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ETTING

TARTED WITH THE

CBR 2™

ONIC

OTION

ETECTOR

1997,

2004,

2006

EXAS

NSTRUMENTS

NCORPORATED

Activity 5—Rolling Ball

(cont.)

Parabolic

g. Select Next (press

) to display a summary of the new

settings.

h. Select OK (press

) to return to the main screen.

When the settings are correct, choose Start (press

) to begin sampling.

When the clicking begins, release the ball immediately (don’t push) and step back.

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.

Explorations

Examine what happens for differing inclines.

Predict what will happen if the incline increases.

Answer question 6.

Adjust the incline to 30

. Repeat steps 2 through 6.

Add this plot to the drawing in

question 6, labeled

Repeat 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:L1

Calculate the values for

, and

for the family of curves in the form

y = ax

+ bx + c

at 0

, 15

, 30

, 45

, 60

, 90

What are the minimum and maximum values for

? Why?

Write an expression describing the mathematical relationship between

and the angle

of inclination.

Содержание CBR 2

Страница 1: ...Getting Started with the CBR 2 Sonic Motion Detector ...

Страница 2: ...hts reserved Permission is hereby granted to teachers to reprint or photocopy in classroom workshop or seminar quantities the pages in this work that carry a copyright notice These pages are designed to be reproduced by teachers for use in their classes workshops or seminars provided each copy made shows the copyright notice Such copies may not be sold and further distribution is expressly prohibi...

Страница 3: ...ivity sheets Activity 1 Graphing your motion linear 10 Activity 2 Match the graph linear 14 Activity 3 A Speedy slide parabolic 18 Activity 4 Bouncing ball parabolic 24 Activity 5 Rolling ball parabolic 28 Teacher information 32 Technical information Sonic motion detector data is stored in lists 36 EasyData settings 37 Using a CBR 2 Sonic Motion Detector with a CBL 2 System or with CBL 2 System pr...

Страница 4: ...ts 0 functions linear quadratic exponential sinusoidal 0 calculus derivatives integrals 0 statistics and data analysis data collection methods statistical analysis 0 Physics motion use with dynamics tracks pendulum analysis position velocity acceleration 0 Physical Science motion experiments What s in this guide Getting Started with the CBR 2 Sonic Motion Detector is designed to be a guide for tea...

Страница 5: ... 5 fun classroom activities 0 Standard B to Mini A USB cable unit to CBR 2 sonic sensor to record up to 200 samples per second with a range between 15 centimeters and 6 meters 5 9 inches and 19 7 feet pivoting head to aim sensor accurately button to initiate sampling standard threaded socket to attach a tripod or the included mounting clamp on back battery door on bottom USB and I O ports to conne...

Страница 6: ... calculator users Connect the CBR 2 motion detector to your TI graphing calculator using the Standard B to Mini A USB cable unit to CBR 2 or I O unit to unit cable and push in firmly at both ends to make a secure connection Set the Sensitivity switch to Normal mode for walking ball toss pendulum etc or to Track mode for use with dynamics tracks and carts About the unit to CBR 2 cable 0 Can only be...

Страница 7: ...hesis and press Í to start the program Important information 0 This guide applies to all TI graphing calculators that can be used with the CBR 2 motion detector see page 2 therefore you may find that some of the menu names do not match exactly those on your calculator 0 When setting up activities ensure that the CBR 2 motion detector is securely anchored and that the cord cannot be tripped over 0 ...

Страница 8: ... 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...

Страница 9: ...object in the clear zone 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 calculat...

Страница 10: ...CBR 2 motion detector will then display a graph of the sampled data on the graphing calculator To stop sampling before it automatically stops select Stop press and hold q at any time during the sampling process When sampling stops a graph of the sampled data is displayed Noise what is it and how do you get rid of it When the CBR 2 motion detector receives signals reflected from objects other than ...

Страница 11: ... 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 det...

Страница 12: ...tance graph to see if it makes sense If not the CBR 2 motion detector may not be properly targeting the target 0 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 0 Sometimes a target may not supply a strong reflection of the ultrasound For example if the targe...

Страница 13: ...d be at a height of about 15 centimeters above your waist level Ë 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 Ì Connect the CBR 2 motion detector to the calculator using an appropriate cable see below and firmly press in the cable ends 0 If TI 83 Plus TI 89 TI 92 Plus TI 89 Titanium Voyage 200 use an I O unit to unit cable ...

