User manual TEXAS INSTRUMENTS THE CBR 2 GETTING STARTED

[. . . ] TI GETTING STARTED WITH THE CBR 2TM SONIC MOTION DETECTOR INCLUDING 5 STUDENT ACTIVITIES Important notice regarding book materials Texas Instruments and any third party contributors make no warranty, either express or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an "as-is" basis. In no event shall Texas Instruments or any third party contributor be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this product. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party. All rights 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. [. . . ] 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 2TM motion detector, when the ball hits the floor. Students should realize that the x-axis represents time, not horizontal distance. same; mathematically, the coefficient A represents the extent of curvature of the parabola; physically, A depends upon the acceleration due to gravity, which remains constant through all the bounces. Materials Y Y Y Y Y Y calculator (see page 2 for available models) CBR 2TM motion detector unit-to-CBR 2TM) or I/O unit-to-unit cable EasyData application large (9-inch) playground ball TI ViewScreen panel (optional) Hints This activity is best performed with two students, one to hold the ball and the other to select Start on the calculator. If it does not, repeat the sample, ensuring that the CBR 2TM motion detector is aimed squarely at the ball. A large ball is recommended. Advanced explorations The rebound height of the ball (maximum height for a given bounce) is approximated by: y = hp x, where 0 0 0 0 Typical plot y is the rebound height h is the height from which the ball is released p is a constant that depends on physical characteristics of the ball and the floor surface x is the bounce number For a given ball and initial height, the rebound height decreases exponentially for each successive bounce. When x = 0, y = h, so the y-intercept represents the initial release height. Explorations After an object is released, it is acted upon only by gravity (neglecting air resistance). So A depends on the acceleration due to gravity, N9. 8 meterssecond 2 (N32 feetsecond 2). The value for A is approximately one-half the acceleration due to gravity, or N4. 9 meterssecond 2 (N16 feetsecond 2). Ambitious students can find the coefficients in this equation using the collected data. Repeat the activity for different initial heights or with a different ball or floor surface. After manually fitting the curve, students can use regression analysis to find the function that best models the data. Follow the calculator operating procedures to perform a quadratic regression on lists L1 and L2. Extensions Integrate under Velocity-Time plot, giving the displacement (net distance traveled) for any chosen time interval. Note the displacement is zero for any full bounce (ball starts and finishes on floor). Typical answers 1. time (from start of sample); seconds; height distance of the ball above the floor; meters or feet 2. initial height of the ball above the floor (the peaks represent the maximum height of each bounce); the floor is represented by y = 0. 24 GETTING STARTED WITH THE CBR 2TM SONIC MOTION DETECTOR 2004 TEXAS INSTRUMENTS INCORPORATED Activity 4--Bouncing ball Data collection parabolic Begin with a test bounce. Drop the ball (do not throw it). Hints: Position the CBR 2TM 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). 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 2TM motion detector, while another person holds the ball beneath the sensor. Select Start (press q). When the CBR 2TM motion detector begins clicking, release the ball, and then step back. (If the ball bounces to the side, move to keep the CBR 2TM motion detector directly above the ball, but be careful not to change the height of the CBR 2TM 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 doesn't look good, select Main, Start, Start to repeat the sample. [. . . ] Other than the postage requirement, no charge will be made for such repair and/or replacement. TI strongly recommends that you insure the product for value prior to mailing. TI and its licensors do not warrant that the software will be free from errors or meet your specific requirements. The software and any documentation supplied with this product are protected by copyright. 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