The Simple Pendulum_Hypothesis Testing_PHYS 130

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Physics

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Apr 3, 2024

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The Simple Pendulum Purpose: To investigate how the period of a pendulum is affected by its mass, angle of swing, and length. Discussion The simple pendulum is of historic and basic importance. Its regular swing, discovered by Galileo Galilei, makes it an accurate and simple timekeeper and, in the hands of Isaac Newton, resulted in the first evidence that inertial and gravitational masses are proportional. Until relatively recently, the motion of a pendulum provided the most accurate and convenient method for measuring the local gravitational pull of the Earth. Although “pendular” motion had been likely observed for centuries, Galileo (1564-1642) was intrigued by the back and forth motion of a suspended weight. Legend has it that he began his studies of pendulums after watching a ceiling lamp swing back and forth in the cathedral of Pisa (no doubt during a particularly long winded sermon!) Using his pulse to time the motion of the swinging lamp, the crude measurements indicated the period (the amount of time required for one swing) remained constant although the swinging motion varied as time passed. The motion of the pendulum bob posed interesting problems. What causes it to swing back and forth? What keeps it moving after it is released? Which factors influence the time it takes to complete one swing (called the period)? Throughout his experimental work, the pendulum was never very far from Galileo's thought. Although he did not address the first two questions, he did figure out the third which led to the development of the pendulum clock, although it would take another 60 – 70 years before it became a practical time keeping device. Model Testing When setting up a simple pendulum, you have three variables you can adjust: (1) the bob mass, (2) the pendulum length, and (3) the pendulum swing amplitude ( θ ). The “physics analysis” of the motion of the simple pendulum as it swings forth and back makes the following prediction for the period measurement: T = 2 π √ L g In this model, T ≡ period ,L≡length, ∧ g≡gravity constant . You can see that the model predicts that the period is independent of the amplitude of the swing ( θ ) and the mass of the pendulum bob ( m ). But under what conditions, if any, is this model valid? It is your goal to test the limits of this model to discover when it is appropriate to use in an experimental setting. (That is, when can we use the formula to get reliable and valid results from measurements made in an experimental system?)

Link for online simulation: https://phet.colorado.edu/sims/html/pendulum-lab/latest/pendulum-lab_en.html PROCEDURE: When the pendulum simulation has opened “Click” on the lab window . Click on Period Timer. Make sure that speed is set to Normal and Friction (slider) is set to None. To get a period measurement, simply pull the pendulum to the side and release it. Click on the period timer to get the measurement.

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