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C

OPYING PERMITTED PROVIDED

TI

COPYRIGHT NOTICE IS INCLUDED

28

G

ETTING

S

TARTED WITH

CBR

© 1997 T

EXAS

I

NSTRUMENTS

I

NCORPORATED

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.

What does the highest point on the plot represent? ________________________________________

The lowest point? _____________________________________________________________________

3.

Why did the

BALL BOUNCE

program flip the plot? __________________________________________

4.

Why does the plot look like the ball bounced across the floor? _______________________________

Explorations

5.

Record the maximum height and corresponding time for the first full bounce. __________________

6.

Did the graph for

A

= 1 match your plot? _________________________________________________

7.

Why or why not? _____________________________________________________________________

8.

Complete the chart below.

A

How do the data plot and the Yn graph compare?

1

2

0

-

1

9.

What does a positive value for

A

imply? __________________________________________________

What does a negative value for

A

imply? _________________________________________________

What does a zero value for

A

imply? _____________________________________________________

10.

Record the maximum height and corresponding time for the last full bounce. __________________

11.

Do you think

A

will be bigger or smaller for the last bounce? ________________________________

12.

How did

A

compare? __________________________________________________________________

What do you think

A

might represent? ___________________________________________________

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Summary of Contents for CBR

Page 1: ...G GETTING ETTING S STARTED WITH TARTED WITH CBR CBR INCLUDING INCLUDING 5 5 STUDENT ACTIVITIES STUDENT ACTIVITIES ...

Page 2: ...liable for any claim of any kind whatsoever against the use of these materials by any other party 1997 Texas Instruments Incorporated All rights reserved Permission is hereby granted to teachers to reprint or photocopy in classroom workshop or seminar quantities the pages or sheets in this work that carry a Texas Instruments copyright notice These pages are designed to be reproduced by teachers fo...

Page 3: ... 6 Activities with teacher notes and student activity sheets Activity 1 Match the graph linear 13 Activity 2 Toy car linear 17 Activity 3 Pendulum sinusoidal 21 Activity 4 Bouncing ball parabolic 25 Activity 5 Rolling ball parabolic 29 Teacher information 33 Technical information CBR data is stored in lists 37 RANGER settings 38 Using CBR with CBL or with CBL programs 39 Programming commands 40 Se...

Page 4: ...ey perform Students can explore math and science concepts such as 0 motion distance velocity acceleration 0 graphing coordinate axes slope intercepts 0 functions linear quadratic exponential sinusoidal 0 calculus derivatives integrals 0 statistics and data analysis data collection methods statistical analysis What s in this guide Getting Started with CBRé is designed to be a guide for teachers who...

Page 5: ...ogram in the CBR 0 4 AA batteries 0 5 fun classroom activities sonic sensor to record up to 200 samples per second with a range between 0 5 meters and 6 meters 1 5 feet and 18 feet pivoting head to aim sensor accurately buttons to transfer RANGER program to calculators button to initiate sampling standard threaded socket to attach a tripod or the included mounting clamp on back battery door on bot...

Page 6: ...K Ÿ LINK Go to the Home screen Next open the pivoting head on the CBR and then press the appropriate program transfer button on the CBR During transfer the calculator displays RECEIVING except TI 92 When the transfer is complete the green light on CBR flashes once CBR beeps once and the calculator screen displays DONE If there is a problem the red light on CBR flashes twice and CBR beeps twice Onc...

Page 7: ...ET CALC DATA STATUS STOPàCLEAR From the MAIN MENU choose SET DEFAULTS The SETUP screen is displayed Press to choose START NOW Set up the activity and then press to begin data collection It s that easy Important information 0 This guide applies to all TI graphing calculators that can be used with CBR so you may find that some of the menu names do not match exactly those on your calculator 0 When se...

Page 8: ...s in L1 in conjunction with the distance data in L2 to calculate the velocity of the object at each sample time Then compare the results to the velocity data in L3 L2n 1 L2n à2 N L2n L2n 1 à2 L3n L1n 1 N L1n Use the velocity data in L3 or the student calculated values in conjunction with the sample times in L1 to calculate the acceleration of the object at each sample time Then compare the results...

Page 9: ...ect 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 no...

Page 10: ...he sampling is closest to the CBR In this option you also can choose to detach the CBR This lets you set up the sample disconnect the cord from the CBR take the CBR where the action is press sample reattach the CBR and press to transfer the data Use BEGIN ON TRIGGER when the cord is not long enough or would interfere with data collection This is not available in REALTIME YES mode such as the MATCH...

