CBL/CBR App and available for other calculators, allows you to collect motion data using the I/O unit-to-unit cable. Many TI Explorations workbooks use the RANGER program. You can also use CBR 2 unit as a motion sensor with your CBL 2 data collection device. Use the DataMate App that comes with the CBL 2 system to operate the CBR 2 motion detector through a CBL 2 system. A special CBL-to-CBR cable is required to use this system. For more information about this cable visit the TI webstore at education.ti.com.
Activity 1Graphing your motion

Concepts

Function explored: linear This activity requires the EasyData App.

notes for teachers

Sometimes a target may not supply a strong reflection of the ultrasound. For example, if the target is a person wearing a bulky sweater, the resulting graph may be inconsistent. If the velocity and acceleration graphs are noisy, try to increase the strength of the ultrasonic reflection from the target by increasing the targets area.

Materials

calculator (see page 2 for available models) CBR 2 motion detector unit-to-CBR 2 or I/O unit-to-unit cable EasyData application Masking tape Meter stick
You may want to have your students hold a large book in front of them as they walk in front of the CBR 2 motion detector. This will produce better graphs because it smoothes out the motion.
This experiment may be the first time your students use the CBR 2 motion detector. A little coaching on its use now will save time later in the year as the CBR 2 motion detector is used in many experiments. The following are hints for effective use of the CBR 2 motion detector:

Typical plots

In using the CBR 2 motion detector, it is important to realize that the ultra sound is emitted in a cone about 30 wide. Anything within the cone of ultrasound can cause a reflection and possibly an accidental measurement. A common problem in using motion detectors is getting unintentional reflections from a desk or chair in the room. Often unintended reflections can be minimized by tilting the CBR 2 motion detector slightly. If you begin with a velocity or acceleration graph and obtain a confusing display, switch back to a distance graph to see if it makes sense. If not, the CBR 2 motion detector may not be properly targeting the target. The CBR 2 motion detector does not properly detect objects closer than 15 cm. The maximum range is about 6 m, but stray objects in the wide detection cone can be problematic at this distance.

Distance vs. Time

Matching Distance vs. Time

Answers to questions

9. The slope of the portion of the graph corresponding to movement is greater for the faster trial. Results will probably vary between groups as they may walk at different rates. Walking towards the motion detector will produce a negative slope. While walking away from the motion detector will produce a positive slope. 12. Note that the slope is close to zero (if not zero) when standing still. The slope should be zero, but expect small variation due to the variation in collected data.
2000 VERNIER SOFTWARE & TECHNOLOGY

linear

Graphs made using a CBR 2 motion detector can be used to study motion. In this experiment, you will use a CBR 2 motion detector to make graphs of your own motion.

Objectives

In this experiment, you will:
use a motion detector to measure distance and velocity produce graphs of your motion analyze the graphs you produce
Data collection: Distance vs. Time Graphs
Place a CBR 2 motion detector to a tabletop facing an area free of furniture and other
objects. The CBR 2 motion detector should be at a height of about 15 centimeters above your waist level.
walk back and forth in front of the CBR 2 motion detector
Use short strips of masking tape on the floor to mark the 1-m, 2-m, 3-m, and 4-m
distances from the CBR 2 motion detector.
Connect the CBR 2 motion detector to the calculator using an appropriate cable (see
below) and firmly press in the cable ends.
If TI-83 Plus, use an I/O unit-to-unit cable If TI-84 Plus, use a Standard-B to Mini-A USB cable (unit-to-CBR 2)
On the calculator, press and select EasyData to launch the EasyData App.
Note: EasyData will launch automatically if the CBR 2 motion detector is connected to a TI-84 Plus using a unit-to-CBR 2 cable.
Activity 1Graphing your motion (cont.)
To set up the calculator for data collection:
a. b. Select Setup (press p) to open the Setup menu. Press 2 to select 2: Time Graph to open the Time Graph Settings screen. Select Edit (press q) to open the Sample Interval dialog window. Enter 0.1 to set the time between samples to 1/10 second. Select Next (press q) to advance to the Number of Samples dialog window. Enter 50 to set the number of samples to collect. The experiment length will be 5 seconds (number of samples multiplied by the sample interval). g. h. Select Next (press q) to display a summary of the new settings. Select OK (press s) to return to the main screen.

c. d. e. f.

Explore making distance vs. time graphs.
a. b. c. d. Stand at the 1.0-m mark, facing away from the CBR 2 motion detector. Signal your partner to select Start (press p). Slowly walk to the 2.5-m mark and stop. When data collection ends, a graph plot is displayed.

r) to return to the main screen
Select Quit (press s) and OK (press s) to exit the EasyData App.
Name ___________________________________
1. What physical property is represented along the x-axis? _____________________________________ What are the units? How far apart are the tick marks? ________________
What physical property is represented along the y-axis? _____________________________________ What are the units? How far apart are the tick marks? ________________
2. How far from the CBR 2 motion detector do you think you should stand to begin? ____________ 3. Did you begin too close, too far, or just right? _____________________________________________ 4. Should you walk forward or backward for a segment that slopes up? _________________________ Why? _______________________________________________________________________________ 5. Should you walk forward or backward for a segment that slopes down? _______________________ Why? _______________________________________________________________________________ 6. What should you do for a segment that is flat? ____________________________________________ Why? _______________________________________________________________________________
7. If you take one step every second, how long should that step be? ____________________________ 8. If, instead, you take steps of 1 meter (or 1 foot) in length, how many steps must you take? _______ 9. For which segment will you have to move the fastest? ______________________________________ Why? _______________________________________________________________________________ 10. For which segment will you have to move the slowest? _____________________________________ Why? _______________________________________________________________________________ 11. In addition to choosing whether to move forward or backward, what other factors entered into matching the graph exactly? ____________________________________________________________ ____________________________________________________________________________________ 12. What physical property does the slope, or steepness of the line segment, represent? ____________ 13. For the first line segment, how many meters must you walk in how many seconds? _____________ 14. Convert the value in question 13 (the velocity) to meters1 second: ___________________________ Convert to metersminute: _____________________________________________________________ Convert to metershour: _______________________________________________________________ Convert to kilometershour: ____________________________________________________________ 15. How far did you actually walk? _________________________________________________________

Sample results

Speed (m/sec) Trial 1

Part 1 Part 2

Trial 2 2.02 3.07

Trial 3 2.00 2.82

Average 2.00 2.90

1.97 2.80

parabolic
You have been familiar with playgrounds and slides since you were a small child. The force of gravity pulls you down a slide. The force of friction slows you down. In the first part of this experiment, you will use a CBR 2 motion detector to determine your speed or velocity going down a playground slide. In the second part, you will experiment with different ways to increase your speed going down the slide.
use a CBR 2 motion detector to determine your speed going down a slide experiment with ways to increase your speed going down the slide explain your results
Data collection, Part 1, Sliding Speed
a. b. Select Setup (press p) to open the Setup menu. Press 2 to select 2: Time Graph to open the Time Graph Settings screen.
Activity 3A Speedy slide (cont.)
c. d. e. f. Select Edit (press q) to open the Sample Interval dialog window. Enter 0.2 to set the time between samples in seconds. Select Next (press q) to advance to the Number of Samples dialog window. Enter 25 to set the number of samples. Data collection will last for 5 seconds.
Select Next (press q) to display a summary of the new settings. Select OK (press s) to return to the main screen.
Take your preliminary data-collection positions.
a. b. One member of the group should first go up the slide steps and sit at the top of the slide. A second person, while holding the CBR 2 motion detector, should go high enough on the slide steps to hold the CBR 2 motion detector behind the person who will slide. The third person should stand on the ground next to the slide, while holding the calculator and interface.
Take your final data-collection positions.
a. b. c. The slider, while holding on, should move forward enough to allow a 15-cm distance between his or her back and the CBR 2 motion detector. The person holding the CBR 2 motion detector should hold the CBR 2 motion detector steady and aim it at the sliders backside. The person holding the calculator and interface should move to a comfortable position that does not cause a pull on the CBR 2 motion detector cable.

Run the EasyData App. From the Setup menu, choose 4:Ball Bounce, and then select Start (press q).
General instructions are displayed. Ball Bounce automatically takes care of the settings.
Have one person hold the calculator and CBR 2 motion detector, while another
person holds the ball beneath the sensor.
Select Start (press q). When the CBR 2 motion detector begins clicking, release the
ball, and then step back. (If the ball bounces to the side, move to keep the CBR 2 motion detector directly above the ball, but be careful not to change the height of the CBR 2 motion detector.)
When the clicking stops, the collected data is transferred to the calculator and a plot of
distance vs. time is displayed.
If the plot doesnt look good, select Main, Start, Start to repeat the sample. Study the
plot. Answer questions 1 and 2 on the activity sheet.
Observe that Ball Bounce automatically flipped the distance data. Answer questions 3

and 4.

