: : : e d/simple- o https://www.khanacademy.ora/science/physics/mechanical-waves-and-soun harmonic-motion-with-calculus/v/introduction-to-harmonic-motion Part A: Relationship between Mass and Period (25 points) To earn full credit, you must justify your solutions by showing your work. Using some string and a mass, build a simple pendulum. The higher your pendulum !s, e |)nger your string is and the easier it will be to measure (and more accurate). (A pendulum 1S /0936 Y t defined as something hanging from a fixed point which, when pulled back and releasgd, is fr'ee 0 swing down by gravity and then out and up because of its inertia, or tendency to stay in motion.) 1. a Measure your mass, length of string, and planned amplitude carefully. Remember that the amplitude is the distance the mass is pulled from the centerline. (1 pt each) Length of String (from pivot to center of mass),incm: Amplitude (from centerline to farthest distance); In c S sE S b. The "period\" of a pendulum is the amount of time it takes the mass to complete one full cycle. Pull the mass back 10 or 20 centimeters from the starting point; let it swing out to the other side and back to its original starting point. The time it takes to complete that entire path is the period. Because this happens very quickly, it is a good idea to measure the time it takes to complete 10 cycles and then divide by 10 to get the time for one cycle. Prediction: What do you think will happen to the period as you change the mass? (1 pt) _ - 2. When you are ready to begin, pull the mass back to the desired amplitude and let the pendulum start swinging. Let the pendulum complete one full cycle before you begin timing. Using a stopwatch (or your watch with a second hand), measure the time it takes to complete 10 full cycles. Repeat this approximately 6 times. Calculate the period by dividing each time by 10 and then find the average period. Record your results in the table that follows. (3 pts) Project 2 208 SCIH 036 Mass (in grams): Time for 10 full cycles Period (in seconds) in seconds) CEwe Average (in seconds): 3. Repeat this procedure with at least two additional masses. Be sure to keep your pendulum St\"fl'tg the same length and to pull the mass back to the same amplitude each time. Record your resufts in the tables that follow. (6 pts total, 3 pts each) Mass (in grams): Mass (in grams): Time for 10 full cycles Period (in seconds) (in seconds) Period (in seconds) Time for 10 full cycles (in seconds) Average (in seconds): 4. Record your overall results in the following table. (3 pts) Mass (in grams): T ' Period (in seconds): Mass (in grams): ' Period (in seconds): Mass (in grams): ' Period (in seconds): 5. Graph your results with mass as the independent variable (x-axis) and period as the dependent variable (y-axis). Although graphing by hand is acceptable, it is often helpful to use a graphing program like Excel. If you choose to graph on your computer and then import it into this project be sure to use the following settings: (4 pts) ; e R e e e Project 2 rojec 209 SCIH 036 Use a scatterplot with no lines. . Adjust scale to start from zero and show all the data. Add a trendline to your data. o Do NOT force the trendline to go through the origin (0,0). o DO add the equation of the line to the graph. o DO add the r value to the graph (If the r value is greater than 0.9 you have a reasonably linear graph. If it is less than 0.9 you may want to think about collecting your data again.). If you choose to make the graph by hand, you can use the following or your own graph paper: 6. Determine the slope of the line. What does the slope mean? (2 pts) 7. Record the general equation of the line using slope-intercept form. (y = mx + b) (1 pt) Project 2 210 SCIH 036Introduction: Both light and sound are dependent on waves. Sound is communicated via pressure waves in air and other materials while light is communicated via electromagnetic waves. Both light and sound, are examples of simple harmonic motion. In this project you will construct and use a simple pendulum (a mass on a string) to illustrate the principles of simple harmonic motion. You will need the following materials to complete this project. You will be responsible for providing the necessary lab materials. . Mass (Various materials can be used. You can use small household items such as metal washers, a small bag of sand, a rock, a 9-V battery, or any other small item that has a significant mass for its size and can be attached to the end of the string.) String (lightweight, strong - like dental floss) . Protractor Scale or balance Timer / Stopwatch / Watch with a second hand Meter stick (or equivalent) Resources For additional help: If you have access to the internet, review the following resources from Khan Academy: https://www.khanacademy.org/science/ap-physics-1/simple-harmonic-motion- ap/introduction-to-simple-harmonic-motion-ap/a/introduction-to-simple-harmonic-motion- review Project 2 207 SCIH 0368. Did your findings match your prediction? (1 pt) 9. Explain any discrepancy between your prediction and your findings. (1 pt) 10. What is the relationship between mass and period? (1 pt)