Instructors Guide to:

Transcription

1 Instructors Guide to: Swinging with Gravity In this experiment the light sensor is attached to the RCX allowing taking realtime data on the received signal change as the pendulum swings over light/dark transition. The time dependence is shown in the graph. The graph allows to calculate the period of the pendulum. The data also can be used to determine the gravitational acceleration on Earth if length and period of the pendulum are measured.

2 In the Classroom: Grade Level: 9-12 Time: min Building Skills: any skills Programming Skills: Investigator Level 1-4 Swinging with Gravity This exercise shows how to build a pendulum and analyze the results of the light sensor readings. Challenge Build the LEGO pendulum using RCX, wire with 2 2 plates and a string and use the light sensor readings to calculate the period of oscillations (T). Thus, if both L (length of the pendulum in meters) and T of the pendulum are known it is possible to calculate the Earth s gravitational acceleration. Materials RCX, light sensor, wire with 2 2 plates, string Skills Learned Sensor data collection, interpretation and analysis of the graphically represented data. Procedure 1. Build the LEGO pendulum. 2. Attach the pendulum and swing it over light/dark transition. A piece of white paper on a dark table can be used for this experiment. 3. Program the RCX to collect light sensor readings. 4. Upload the collected data using ROBOLAB. 5. The resulting graph should be similar to the one shown below:

3 6. Measure the length of the string used in the experiment. 7. Calculate the period of the pendulum (T) using the formula T = 2pi(sqrt(L/g)), where T is the period of oscillation seconds), L is the length of the pendulum (meters) and g is the Earth s gravitational acceleration (m/s^2). 8. The value of the period of the pendulum (T) can also be directly calculated from the graph by choosing the time interval and calculating the value for the period ( 2 intervals correspond to one complete period). 9. Compare the results from Part (7) and Part (8). 10. The data also can be used to determine the gravitational acceleration on Earth if length and period of the pendulum are measured.

4 Lego Tips The LEGO pendulum used in this demonstration is build using some strings, the RCX, and a light sensor which can be attached to any of the output ports (1-3). In this experiment the light data is collected from Port 1. Extensions 1. To determine the value for T (period of the pendulum) directly from the graph and compare this result with calculated value for the period of oscillation of a pendulum. 2. Estimate the mass of the Earth using experimentally obtained the value of the acceleration due to gravity. Take R(earth) (need to convert the result in the m). g = G (M/R^2) this equation is derived from: F = G (Mm/R^2)*m; F = mg; 3. Use the ROBOLAB Compute Tools 4,5 to perform Fast Fourier Transform (FFT) on your data set to find frequency content of the data set. Define the dominant frequency as a natural frequency of the oscillator in this experiment from the FFT graph. Example of this program is shown below. Using this program perform the FFT on your time series data (stored in the red bin) to produce the frequency domain data, which is stored in the green bin in this example program.

5 When result of the FFT is plotted, the natural frequency is evident as the most dominant peak in the graph. The x-axis shown on the graph as time but actually this is a frequency (Hz). For this example, the dominant frequency is at Hz, which corresponds to a natural period of (T(s) = 1/f(Hz) ). Insert the graph. For more information about Fourier Transform go to: Check the simulation from Sounds and Waves link, called Fourier: Making Waves. Sample Program Investigator Program Level 1, 2, 3, or 4 can be used to write a program to collect light sensor data. Sample Project For the video example go to: