PWV 14 Pendulum Periods

Physics with Vernier 14 - 1 Name: Christian Gavidia Date: 11/20/2023 LAB ANSWER LabQuest App 14 Pendulum Periods A swinging pendulum keeps a very regular beat. It is so regular, in fact, that for many years the pendulum was the heart of clocks used in astronomical measurements at the Greenwich Observatory. There are at least three things you could change about a pendulum that might affect the period (the time for one complete cycle): ⚫ The amplitude of the pendulum swing ⚫ The length of the pendulum, measured from the center of the pendulum bob to the point of support ⚫ The mass of the pendulum bob To investigate the pendulum, you need to do a controlled experiment; that is, you need to make measurements, changing only one variable at a time. Conducting controlled experiments is a basic principle of scientific investigation. In this experiment, you will use a Photogate to measure the period of one complete swing of a pendulum. By conducting a series of controlled experiments with the pendulum, you can determine how each of these quantities affects the period. Figure 1 OBJECTIVES ⚫ Measure the period of a pendulum as a function of amplitude. ⚫ Measure the period of a pendulum as a function of length. ⚫ Measure the period of a pendulum as a function of bob mass.

©Vernier Software & Technology Experiment 14 MATERIALS LabQuest LabQuest App Vernier Photogate protractor string 2 ring stands and pendulum clamp masses of 100 g, 200 g, and 300 g meter stick (optional) graph paper PRELIMINARY QUESTIONS 1. Make a pendulum by tying a 100 cm string to a mass. Hold the string in your hand and let the mass swing. ⚫ Observing only with your eyes, does the period depend on the length of the string? ⚫ Does the period depend on the amplitude of the swing? ⚫ Estimate the period when you hold the mass about 10° from vertical. Note : For a pendulum that is 100 cm long, this corresponds to pulling the bob only about 15 cm to the side. 2. Try a different mass on your string. Does the period seem to depend on the mass? PROCEDURE 1. Use the ring stand to hang the 200 g mass from two strings. Attach the strings to a horizontal rod about 10 cm apart, as shown in Figure 1. This arrangement will let the mass swing only along a line, and will prevent the mass from striking the Photogate. The length of the pendulum is the distance from the point on the rod halfway between the strings to the center of the mass. Start with a pendulum length of at least 100 cm. 2. Attach the Photogate to the second ring stand. Position it so that the mass blocks the Photogate while hanging straight down. 3. Connect the Photogate to a digital (DIG) port on LabQuest and choose New from the File menu. 4. Set up LabQuest for data collection with a pendulum. a. On the Meter screen, tap Mode. b. Change Photogate Mode to Pendulum Timing and select OK. 5. Temporarily hold the mass out of the center of the Photogate. Observe the live readings on the Meter screen. Block the Photogate with your hand. Note that the Photogate is shown as Blocked . Remove your hand and the display should change to Unblocked . Start data collection and move your hand through the Photogate repeatedly. After the first blocking LabQuest reports the time interval between every other block as the period. Verify this is so. Stop data collection when your investigation is complete.

Length (cm) Average period (s) 26 0.92 46 1.27 87 2 16 0.77 Part III Mass Mass (g) Average period (s) 50 1.43 200 1.41 500 1.36 ANALYSIS 1. When measuring the pendulum period, should the interface measure the time between two adjacent blocks of the Photogate? Or is some other measurement logic used? Explain. When measuring the pendulum period , the interface should measure the time between two adjacent blocks of the photogate . This method is used because it accurately captures the time taken for the pendulum to complete one full oscillation. The photogate is an optical device that detects the interruption of a light beam by the pendulum bob. As the pendulum swings, it passes through the photogate and blocks the light, triggering a timing event. When the pendulum returns and blocks the light again, another timing event is triggered. Other measurement techniques, such as recording the time of multiple oscillations and dividing by the number of cycles, can also be used. However, using the time between adjacent blocks of the photogate provides a more direct and accurate measurement of the pendulum period. 2. Plot a graph of the pendulum period, T , vs. amplitude, A , in degrees using LabQuest App or graph paper. Scale each axis from the origin (0,0). According to your data, does the period depend on amplitude? Explain Yes, the period does depend on amplitude. 3. Plot a graph of the pendulum period, T , vs. length, ℓ , using LabQuest App or graph paper. Scale each axis from the origin (0,0). Does the period appear to depend on length?

Physics with Vernier 14 - 5 . The answer is that it may depend on mass, but there is not enough data to answer this conclusively . 4. Plot a graph of the pendulum period, T , vs. mass, m 2 , using LabQuest App or graph paper. Scale each axis from the origin (0,0). Does the period appear to depend on mass? Do you have enough data to answer this conclusively? one of the graphs should show a direct proportion, and the T vs. L graph should support the relationship T^2 = L/g. To examine more carefully how the period, T , depends on the pendulum length, ℓ , create the following two additional graphs of the same data: T 2 vs. and T vs. ℓ 2 . Of the three period length graphs, which is closest to a direct proportion; that is, which plot is most nearly a straight line that goes through the origin ? the rules may include adjusting the length and mass of the pendulum to achieve the desired period, and ensuring that the pendulum is free from external disturbances such as air resistance. 5. 14 - 4 Physics with Vernier Pendulum Periods 6. Using Newton’s laws, we could show that for a simple pendulum the period, T , is related to the length, ℓ , and free-fall acceleration g by Does one of your graphs support this relationship? Explain. Hint : Can the term in parentheses be treated as a constant of proportionality? Yes, If we plot a graph between T² and length,l-we get a straight line with a slope given by the terms in parantheses,which is a constant of proportionality as all the terms involved are constants. , or