Страница 14: ...he number of samples to collect The experiment length will be 5 seconds number of samples multiplied by the sample interval g Select Next press q to display a summary of the new settings h Select OK press s to return to the main screen To set up the calculator for data collection using RANGER a Choose 1 Setup Sample from the Main Menu b Use C D to move to each parameter line Use B to view the opti...

Страница 15: ...towards the 1 0m mark One time walking slowly and again walking more quickly Point 1 ________ Point 2 ________ Slope ___________ Ñ Sketch your new plots on the empty graph provided Ò Describe the differences between your graphs step 6e and step 8 ___________________________________________________________________________ ___________________________________________________________________________ _...

Страница 16: ...n to jump up Instructions suggest that the activity be done in meters which matches the questions on the student activity sheet See pages 6 9 for hints on effective data collection Typical plot Distance vs Time Matching Distance vs Time Typical answers 1 time from start of sample seconds 1 second distance from the CBR 2 motion detector to the object meters 1 meter 2 the y intercept represents the ...

Страница 17: ...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 Distance Match automatically takes care of the settings RANGER Users From the Main Menu choose 3 Applications Choose the distance units then choose 1 Distance Match and follow the directions on the screen Í Select Start press q and follow the instruc...

Страница 18: ... to improve your walking technique and then answer questions 4 5 and 6 Explorations In Distance Match all graphs are comprised of three straight line segments Ê Select New press p to display a new graph to match Study the first segment and answer questions 7 and 8 Ë Study the entire graph and answer questions 9 and 10 Ì Position yourself where you think the graph begins select Start press p to beg...

Страница 19: ...f 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 t...

Страница 20: ...elves for data collection Some slides have large platforms where the student with the Motion Detector and the student with the calculator and interface can be located Students can use wax paper slippery cloth sand and other materials to increase their speed To enable your students to be prepared be sure to alert them to Part II in advance Typical plots A Speedy Slide Typical answers 1 See the Samp...

Страница 21: ...with ways to increase your speed going down the slide 0 explain your results Data collection Part 1 Sliding Speed Ê Connect the CBR 2 motion detector to the calculator using an appropriate cable see below and firmly press in the cable ends 0 If TI 83 Plus TI 89 TI 92 Plus TI 89 Titanium Voyage 200 use an I O unit to unit cable 0 If TI 84 Plus use a Standard B to Mini A USB cable unit to CBR 2 Ë On...

Страница 22: ...d the CBR 2 motion detector behind the person who will slide c The third person should stand on the ground next to the slide while holding the calculator and interface Î Take your final data collection positions a 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 b The person holding the CBR 2 motion detector shou...

Страница 23: ...me 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 Record this highest speed in the Data table Round to the nearest 0 01 m s In the example to the right the highest speed is...

Страница 24: ... best increase the slider s speed c Describe your plan in the Speedier Slide Plan section below 2 Test your plan using Part 1 Steps 4 8 Speedier Slide Plan Data Speed m sec Trial 1 Trial 2 Trial 3 Average Part 1 Part 2 Data processing 1 Calculate the average speed for your three trials in Part 1 Record the average in the space provided in the Data table Calculate and record the average speed for P...

Страница 25: ... 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 What is the purpose of the level portion at the bottom of many slides ...

Страница 26: ...nce the floor is represented by y 0 3 The Distance Time plot for this activity does not represent the distance from the CBR 2 motion detector 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 2 motion detector when the ball hits the floor 4 Students ...

Страница 27: ...ings RANGER Users From the Main Menu choose 3 Applications Choose the distance units then choose 3 Ball Bounce Í Have one person hold the calculator and CBR 2 motion detector while another person holds the ball beneath the sensor Î 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 de...

Страница 28: ... Titanium TI 92 Plus and Voyageé 200 users enter yn x a x h 2 k TI83 84 Family TI89 Titanium 92 V200 Í 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 TI 83 TI 84 Family users Press 4 v t K Í 2 5 v t H Í 1 v t A Í to set K 4 H 2 5 and A 1 Tip all users At the beginning you may wa...

