You should be working with new lab partners starting with this lab. Exploration: Swinging your arms and legs back and forth Discuss and try out the following questions within your lab group. After you discuss each question, record a brief answer in your logbook. 1. (a) Have one person in your group take a little walk in the lab room while the rest of you watch the person's arms as they are walking. What kind of motion do the arms make? (b) Try to walk and hold your arms completely still relative your body. What happens? Why does that feel unnatural? (c) What do you suppose determines how fast your arms swing back and forth? Explain. 2. (a) Relax your lower leg and let it swing freely over the edge of a table. What determines how fast your leg swings back and forth? (b) Try swinging your leg back and forth very slowly and then very fast. How does this feel compared to when you let it swing freely? Describe how your muscles feel when producing these motions. (c) How do you suppose the comfortable speed is related to how fast you normally walk? What determines what a comfortable stride speed is for you? 3. Suppose you model a swinging human leg as a simple pendulum, like one on a Grandfather's clock or set up in the lab room. How would you expect the time it takes a pendulum to swing back and forth to depend upon its mass, its length, and the angle through which it swings? Invention Discussion - Part 1 Your instructor will lead a brief discussion and demonstration of important concepts related to oscillations and a simple pendulum. Answer questions 4-6 based on this discussion. Practice estimating quantities: 4. Identify the following quantities (with units!) and concepts for this graphed data. You can cut out the graph and place it in your logbook. 2003 - UNL page 1 of 8
Amplitude Frequency Period Damping 2003 - UNL page 2 of 8
Invention Discussion - Part 2 Investigating a simple pendulum as a class As a class, predict what variable(s) will influence the period of the different simple pendulums the most. Predict what variable(s) will have the least and/or no perceivable. Carefully observe the motion of each simple pendulum when the mass is displaced from rest and released by your instructor. 5. (a) What variable(s) influences the period of oscillation of the simple pendulum the most? (b) What variable(s) does not seem to influence the period of oscillation of a simple pendulum? 6. How can it be that doubling the mass does not seem to influence the motion of the pendulum? Application Activities 1: Freely-Swinging Motion of Skeleton Legs Each laboratory team will study in detail the to-and-fro motion of a suspended part of a plastic skeleton. There will be six different swinging objects in the room: (1) small lower leg, (2) small whole leg, (3) medium-size lower leg, (4) medium-size whole leg, (5) large lower leg, and (6) large whole leg. These skeleton legs are suspended from a pivot point and their oscillatory motion will be analyzed using a motion sensor (file: MBL Motion sensor). Measure and record the length of the swinging leg at your station (from the pivot to the bottom of the heel). Pull your suspended leg aside and let it swing freely. Once the leg is swinging, start recording data. Try it a few times to be sure you obtain a good, smooth data set. You may have to adjust the alignment of the motion sensor. Select your best data set, showing the motion of the leg for 8 to 10 oscillations. Print out a copy to put in your logbook. Identify which leg your data represents on this graph. 7. (a) What is the maximum angle that the leg is displaced from its resting position? Explain how you obtained that value. Identify the position on your graph. (b) Describe what happens to the maximum angle as time goes by. What is that process called? 8. Identify five complete and consecutive oscillations on your graph. For each of these five oscillations, compute the amplitude of displacement, the period for one swing, and the frequency of the motion. Compute average values as well. You should find it helpful to display your data in a table. How did the amplitude, period, and frequency change (or not change) with time? 2003 - UNL page 3 of 8
