Getting Started with the CBR 2™ Sonic Motion Detector
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Table of Contents Introduction What is the CBR 2™ Sonic Motion Detector? 2 Getting started with the CBR 2™ Sonic Motion Detector 4 Hints for effective data collection 6 Activities with teacher notes and student activity sheets ³ Activity 1 — Graphing your motion linear 10 ³ Activity 2 — Match the graph linear 14 ³ Activity 3 — A Speedy slide parabolic 18 ³ Activity 4 — Bouncing ball parabolic 24 ³ Activity 5 — Rolling ball parabolic 28 Teacher information 32 Technical information So
What is the CBR 2™ Sonic Motion Detector? CBR 2™ (Calculator-Based Ranger™) sonic motion detector use with TI-83 Plus, TI-83 Plus Silver Edition,TI-84 Plus, TI-84 Plus Silver Edition TI-92 Plus, TI-89, TI-89 Titanium, and Voyage™ 200 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 manua
What is the CBR 2™ Sonic Motion Detector? (cont.) ¤ button USB and I/O ports to connect to TI graphing calculators using the included cables to initiate sampling battery door (on bottom) sonic sensor to record up to 200 samples per second with a range between 15 centimeters and 6 meters (5.9 inches and 19.
Getting started with the CBR 2™ Sonic Motion Detector With the CBR 2™ motion detector, you’re just two or three simple steps from the first data sample! 1 Download For TI-83 and TI-84 family calculator users: Your graphing calculator may have been preloaded with a number of Apps (software applications), including the EasyData App. Press Œ to see the Apps installed on your calculator. If EasyData is not installed, you may find the latest version of this App at education.ti.com.
3 1 Run For TI-83 and TI-84 family calculator users: Run the EasyData App on the graphing calculator connected to the CBR 2™ motion detector. Proceed to step 1, if using a TI-83 Plus-family calculator. For the TI-84 Plus connected with a unit-to-CBR 2™ cable, perform steps 1 and 4. 1. 2. 3. Turn on the calculator and have it on the home screen. Press Œ to display the list of Apps on your graphing calculator. Choose EasyData and press Í.
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.
Hints for effective data collection (cont.) The clear zone 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.
Hints for effective data collection (cont.) EasyData settings (for TI-83, TI-83 Plus, TI-84, and TI-84 Plus users only) Setup data collection for Time Graph Experiment length is the total time in seconds to complete all sampling. It’s 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).
Hints for effective data collection (cont.) Speed of sound The approximate distance to the object is calculated by assuming a nominal speed of sound. However, actual speed of sound varies with several factors, most notably the air temperature. The CBR 2™ motion detector has a built-in temperature sensor to automatically compensate for changes in the speed of sound due to the temperature of the surrounding air.
Activity 1—Graphing Your Motion Concepts 0 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. 0 If the velocity and acceleration graphs are noisy, try to increase the strength of the ultrasonic reflection from the target by increasing the target’s area.
Activity 1—Graphing Your Motion 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: 0 use a motion detector to measure distance and velocity 0 produce graphs of your motion 0 analyze the graphs you produce Data collection: Distance vs.
Activity 1—Graphing Your Motion (cont.) Linear Î To set up the calculator for data collection using EasyData: a. Select Setup (press p) to open the Setup menu. b. Press 2 to select 2: Time Graph to open the Time Graph Settings screen. c. Select Edit (press q) to open the Sample Interval dialog window. d. Enter 0.1 to set the time between samples to 1/10 second. e. Select Next (press q) to advance to the Number of Samples dialog window. f. Enter 50 to set the number of samples to collect.
Activity 1—Graphing Your Motion (cont.) e. Sketch your graph on the empty graph provided. f. Pick two points on the graph and determine the slope from the x and y-coordinates. Linear Point 1:________ Point 2: ________ Slope:___________ g. Select Main (press r) to return to the main screen. Ð Repeat Step 6, this time standing on the 2.5m-mark and walk towards the 1.0m-mark. One time walking slowly, and again walking more quickly.
Activity 2—Match the Graph Notes for Teachers Concepts Function explored: linear Typical answers Distance Match introduces the real-world concepts of distance and time—or more precisely, the concept of distance versus time. 1. time (from start of sample); seconds; 1 second; distance (from the CBR 2™ motion detector to the object); meters; 1 meter In Explorations, students are asked to convert their rate of walking in meters per second to kilometers per hours. 2.