Страница 29: ...d 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 of the data from the first complete bounce ____________ 7 Why or why not _____________________________________________________________________ 8 Complete the chart below A How do the data plot and the...

Страница 30: ...ctor feet or meters 3 varies should be half of a parabola concave up 4 a parabola quadratic 5 varies 6 varies 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 o...

Страница 31: ...s the calculator and CBR 2 motion detector Hints Aim the sensor directly at the ball and make sure that there is nothing in the clear zone see page 7 Ë Run the EasyData app or RANGER program Note RANGER users should follow set up instructions on the screen Ì 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...

Страница 32: ...ring inclines Ê Predict what will happen if the incline increases Answer question 6 Ë Adjust the incline to 30 Repeat steps 2 through 6 Add this plot to the drawing in question 6 labeled 30 Ì Repeat steps 2 through 6 for inclines of 45 and 60 and add to the drawing Í Answer question 7 Advanced explorations Adjust the time values so that x 0 for the initial height the time at which the ball was rel...

Страница 33: ..._____ 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 between the two points you identified represent __________ 5 Discuss your change in understanding between the graph ...

Страница 34: ...time for data collection and have more time for analysis and exploration 0 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 0 The power of ...

Страница 35: ... represents the approximate position of an object distance from the CBR 2 motion detector at each instant in time when a sample is collected y axis units are meters or feet x axis units are seconds 0 A Velocity Time plot represents the approximate speed of an object relative to and in the direction of the CBR 2 motion detector at each sample time y axis units are metersàsecond or feetàsecond x axi...

Страница 36: ... CBR 2 motion detector The CBR 2 motion detector measures distance only along a line from the detector Thus if an object is moving at an angle to the line it only computes the component of velocity parallel to this line For example an object moving perpendicular to the line from the CBR 2 motion detector shows zero velocity The mathematics of distance velocity and acceleration Distance Time plot V...

Страница 37: ... and TI graphing calculators 0 an activities page with applications developed and shared by teachers like you 0 CBR 2 motion detector programs that access additional CBR 2 motion detector features 0 more detailed information about the CBR 2 motion detector settings and programming commands At Vernier s Web Site www vernier com you will find the the RANGER program Additional resources Texas Instrum...

Страница 38: ...element in list L6 represents the distance of the 5th data point Collected data is stored in lists L1 L2 L3 L4 in RANGER RANGER also stores collected data in lists These are 0 L1 contains time data 0 L2 contains distance data 0 L3 contains velocity data 0 L4 contains acceleration data Using the data lists The lists are not deleted when you exit the EasyData application or RANGER program Thus they ...

Страница 39: ...ge a setting enter 1 or 2 digits and then select Next Î When all the settings are correct select OK press s to return to the main screen The new settings remain in effect unless you choose to set EasyData to its default settings run an application or run another activity that changes the settings If you manipulate L5 outside the EasyData App or delete L5 the default settings may be restored the ne...

Страница 40: ...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 Collecting Motion Data Using the CBR 2 sonic motion detector with a CBL 2 System Ê Insert batteries into the CBL 2 Ë Connect the CBL 2 motion detector to...

Страница 41: ...alibration 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 Ð Walk towards a wall while holding the CBR 2 motion detector pointed towards the wall W...

Страница 42: ...ery warnings The CBR 2 motion detector has two mechanisms to alert you that the batteries are low 0 The EasyData App displays a warning message on calculator screen while trying to collect data 0 The red light flashes intermittently while the CBR 2 motion detector is collecting sample data You can check battery status using the RANGER program From the Main Menu select 5 Tools then select 3 CBR Sta...

Страница 43: ...lator 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 doesn t 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 c...

Страница 44: ... 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 1 Dist Units 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 Instructions Sample Plot For ...

Страница 45: ...ends only to the original purchaser and user of the product Warranty Duration This TI electronic product is warranted to the original purchaser for a period of one 1 year from the original purchase date Warranty Coverage This TI electronic product is warranted against defective materials and construction THIS WARRANTY IS VOID IF THE PRODUCT HAS BEEN DAMAGED BY ACCIDENT OR UNREASONABLE USE NEGLECT ...

Страница 46: ...s or consequential damages so the 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 jurisdiction to jurisdiction Warranty Performance During the above one 1 year warranty period your defective product will be either repaired or replaced with a new or reconditioned model of an equivalen...

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