The Distance-Time plot of the bounce forms a parabola.
The plot is in Trace mode. Press ~ to determine the vertex of the first good bouncea
nice shape without lots of extra noise. Answer question 5 on the activity sheet.
Select Main to return to the main screen. Choose Quit, and then select OK to quit

EasyData.

The vertex form of the quadratic equation, Y = A(X H) 2 + K, is
appropriate for this analysis. Press. In the Y= editor, turn off any functions that are selected. Enter the vertex form of the quadratic equation: Yn=A(XH)^2+K.
Note: If you have the Transformation Graphing App installed on your calculator, this is accomplished much easier by changing coefficient values directly on the graph screen.
On the Home screen, store the value you recorded in question 5 for the height in
variable K; store the corresponding time in variable H; store 1 in variable A. For example: Press 4 v t K , 2.5 v t H , 1 v t A to set K=4, H=2.5, and A=1.
Press to display the graph. Answer questions 6 and 7. Try A = 2, 0, 1. Complete the first part of the chart in question 8 and answer

question 9.

Choose values of your own for A until you have a good match for the plot. Record
your choices for A in the chart in question 8.
Repeat the activity, but this time choose the last (right-most) full bounce. Answer
questions 10, 11, and 12.
Repeat the data collection, but do not choose a single parabola. Record the time and height for each successive bounce. Determine the ratio between the heights for each successive bounce. Explain the significance, if any, of this ratio.

How might your classes change with a CBR 2 sonic motion detector?
The CBR 2 motion detector is an easy-to-use system with features that help you integrate it into your lesson plans quickly and easily. The CBR 2 motion detector offers significant improvements over other data-collection methods you may have used in the past. This, in turn, may lead to a restructuring of how you use class time, as your students become more enthusiastic about using real-world data.
Youll find that your students feel a greater sense of ownership of the data because they actually participate in the data-collection process rather than using data from textbooks, periodicals, or statistical abstracts. This impresses upon them that the concepts you explore in class are connected to the real world and arent just abstract ideas. But it also means that each student will want to take his or her turn at collecting the data. Data collection with CBR 2 motion detector is considerably more effective than creating scenarios and manually taking measurements with a ruler and stopwatch. Since more sampling points give greater resolution and since a sonic motion detector is highly accurate, the shape of curves is more readily apparent. You will need less time for data collection and have more time for analysis and exploration. With CBR 2 motion detector students can explore the repeatability of observations and variations in what-if scenarios. Such questions as Is it the same parabola if we drop the ball from a greater height? and Is the parabola the same for the first bounce as the last bounce? become natural and valuable extensions. The power of visualization lets students quickly associate the plotted list data with the physical properties and mathematical functions the data describes.
Other changes occur once the data from real-world events is collected. CBR 2 motion detector lets your students explore underlying relationships both numerically and graphically.

Explore data graphically

Use automatically generated plots of distance, velocity, and acceleration with respect to time for explorations such as:
What is the physical significance of the y-intercept? the x-intercept? the slope? the maximum? the minimum? the derivatives? the integrals? How do we recognize the function (linear, parabolic, etc.) represented by the plot? How would we model the data with a representative function? What is the significance of the various coefficients in the function (e.g., AX2 + BX + C)?

You may order the cable by calling 1-800-TI-CARES. Do not connect a CBR 2 motion detector to a CBL 2 system at the same time that the CBR 2 motion detector is connected to a calculator. The calculator must be connected to the CBL 2 system. You may need to change the CBL 2 system program as noted below. The EasyData App does not function with a CBL 2 system.
Collecting Motion Data Using the CBR 2 sonic motion detector with a CBL 2 System
Insert batteries into the CBL 2. Connect the CBL 2 motion detector to a TI graphing calculator using the I/O unit-tounit link cable.
Plug your CBR 2 motion detector into the DIG/SONIC port of
the CBL 2 system using a CBL-to-CBR cable (sold separately).
Run DataMate from the Apps menu on the TI-83 Plus or
TI-84 Plus family of products.
DataMate automatically identifies the CBL 2 sensors, loads its calibration factors, and
displays the name of the sensor (Motion in this case), as well as the current distance reading in meters. It also loads a default motion experiment of 5 seconds.
Using a CBR 2 Sonic Motion Detector with a CBL 2 System or with CBL 2 System programs (cont.)
Start collecting data with the default experiment.
Hold the motion sensor in your hand and choose 2: START to begin data collection.
Walk towards a wall while holding the CBR 2 motion
detector pointed towards the wall. When finished, your graph will be similar to the one shown here.