Activity 2—Match the Graph Linear Data collection Ê Hold the CBR 2™ motion detector in one hand, and the calculator in the other. Aim the sensor directly at a wall. Hints: The maximum distance of any graph is 6 meters (about 20 feet) from the CBR 2™ motion detector. The minimum range is 15 centimeters (about 6 inches). Make sure that there is nothing in the clear zone (see page 7). Ë Run the EasyData application or RANGER program. Ì EasyData Users: From the Setup menu choose 3:Distance Match.
Activity 2—Match the Graph (cont.) Linear Ï Position yourself where you think the graph begins. Select Start (press p) to begin data collection. You can hear a clicking sound and see the green light as the data is collected. Ð Walk backward and forward, and try to match the graph. Your position is plotted on the screen. Ñ When the sample is finished, examine how well your “walk” matched the graph, and then answer question 3. Ò Select Retry (press q) to redisplay the same graph to match.
Activity 2—Match the Graph Name ___________________________________ Data collection 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.
Activity 3—A Speedy Slide Concepts Notes for Teachers Typical plots Function explored: parabolic The motion of sliding down a playground slide is used to illustrate the real-world concept of changing velocity due to friction. Materials Ÿ Ÿ Ÿ Ÿ Ÿ calculator (see page 2 for available models) CBR 2™ motion detector unit-to-CBR 2™ or I/O unit-to-unit cable EasyData application or RANGER program Playground slide A Speedy Slide Typical answers 1. See the Sample Results. Hints 2.
Activity 3—A Speedy Slide 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.
Activity 3—A Speedy Slide (cont.) Parabolic c. Select Edit (press q) to open the Sample Interval dialog window. d. Enter 0.2 to set the time between samples in seconds. e. Select Next (press q) to advance to the Number of Samples dialog window. f. Enter 25 to set the number of samples. Data collection will last for 5 seconds. g. Select Next (press q) to display a summary of the new settings. h. Select OK (press s) to return to the main screen. Í Take your preliminary data-collection positions.
Activity 3—A Speedy Slide (cont.) Parabolic Ð Determine the slider’s speed. a. After data collection stops and a graph of distance versus time is displayed, select Plots (press p). b. Press 2 to select 2: Vel vs Time to display velocity versus time. c. Use ~ to examine data points along the graph. As you move the cursor right and left, the time (X) and velocity (Y) values of each data point are displayed above the graph. The highest point on the graph corresponds to the highest speed of the slider.
Activity 3—A Speedy Slide Name __________________________________ Data collection, Part 2, A Speedier Slide 1. 2. Design a plan to increase the slider’s speed. a. Try out some ideas for increasing the slider’s speed. You may not coat the slide with anything that must be washed off. b. Decide on a plan to best increase the slider’s speed. c. Describe your plan in the Speedier Slide Plan section below. Test your plan using Part 1, Steps 4–8.
Activity 3—A Speedy Slide (cont.) 4. Which of the methods worked best? Explain why it worked best. 5. If you could increase the height of the slide, how would the slider’s speed be affected? 6. If a stone was dropped from the top of the slide at the same time a similar stone was rolled down the slide, which stone would reach the ground first? Explain. 7.
Activity 4—Bouncing Ball Concepts Function explored: parabolic Real-world concepts such as free-falling and bouncing objects, gravity, and constant acceleration are examples of parabolic functions. This activity investigates the values of height, time, and the coefficient A in the quadratic equation, Y = A(X – H) 2 + K, which describes the behavior of a bouncing ball.
Activity 4—Bouncing Ball Parabolic Data collection Ê Begin with a test bounce. Drop the ball (do not throw it). Hints: Position the CBR 2™ motion detector at least 0.5 meters (about 1.5 feet) above the height of the highest bounce. Hold the sensor directly over the ball and make sure that there is nothing in the clear zone (see page 7). Ë Run the EasyData application or RANGER program. Ì EasyData Users: From the Setup menu, choose 4:Ball Bounce, and then select Start (press q).
Activity 4—Bouncing Ball Parabolic (cont.) Explorations The Distance-Time plot of the bounce forms a parabola. Ê The plot is in Trace mode. Press ~ to determine the vertex of the first good bounce—a nice shape without lots of extra noise. Answer question 5 on the activity sheet. Ë Select Main to return to the main screen. Choose Quit, and then select OK to quit EasyData. Ì The vertex form of the quadratic equation, Y = A(X – H) 2 + K, is appropriate for this analysis. Press œ.