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9. (a) Consider the speed of the moving leg. Identify on the graph where in the swing the magnitude of the speed is a maximum and where it is zero. Explain in words. (b) Consider the acceleration of the moving leg. Identify on the graph where in the swing the magnitude of the acceleration is a maximum and when it is zero. Explain. (c) Consider the energy of the moving leg. Identify where in the swing the kinetic energy is at a maximum and where the potential energy is at a maximum. Explain. 10. Suppose the leg was hanging at rest and you wanted to cause the leg to oscillate repeatedly (beginning from rest and then oscillating in a way that overcomes any damping effects). Would you apply a constant or a periodic force to it? Why? How could you determine the frequency with which to apply the force? Explain your ideas. Summary of Freely Swinging Data from all Teams: Share your data on the whiteboard and complete the following table in your lab book for the small, medium and large lower and whole legs: Leg Size Leg Length (from the pivot to the bottom of the heel) Period of Oscillation Frequency of Oscillation Small lower leg Small whole leg Etc. 11. What relationship do you notice between the periods of oscillations for the different-sized legs? Describe in words. Application Activities 2: Forces with the Swinging Motion of Skeleton Legs Assume that the rubber band attached to the skeleton leg represents the main muscle force. [Ask your instructor for assistance if the rubber band is missing.] Using the rubber band, apply a periodic force to the leg that mimics the muscle force needed to cause the leg to oscillate (beginning from rest and then oscillating in a way that overcomes any damping effects). Try a very high-frequency force and a very low-frequency force as well and note what happens. 12. (a) Describe the frequency of the force necessary to cause the leg to oscillate (beginning from rest and then oscillating in a way that overcomes any damping effects). (b) Describe what happens when you applied high-frequency and low-frequency forces to the stationary leg. (c) Can you relate the results of this experiment to what children do when they want to go high on a playground swing? Explain your ideas. 2003 - UNL page 5 of 8
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Application Activities 3: Studying Freely Swinging Motion of Your Leg Pick one person in your group to be the subject for Activities 3 and 4. You will study the to-and-fro motion of a free-swinging part of that person's leg, both the lower leg, swinging freely from the knee, and the whole stiff leg, swinging freely from the hip. To save time, you will simply use a stopwatch to measure the period of the swinging legs. Prepare to study the motion of the subject's freely swinging lower leg while he/she is sitting on a lab table. Relax your leg muscles and have a team member pull your suspended leg aside and let it swing freely and time its motion for five complete oscillations and estimate the amplitude of the swing. Try it at least 3 times and record the time and amplitude for each trial. Next, the subject should stand on a thick textbook so his/her whole leg is slightly raised off of the floor so the whole leg, with the knee in a straight position, can swing freely. Relax your whole leg muscles and have a team member pull your suspended leg aside and let it swing freely while timing its motion and estimating the amplitude. Try it at least 3 times and record the time and amplitude for each trial. Complete the following summary data table in your lab book. Leg Portion lower leg whole leg Leg Length (from the pivot to the bottom of the heel) Average Amplitude Average Period Average Frequency 13. How does the period of oscillation seem to relate to the length of the swinging leg? 14. Carefully sketch a motion graph showing 5 complete oscillations for one of these two experimental conditions (whole leg or lowerleg) based on your observations and times. Compare the graph of the leg motion to the motion of the skeletons. How are they most different? Explain why you think that is. Application Activities 4: Relating the Swinging Motion of your Leg to Walking 15. (a) Consider how you would expect the swinging motion of your leg to be related to your natural walking speed. In the hallway, measure the time it takes the subject to take ten normal strides. You might want to start walking and have the group time your ten strides while you are walking at a constant, natural gait. Record the time and determine the average stride period and frequency. (b) Compare and contrast the oscillatory frequency of the subject's freely swinging legs to his/her leg's natural walking oscillatory frequency. 2003 - UNL page 7 of 8
16. Describe the timing of the engagement of your leg muscles that enable you to walk. How are they related to the natural freely swinging oscillatory behavior of your legs? 17. How is a simple pendulum similar to and different from a swinging arm or leg? Explain. End of Lab Procedures! Return stopwatch and motion sensor to the top of your lab table. If you are in the last lab section of the day, then shut down the computer. Want More Information? Periodic motion (see Walker, Sections 13-1 and 13-2) Simple and physical pendulum (see Walker, Section 13-6) Damped and Driven Oscillations and Resonance (see Walker, Section 13-7 and 13-8) 2003 - UNL page 8 of 8