Batteries

Battery type CBR 2 motion detector is designed to operate with 4 AA alkaline batteries. CBR 2 motion detector can run without batteries only if attached to a CBL 2. Battery installation
Exit the EasyData App before changing batteries. 1. Holding the CBR 2 motion detector upside down, use your thumb to slide the battery compartment cover toward the back of the CBR 2 motion detector. Position batteries according to the diagram on the inside of the CBR 2 motion detector battery compartment. Two batteries fit positive side up in the side marked +. Two batteries fit negative side up in the side marked -. Slide the cover back on. CBR 2 motion detector is ready to begin sampling.

2. 3. 4.

CBR 2 sonic motion detector low battery warnings
The CBR 2 motion detector has two mechanisms to alert you that the batteries are low:
The EasyData App displays a warning message on calculator screen while trying to collect data. The red light flashes intermittently while the CBR 2 motion detector is collecting sample data.

Battery precautions

DO NOT use rechargeable batteries. Replace all four batteries at the same time. Do not mix brands of batteries. Do not mix types within a battery brand. Install batteries according to the diagrams inside the battery compartment. Properly dispose of used batteries immediately. Do not leave them within the reach of children. Do not heat, burn, or puncture batteries. Batteries contain hazardous chemicals and may explode or leak. Do not mix rechargeable and nonrechargeable batteries. Do not place nonrechargeable batteries in a battery recharger.

In case of difficulty

If you have this problem: Difficulty collecting data Try this: Check for a poor calculator-to-CBR 2 motion detector connection. Always push in firmly on both ends of the cable. Check for low batteries (see page 40).
The CBR 2 motion detector begins collecting data by itself
If you set down the CBR 2 motion detector with the button face down, the button may depress and activate sampling. Press again to stop sampling. Before storing the CBR 2 motion detector, properly exit the EasyData App (using Quit) or any other CBR 2 motion detector or CBL 2 system App.
The CBR 2 motion detector doesnt quit collecting data
Press to stop sampling. Repeat sample. If problem continues, remove one battery and put it back in. Note: Any data stored in the CBR 2 motion detector will be lost. Attach the CBR 2 motion detector to the calculator with the Standard-B to MiniA USB cable (unit-to-CBR 2). Check for a poor calculator-to-CBR 2 motion detector connection. Always push in firmly on both ends of the cable. If you do not want to (or cannot) attach the CBR motion detector to the calculator, quit the EasyData App.

Communication Error

Insufficient memory
You must have sufficient memory for the EasyData App and the data lists. EasyData needs 5000 bytes to run effectively. You need to delete items from the calculator memory. On the TI calculator, press y L 2:Mem Mgmt./Del. Choose items to delete and press DEL to delete the selected items.
Calculator doesnt match activity instructions

This guide applies to all the TI calculators that can load the EasyData App. You may find that some of the menu names, screens, or keys in this guide do not match exactly those on your calculator. If using Ranger, or other programs, choose the closest match. For example, if the instructions say Choose DISTANCE MATCH, on the TI-83 you would choose DIST MATCH. Repeat the sample, ensuring that the CBR 2 motion detector is aimed directly at the object. Read pages 69 on getting good data samples. Check that the clear zone does not contain students, tables, or other objects. Check the position of the Sensitivity switch. When using two CBR 2 units at the same time in the same room, one group should complete a sample before the next group begins their sample. Check for a poor calculator-to-CBR 2 motion detector connection. Always push in firmly on both ends of the cable. Check for low batteries (see page 40).

Data doesnt look right:

points not on the curve jagged plots flat plots broken plot

Lost unit-to-CBR 2 cable

You can use the I/O unit-to-unit cable that came with the calculator. (The unit-to-
CBR 2 cable allows auto-launching of EasyData and a more reliable connection,
so you may wish to order a replacement cable.) Frequently low batteries Before storing the CBR 2 motion detector, properly exit the EasyData App (using Quit) or any other CBR 2 motion detector or CBL 2 program, and disconnect the CBR 2 motion detector from the calculator.

