PHY201 Lab8 Pendulum

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Feb 20, 2024

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Physics 201L Lab #8: Pendulum Motion Introduction: This week our experiment will investigate the periodic motion of a simple pendulum. The periodic motion of a simple pendulum is another discovery of Galileo (which originated from observations of swinging lamps in chapel) and resulted in the pendulum clock being used for centuries as the first precise timepiece. A requirement for periodic motion is a restoring force that is opposite the direction of motion and pulls the object back to an equilibrium position. The word periodic tells us that the motion repeats itself – it runs on a cycle. The period T is the time in seconds it takes to complete one cycle of its motion. Some common examples: a child swinging back and forth on a swing-set, a floating object that bobs up and down as waves travel through the water, or an object bouncing on a spring. One example of periodic motion is a simple pendulum that bobs back and forth (like the child on a swing). A pendulum consists of a bob of mass m suspended by a light string of length L fixed at its upper end, as shown in the figure below. Since the string is light, we ignore its mass. When the bob is released it swings back and forth over its path. Note that mgsin  is the tangential force that acts as the restoring force that pulls the bob back to its equilibrium position, causing the pendulum to have periodic motion. For small angles this force can be simplified using the small angle approximation, which says that sin    when the angle is in radians (not degrees). For small angles the restoring force of a simple pendulum is approximated as F r  -mg  . This restoring force is directly proportional to the displacement and in the opposite direction of motion. When the restoring force is directly proportional to the displacement, the object exhibits simple harmonic motion . (The restoring force of Hooke’s l aw is also directly proportional to the displacement, so masses bouncing on springs will also experience simple harmonic motion).

2 In this experiment you will examine what variables influence the period T of a pendulum (and which do not influence the period of a pendulum). You will consider the pendulum variables: pendulum mass (m), the string length (L), and release angle (  ). Each measurement run you will measure the period T as you change one of the variables (and keep the others constant). Prelab Reading Assignment: Read sections 15.1, 15.2, and 15.5 of the textbook for background information. Equipment: Vertical stand with suspension arm, meter stick, string, pendulum bobs, PASCO 850 Universal Interface and Capstone program Procedure: Part 1: Equipment Setup The experiment will be conducted using a simple pendulum that will swing between a photogate at the bottom of its motion. We will vary the pendulum length, mass, and angle amplitude and measure the period T of the pendulums motion. 1. Setup your simple pendulum by suspending the string from two support points on the horizontal suspension arm. 2. Check that the photogate is plugged into the PASCO 850 Universal Interface. Turn on the PASCO 850 Universal Interface, and open the PASCO Capstone program from the lab computer’s desktop. 3. Click on the Classic Templates to begin. Now select Hardware Setup on the left- hand side. Click on the Channel 1 port input and select the photogate option. 4. Now select Timer setup on the left-hand side of the screen. Click next for pre- configured timer. The photogate should appear and already be selected. If not ask for help from your lab instructor. Click Next. 5. Select the Pendulum Timer option. 6. For the measurement data select the period option. Deselect all the other data options. Click Next. 7. Check the diameter (width) of your pendulum bob and input it into the requested box. The standard pendulum bob width is 1.60 cm. Click next. 8. Now rename your timer or leave as is. Click Finish. Click again on Timer setup to minimize the window. 9. Add a data table to your experiment. Display the period data in the data column.

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