Student Worksheet for Activity 6.1.1 The Pendulum Questioning Hypothesizing Predicting Planning Conducting INQUIRY SKILLS Recording Analyzing Evaluating Communicating A pendulum swings with a regular period, so it is a useful device for measuring time. In fact, early drawings of a pendulum clock were developed by Galileo Galilei in 1641. His ideas for a pendulum clock were based on his observations of the regular period of vibration of a lamp hanging in a church in Pisa, Italy. He then postulated laboratory experiments similar to this one to determine the factors that affected the period and frequency of a swinging pendulum (Figure 5). Question What are the relationships between the frequency of a simple pendulum and its mass, amplitude, and length? Materials utility stand clamp test-tube clamp split rubber stopper string stopwatch metre stick metal masses (50 g, 100 g, and 200 g) Figure 5 A strobe photograph of an oscillating pendulum Prediction (a) Predict what will happen to the frequency of the pendulum in the following situations: (i) the mass increases, but the length and amplitude remain constant (ii) the amplitude increases, but the mass and length remain constant (iii) the length increases, but the mass and amplitude remain constant Unit 3 Waves and Sound LAW-47
Procedure 1. Set up a chart as shown in Table 1. Table 1 Length (cm) Mass (g) Amplitude (cm) Time for 20 cycles (s) Frequency (Hz) 100 200 10 test-tube clamp utility stand split rubber stopper length of pendulum 2. Set up the utility stand as illustrated, ensuring that it is clamped securely and there is clearance on either side of at least 30 cm. 3. Obtain a string about 110 cm long and securely attach a 200-g mass to one end. Place the other end of the string into the split rubber stopper (Figure 6), adjust the pendulum length to 100 cm, and clamp the rubber stopper firmly so the string does not slip. Remember that the length is measured to the centre of the mass. 4. Keeping the string fully extended, pull the mass to one side for an amplitude of 10 cm. Release the mass, making sure not to push it as you let it go. 5. Measure the time taken for 20 complete cycles. Repeat once or twice for accuracy, then calculate the frequency. Enter the data in your observation table. 6. Repeat step 5 using amplitudes of 20 cm and 30 cm. Tabulate your data. C clamp mass Figure 6 Setup for Investigation 6.1.1 LAW-48 Unit 3 Waves and Sound
7. Determine the time taken for 20 complete cycles of the pendulum using a pendulum length of 100 cm, an amplitude of 10 cm, and 50 g, 100 g, and 200 g masses. Make sure you measure the length to the middle of each mass. Tabulate your data. 8. Determine the time taken for 20 complete cycles of the pendulum using an amplitude of 10 cm and a constant mass. Use pendulum lengths of 100 cm, 80 cm, 60 cm, 40 cm, and 20 cm. Tabulate your data. Unit 3 Waves and Sound LAW-49
Analysis (b) With frequency as the dependent variable, plot graphs of frequency versus (i) amplitude, for a length of 100 cm and a constant mass (ii) mass, for a length of 100 cm and a constant amplitude (iii) length, for a constant amplitude and a constant mass (c) Answer the Question by describing the relationship between frequency and amplitude, frequency and mass, and frequency and length, both in words and mathematically. LAW-50 Unit 3 Waves and Sound
(d) For each of the different lengths, calculate the period of vibration. Plot a graph of period as a function of the length of the pendulum. Replot the graph to try to obtain a straight line. (Hint: You can either square the values of the period or find the square roots of the values of the length.) Evaluation (e) Evaluate the predictions you made regarding the frequency, mass, amplitude, and length of a pendulum. (f) Describe the sources of error in the investigation and evaluate their effect on the results. Suggest one or two improvements to the experimental design. Unit 3 Waves and Sound LAW-51
Synthesis (g) Calculate the maximum speed of the 100 g pendulum mass when it has a length of 100 cm and an amplitude of 50 cm. (Hint: You can apply the law of conservation of mechanical energy to this problem. The maximum vertical displacement of the mass above its rest position can be found by means of a scale diagram, by actual measurement using the pendulum, by applying the Pythagorean theorem, or by using trigonometry.) LAW-52 Unit 3 Waves and Sound