EasyData menu map

Each screen displays one or more options along the bottom of the screen. To select an option, press the graphing key directly below the option. To navigate the menus as indicated below, select the menu options indicated by. indicates data is being collected.
Main Menu File Menu Setup Menu Quit Menu
For example, press s to select Quit.

o p q r s

1: Dist

2: Time Graph

Set sample interval

Set # of samples

Time Graph Mode

Sample plot

3: Distance Match

Instructions

Graph to Match

Sample Match

4 :Ball Bounce

Sample Plot

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Activity TEACHER INFORMATION
Tic, Toc: Pendulum Motion
1. There are currently four Motion Detectors that can be used for this lab activity. Listed below is the best method for connecting your type of Motion Detector. Optional methods are also included: Vernier Motion Detector: Connect the Vernier Motion Detector to a CBL 2 or LabPro using the Motion Detector Cable included with this sensor. The CBL 2 or LabPro connects to the calculator using the black unit-to-unit link cable that was included with the CBL 2 or LabPro. CBR: Connect the CBR directly to the graphing calculators I/O port using the extended length I/O cable that comes with the CBR. Optionally, the CBR can connect to a CBL 2 or LabPro using a Motion Detector Cable. This cable is not included with the CBR, but can be purchased from Vernier Software & Technology (order code: MDC-BTD). CBR 2: The CBR 2 includes two cables: an extended length I/O cable and a Calculator USB cable. The I/O cable connects the CBR 2 to the I/O port on any TI graphing calculator. The Calculator USB cable is used to connect the CBR 2 to the USB port located at the top right corner of any TI-84 Plus calculator. Optionally, the CBR 2 can connect to a CBL 2 or LabPro using the Motion Detector Cable. This cable is not included with the CBR 2, but can be purchased from Vernier Software & Technology (order code: MDC-BTD).

MDC cable

I/O cable

USB cable

Go! Motion: This sensor does not include any cables to connect to a graphing calculator. The cable that is included with it is intended for connecting to a computers USB port. To connect a Go! Motion to a TI graphing calculator, select one of the options listed below: Option Ithe Go! Motion connects to a CBL 2 or LabPro using the Motion Detector Cable (order code: MDC-BTD) sold separately by Vernier Software & Technology. Option IIthe Go! Motion connects to the graphing calculators I/O port using an extended length I/O cable (order code: GM-CALC) sold separately by Vernier Software & Technology. Option IIIthe Go! Motion connects to the TI-84 Plus graphing calculators USB port using a Calculator USB cable (order code: GM-MINI) sold separately by Vernier Software & Technology. 2. When connecting a CBR 2 or Go! Motion to a TI-84 calculator using USB, the EasyData application automatically launches when the calculator is turned on and at the home screen. 3. This activity has the student measure the amplitude, period, and offset distance for a pendulum using a meter stick and a stopwatch. Although these values could be obtained from
Real-World Math Made Easy 2005 Texas Instruments Incorporated

25 - 1 T

Activity 25 the Motion Detector graph, independent measurements show the student that the Motion Detector is using the same distance and time standards as conventional instruments. 4. Avoid using a soft or felt-covered ball for the pendulum bob, as the ultrasonic waves from the motion detector tend to be absorbed by these surfaces. A ball with a hole drilled through its center works well as a pendulum bob. Other objects such as a large fishing bobber or an empty soft drink can also work well.

SAMPLE RESULTS

Raw data graphed outside of EasyData
Model superimposed on data

DATA TABLE

A (m) B C (s) D (m) Time for ten cycles (s) Period (s)
0.17 3.27 1.53 0.85 19.2 1.92

ANSWERS TO QUESTIONS

1. The model fits the experimental data well. y = 0.17*sin(3.27*(x 1.53)) + 0.85. 2. The values of A, B, and D would not change. The value of C would change because the horizontal shifts needed to fit a sine and cosine curve are different. Students may use a trial and error method to find the new value of C. Some students may reason that the sine curve is the cosine curve shifted right by one-fourth of the period. They may calculate one-fourth of the period and subtract it from the current value of C to find the new value of C. In this case, 1.53 (1.53/4) = 1.91. This would be a good method to share in a post-activity discussion for those students who do not discover it. 3. The new sine model fits as well as the cosine model, as long as the appropriate adjustment is made in the C parameter. 4. A is the distance that the pendulum swings to either side of the stationary point. B is the number of cycles in the natural period of the function. C is the amount of time that passed between the start of the program and the time the pendulum was a maximum distance from the detector. D is the stationary point of the pendulum or the position of the pendulum when it is at rest. 25 - 2 T

2005 Texas Instruments Incorporated Real-World Math Made Easy