Page 11: ...neral pattern of the plot To minimize noise 0 Make sure the CBR is pointed directly at the target Try adjusting the sensor head while viewing a REALTIME YES sample until you get good results before collecting a REALTIME NO sample 0 Try to sample in a clutter free space see the clear zone drawing on page 7 0 Choose a larger more reflective object or move the object closer to the CBR but farther tha...

Page 12: ...TIME NO Use REALTIME NO mode 0 for faster objects 0 when smoothing is required see page 9 0 to operate the CBR in detached mode see page 11 0 when you need to collect or plot all types of data distance velocity and acceleration for a sample In REALTIME NO mode data is stored in the CBR and not transferred to the calculator until after all sampling is completed The sample rate can be as fast as onc...

Page 13: ...e CBR using either the calculator to CBR cable or the calculator to calculator cable From the MAIN MENU in the RANGER program choose TOOLS From the TOOLS menu choose GET CBR DATA TRANSFERRING is displayed and the plot appears Press to return to the PLOT MENU and then choose QUIT Detach the cable Connect another calculator of the same type to the calculator with the data On the receiving calculator...

Page 14: ... editor 0 Automatically determine the equation that best fits the data using the calculator s regression capabilities Other relationships can be explored beyond those represented by the plot options in RANGER For instance simultaneous plots of Distance Time and Velocity Time can be viewed as statistical plots From the MAIN MENU in the RANGER program choose QUIT and then set Plot1 as L1 versus L2 a...

Page 15: ...ays perpendicular to the line to the CBR or even to jump up Instructions suggest that the activity be done in meters which matches the questions on the student activity sheet See pages 6 12 for hints on effective data collection Typical plots Typical answers 1 time from start of sample seconds 1 second distance from the CBR to the object meters 1 meter 2 the y intercept represents the starting dis...

Page 16: ...oose METERS From the APPLICATIONS menu choose DISTANCE MATCH General instructions are displayed DISTANCE MATCH automatically takes care of the settings Press to display the graph to match Take a moment to study the graph Answer questions 1 and 2 on the activity sheet Position yourself where you think the graph begins Press to begin data collection You can hear a clicking sound and see the green li...

Page 17: ...aph begins press to begin data collection and try to match the graph When the sampling stops answer questions 11 and 12 Press to display the OPTIONS menu and choose NEW MATCH Study the graph and answer questions 13 14 and 15 Press to display the OPTIONS menu Repeat the activity if desired or return to the MAIN MENU and then choose QUIT to exit the RANGER program Advanced explorations The graphs ge...

Page 18: ...ations 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 ...

Page 19: ...Distance Time plot is not linear at the beginning of the plot Why The car begins at rest v 0 It cannot instantaneously attain its constant velocity Acceleration is given by a v t In order for the object to go instantaneously from rest to its constant velocity t 0 But this implies infinite acceleration which is not physically possible In fact by Newton s Second Law F ma an infinite acceleration cou...

Page 20: ...okes for each calculator From the MAIN MENU choose SETUPàSAMPLE For this activity the settings should be REALTIME NO TIME S 5 SECONDS DISPLAY DISTANCE BEGIN ON ENTER SMOOTHING LIGHT UNITS METERS Instructions for changing a setting are on page 38 Choose START NOW Press when you are ready to begin Start the car and quickly move out of the clear zone You can hear a clicking sound as the data is colle...

Page 21: ...stance meters for 1 5 seconds subtract Distance at 1 second from Distance at 1 5 seconds The function illustrated by this activity is y mx b m is the slope of a line It is calculated by distance time or distance2 N distance1 time2 N time1 or y2 N y1 x2 N x1 The y intercept represents b Calculate m for every point Enter the values in the table in question 2 Answer questions 5 6 and 7 Advanced Explo...

Page 22: ...__ 4 How do these results show that the toy car had constant velocity ____________________________ 5 Calculate distanceà time between Time 2 and Time 4 ________________________________ What did you notice about this result ___________________________________________________ What do you think m represents _______________________________________________________ 6 For the linear equation y mx b what ...

Page 23: ...when T is in seconds The derivatives of a sinusoidal plot are also sinusoidal Note particularly the phase relationship between the weight s position and velocity Typical plots Typical answers 1 varies in meters 2 varies in meters 3 varies in seconds T one period total time of 10 periodsà10 averaging over a larger sample tends to minimize inherent measurement errors 4 the total arc length which sho...

Page 24: ...mplete swing back and forth Using a stopwatch time ten full periods Answer questions 3 and 4 Run the RANGER program see page 5 for keystrokes for each calculator An efficient method is for one person start the pendulum while another operates the calculator and CBR From the MAIN MENU choose SETUPàSAMPLE Press to display the settings For this activity they should be REALTIME NO TIME S 10 SECONDS DIS...

Page 25: ...e answer to question 2 was the amplitude of that pendulum swing Answer question 10 Advanced explorations Data collection 5 From the PLOT MENU choose VELOCITY TIME Answer questions 11 12 and 13 Data collection 6 Repeat the data collection with a significantly lighter or heavier weight and then answer question 14 Model the distance time behavior of the pendulum using the form for a sinusoidal functi...

Page 26: ...________ 7 Using data collected from your plot calculate the number of complete cycles per second ________ Why is it easier to determine this using the second plot spanning 5 seconds rather than the first one spanning 10 seconds _____________________________________________________________ 8 Calculate the frequency for one period using the equation __________________________________ 9 How does sho...

Page 27: ...ce from the CBR to the ball BALL BOUNCE flips the distance data so the plot better matches students perceptions of the ball s behavior y 0 on the plot is actually the point at which the ball is farthest from the CBR when the ball hits the floor 4 Students should realize that the x axis represents time not horizontal distance 7 The graph for A 1 is both inverted and broader than the plot 8 A L1 9 p...

Page 28: ...e displayed BALL BOUNCE automatically takes care of the settings Hold the ball with arms extended Press The RANGER program is now in Trigger mode At this point you may detach CBR from the calculator Press When the green light begins flashing release the ball and then step back If the ball bounces to the side move to keep the CBR directly above the ball but be careful not to change the height of th...

Page 29: ...K is appropriate for this analysis Press œ In the Y editor turn off any functions that are selected Enter the vertex form of the quadratic equation Yn A X H 2 K 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 Press to display the graph Answer questions 6 and 7 Try A 2 0 1 Complete the first ...

Page 30: ...e ball bounced across the floor _______________________________ Explorations 5 Record the maximum height and corresponding time for the first full bounce __________________ 6 Did the graph for A 1 match your plot _________________________________________________ 7 Why or why not _____________________________________________________________________ 8 Complete the chart below A How do the data plot ...

Page 31: ...ies should be parabolic with increasing curvature 7 0 is flat ball can t roll 90 is the same as a free falling dropping ball Explorations The motion of a body acted upon only by gravity is a popular topic in a study of physical sciences Such motion is typically expressed by a particular form of the quadratic equation s at2 vit si where 0 s is the position of an object at time t 0 a is its accelera...

Page 32: ... page 5 for keystrokes for each calculator From the MAIN MENU choose SETUPàSAMPLE Press to display the settings For this activity they should be REALTIME NO TIME S 3 SECONDS DISPLAY DISTANCE BEGIN ON ENTER SMOOTHING LIGHT UNITS METERS Instructions for changing a setting are on page 38 When the settings are correct choose START NOW Press to begin sampling When the clicking begins release the ball i...

Page 33: ...steps 2 through 6 for inclines of 45 and 60 and add to the drawing Answer question 7 Advanced explorations Adjust the time values so that x 0 for the initial height the time at which the ball was released You can do this manually by subtracting the x value for the first point from all the points on your plot or you can enter L1 1 A L1NA L1 Calculate the values for a b and c for the family of curve...

Page 34: ...__________________ What are the units ___________________________________________________________________ 3 Sketch what the plot really looks like Label the axis Label the plot at the points when the ball was released and when it reached the end of the ramp 4 What type of function does this plot represent ___________________________________________ 5 Discuss your change in understanding between th...

Page 35: ...ata collection and have more time for analysis and exploration 0 With CBR 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 0 The power of visualization lets students ...

Page 36: ...tersàsecond2 or feetàsecond2 x axis units are seconds 0 The first derivative instantaneous slope at any point on the Distance Time plot is the speed at that instant 0 The first derivative instantaneous slope at any point on the Velocity Time plot is the acceleration at that instant This is also the second derivative at any point on the Distance Time plot 0 A definite integral area between the plot...

