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. Additional dialog and discoveries are possible when functions are entered in the Y= editor and displayed with the data plots.

Performing the same calculations as CBR 2™ motion detector is an interesting classroom activity.

1.Collect sample data. Exit the EasyData application or RANGER program.

2.Use the sample times 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

3.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 to the acceleration data in L4.

0A Distance-Time plot 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.

0A 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-axis units are seconds.

0An Acceleration-Time plot represents the approximate rate of change in speed of an object (relative to, and in the direction of, the CBR 2™ motion detector) at each sample time. y-axis units are metersàsecond2 or feetàsecond2; x-axis units are seconds.

0

0

The first derivative (instantaneous slope) at any point on the Distance-Time plot is the speed at that instant.

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.

0A definite integral (area between the plot and the x-axis between any two points) on the Velocity-Time plot equals the displacement (net distance traveled) by the object during that time interval.

0Speed and velocity are often used interchangeably. They are different, though related, properties. Speed is a scalar quantity; it has magnitude but no specified direction, as in “6 feet per second.” Velocity is a vector quantity; it has a specified direction as well as magnitude, as in “6 feet per second due North.”

© 1997, 2004, 2006 TEXAS INSTRUMENTS INCORPORATED

GETTING STARTED WITH THE CBR 2™ SONIC MOTION DETECTOR 33

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Texas Instruments CBR 2 manual L3n =
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CBR 2 specifications

Texas Instruments has long been a prominent player in the field of educational technology, and the CBR 2 (Calculator-Based Ranger 2) is a testament to their commitment to enhancing the learning experience, particularly in the realms of mathematics and science. Designed to complement graphing calculators, the CBR 2 is a versatile data-collection device that empowers students and educators to explore real-world phenomena through hands-on experimentation.

One of the main features of the CBR 2 is its ability to capture a wide array of data through various sensors. The device is equipped with an array of built-in sensors that can measure motion, including speed and distance. This makes it an invaluable tool for physics experiments, allowing students to visualize concepts such as speed, acceleration, and trajectory.

The CBR 2 utilizes ultrasonic technology to detect distance through sound waves. This feature enables students to conduct experiments that demonstrate principles of sound and motion in a tangible way. With a range of up to 6 meters, the CBR 2 provides accurate and reliable measurements that can be graphically represented using compatible Texas Instruments graphing calculators.

The device is highly user-friendly, with simple interfaces that allow users to easily collect and analyze data. The integration with graphing calculators simplifies the process of data visualization, enabling students to create graphs in real time as they conduct experiments. This capability is particularly beneficial in encouraging interactive learning and fostering a deeper understanding of scientific principles.

The CBR 2 is designed to be portable and durable, making it suitable for classroom settings as well as outdoor experiments. Its compact size and lightweight construction ensure that it can be easily transported, allowing educators to take learning beyond the confines of the classroom.

The CBR 2 also supports various modes of data collection, including Event Mode, which allows users to trigger data collection based on specific events. This feature is useful in demonstrating concepts such as projectile motion and collisions, providing students with hands-on experience that enhances their learning.

In summary, Texas Instruments' CBR 2 is a powerful educational tool that enables students to collect, analyze, and visualize data in an engaging manner. With its built-in sensors, ultrasonic technology, and seamless integration with graphing calculators, the CBR 2 stands out as a versatile device that enriches the educational experience. It not only provides a platform for conducting experiments but also cultivates critical thinking skills and a deeper understanding of scientific concepts, preparing students for a future in STEM fields.
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