Activity 4—Bouncing Ball Name ___________________________________ Data collection 1. What physical property is represented along the x-axis? _____________________________________ What are the units? ___________________________________________________________________ What physical property is represented along the y-axis? _____________________________________ What are the units? ___________________________________________________________________ 2.
Activity 5—Rolling Ball Concepts Function explored: parabolic Plotting a ball rolling down a ramp of varying inclines creates a family of curves, which can be modeled by a series of quadratic equations. This activity investigates the values of the coefficients in the quadratic equation, y = ax 2 + bx + c. Notes for Teachers 7.
Activity 5—Rolling Ball Parabolic Data collection Ê Answer question 1 on the activity sheet. Use the protractor to set the ramp at a 15° incline. Lay the CBR 2™ motion detector on the ramp and flip the sensor head so it is perpendicular to the ramp. Mark a spot on the ramp 15 centimeters (about six inches) from the CBR 2™ motion detector. Have one student hold the ball at this mark, while a second student holds the calculator and CBR 2™ motion detector.
Activity 5—Rolling Ball Parabolic (cont.) g. Select Next (press q) to display a summary of the new settings. h. Select OK (press s) to return to the main screen. Í When the settings are correct, choose Start (press q) to begin sampling. Î When the clicking begins, release the ball immediately (don’t push) and step back. Ï When the clicking stops, the collected data is transferred to the calculator and a plot of distance vs. time is displayed. Answer questions 2, 3, 4, and 5.
Activity 5—Rolling Ball Name ___________________________________ Data collection 1. Which of these plots do you think best matches the Distance-Time plot of a ball rolling down a ramp? 2.
Teacher Information 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.
Teacher Information (cont.) CBR 2™ motion detector plots—connecting the physical world and mathematics The plots created from the data collected by EasyData or RANGER are a visual representation of the relationships between the physical and mathematical descriptions of motion. Students should be encouraged to recognize, analyze, and discuss the shape of the plot in both physical and mathematical terms.
Teacher Information (cont.) A typical CBR 2™ motion detector Velocity-Time plot actually represents speed, not velocity. Only the magnitude (which can be positive, negative, or zero) is given. Direction is only implied. A positive velocity value indicates movement away from the CBR 2™ motion detector; a negative value indicates movement toward the CBR 2™ motion detector. The CBR 2™ motion detector measures distance only along a line from the detector.
Teacher Information (cont.) The area under the Velocity-Time plot from t1 to t2 = @d = (d2Nd1) = displacement from t1 to t2 (net distance traveled). ( ∑ v(@t)) t=2 t=2 So, @d = or t=1 @d = ⌠ ⌡v(dt) t=1 Acceleration-Time plot @t t1 t2 Web-site resources At TI’s Web Site, education.ti.
Sonic motion detector data is stored in lists Collected data is stored in lists L1, L6, L7, and L8 in EasyData When the CBR 2™ motion detector collects data, it automatically transfers it to the calculator and stores the data in lists. Each time you exit the EasyData App, you are reminded of where the data is stored. 0 L1 contains time data. 0 L6 contains distance data. 0 L7 contains velocity data. 0 L8 contains acceleration data.
EasyData Settings (TI-83 and TI-84 Family Calculators) Changing EasyData settings EasyData displays the most commonly used settings before data collection begins. Ê From the main screen in the EasyData App, choose Setup > 1: Dist or 2: Time Graph. The current settings are displayed on the calculator. Note: Settings for 3: Distance Match and 4: Ball Bounce in the Setup menu are preset and cannot be changed. Ë Select Next (press q) to move to the setting you want to change. Press u to clear a setting.
Using a CBR 2™ Sonic Motion Detector with a CBL 2™ System or with CBL 2™ System Programs Using a CBR 2™ sonic motion detector as a conventional motion detector with a CBL 2™ System The CBR™ motion detector can be used as a conventional motion detector with the Texas Instruments CBL 2é (Calculator-Based Laboratoryé) system. A special cable is required to connect the CBR 2™ motion detector to a CBL 2™ system. You may order the cable by calling 1-800-TI-CARES.
Using a CBR 2™ Sonic Motion Detector with a CBL 2™ System or with CBL 2™ System Programs (cont.) Î 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. Ï Start collecting data with the default experiment. Hold the motion sensor in your hand and choose 2: START to begin data collection.
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 application or RANGER program 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. 2.
In case of difficulty If you have this problem: Try this: Difficulty collecting data 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.
EasyData Menu Map (TI-83 and TI-84 Family Calculators) 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 . For example, press s to select Quit. o p q r s indicates data is being collected.
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