Page 37: ... Vaverage d t d2 N d1 t2 N t1 slope of Distance Time plot Vinstantaneous lim t 0 d t d s dt where s distance Velocity Time plot Aaverage v t v2 N v1 t2 N t1 slope of Velocity Time plot Ainstantaneous lim t 0 v t dv dt The area under the Velocity Time plot from t1 to t2 d d2Nd1 displacement from t1 to t2 net distance traveled So d t 1 t 2 v t or d t 1 t 2 v dt Acceleration Time plot t1 t2 t1 t2 t1 ...

Page 38: ...rary of programs for use with CBR CBL and TI graphing calculators 0 an activities page with applications developed and shared by teachers like you 0 CBR programs that access additional CBR features 0 more detailed information about CBR settings and programming commands Additional resources Texas Instruments Explorations books provide supplemental material related to TI graphing calculators includi...

Page 39: ...leration is calculated and transferred In REALTIME NO all the data is calculated and transferred Settings are stored in list L5 The RANGER SETUP screen makes it easy to change the most commonly used CBR parameters see page 38 When you transfer the RANGER program from the CBR L5 is automatically replaced with a new list containing the defaults See pages 40 41 for information about programming comma...

Page 40: ...s are correct press c or b until the cursor is on START NOW 0 To continue press 0 To return to the MAIN MENU press e and then press The new settings remain unless you choose SET DEFAULTS run an application or run another program that changes the settings If you manipulate L5 outside the RANGER program or delete L5 the default settings may be restored the next time you run RANGER Restoring RANGER s...

Page 41: ... only a motion detector with no changes or only minor changes to the program To stop sampling With some CBL programs using REALTIME YES data collection CBR continues to sample indefinitely To stop data collection at the end of the sample time you can do either of the following 0 Press on the CBR 0 Add statements to the existing CBL program to send the command 6 0 to the CBR The statement must be a...

Page 42: ...vative temperature_conversion Results 0 default Disables temperature compensation 1 Enables temperature compensation Command 2 Data setup 2 data_type 0 0 0 0 0 0 0 data_type Results 1 default List Command 3 Sample Trigger 3 sample_time sample trigger 0 0 0 0 record_time filter sample_time Results 0 005 1500 0 1 Time in seconds between each sample 0 0001 0 005 Rounds to 0 005 1500 x 16000 Rounds to...

Page 43: ...ast data element for GET 0 last sample Command 6 Systems options 6 system_command operation system_command Results 0 Stops sampling for CBL compatibility 2 default Stops sampling 3 Turns sound off sound is on at power on 4 Turns sound on sound is on at power on 5 Sets ID Number operation required 6 Applies new filter to previous data operation required operation Results floating point number ID_Nu...

Page 44: ...ms to alert you that the batteries are low 0 The RANGER program displays a warning message on calculator screen while trying to collect data 0 The red light flashes intermittently while the CBR is collecting sample data CBR battery power status You can check the battery power before you begin sampling From the MAIN MENU choose TOOLS and then choose CBR STATUS The battery status OK or REPLACE is sh...

Page 45: ...ructions say Choose DISTANCE MATCH on the TI 83 you would choose DIST MATCH Data doesn t look right 0 points not on the curve 0 jagged plots 0 flat plots 0 broken plot Repeat the sample ensuring that the CBR is aimed directly at the object Read pages 6 12 on getting good data samples Check that the clear zone does not contain students tables or other objects When using two CBR units at the same ti...

Page 46: ... above limitations or exclusions may not apply to you Legal Remedies This warranty gives you specific legal rights and you may also have other rights that vary from state to state or province to province Warranty Performance During the above one 1 year warranty period your defective product will be either repaired or replaced with a reconditioned model of an equivalent quality at TI s option when ...

Page 47: ...UM HEAVY NONE APPLICATIONS DISTANCE MATCH VELOCITY MATCH BALL BOUNCE MAIN MENU ENTER TRIGGER DELAY METERS FEET DISTANCE VELOCITY ACCELERATION NO YES OPTIONS SAME MATCH NEW MATCH APPLICATIONS MAIN MENU QUIT DISTANCE TIME VELOCITY TIME ACCELERATION TIME PLOT TOOLS REPEAT SAMPLE MAIN MENU QUIT 1 99 REALTIME NO SETUP SAMPLE SET DEFAULTS PLOT MENU APPLICATIONS TOOLS QUIT MAIN MENU RANGER SHOW PLOT SELE...

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