Lab 10

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University of Michigan *

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Physics

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Dec 6, 2023

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Physics 201 (General Physics-1) LAB #10 Simple Pendulum and Variables: Study of Scientific Method Your name: Olivia Beall Student ID: 7966485 Date: 7/12/2022 Lab partners name: Lab Instructor’s name: _____ Aiden Pereira ________ Prof. Stephen Kamanda _____ Mohammad Nawal ________ Objectives: The objective of this experiment was to investigate what variables influence the period of a simple pendulum. Theory: A simple pendulum may be described ideally as a point mass suspended by a massless string from some point about which it is allowed to swing back and forth in a place. A simple pendulum can be approximated by a small metal sphere that has a small radius and a large mass when compared relatively to the length and mass of the light string from which it is suspended. If a pendulum is set in motion so that it swings back and forth, its motion will be periodic. When we speak of the motion of the simple pendulum, we refer to the oscillations it performs, when the bob is taken to a height (the string remaining taut) and released. Materials and Methods: A mass was placed on a string and attached to a ring stand. A protractor was used to measure the angle at which the string was initially held, and it was then released. A stopwatch was used to record the time of 10 oscillations, and thus the period was calculated. For the second experiment, different masses were attached to the string, and the same method was used to calculate the period. Finally, the length was adjusted and the period was calculated in a similar manner. Data Tables
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Data analysis and post lab questions: 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? Why? A time period is the time from one extreme to the same extreme position on the pendulum. Therefore, the interface should be measuring the time period between one block to the next block and when it comes back to the same block. The motion of the mass is important, because the time is takes to return to the initial position is apart of the period. 2. From your graph of the pendulum period, T , vs . amplitude in degrees, does the period depend on amplitude? Explain. No, the period stayed consistent for the most part for every trial. No matter where Mass was released from, the period stayed the same. 3. From your graph of the pendulum period, T , vs . length, . Does the period appear to depend on length? Explain Yes, the period is directly related to the length of the system. The equation to calculate the period of a simple pendulum is 2 ᴨ √ ❑ , therefore the only things that impact the period of a pendulum is the length of the system and the gravity acting upon the system. 4. Plot a graph of the pendulum period, T , vs . mass using the collected data. Does the period appear to depend on mass? Do you have enough data to answer this conclusively? There does not seem to be any connection between mass and the period of a pendulum. However, this experiment was limited in the fact that only one trial was run per mass and the mass did not vary greatly. 5. Using Newton’s laws, we could show that for a simple pendulum the period, T , is related to the length, and free-fall acceleration g by the equation. Does one of your graphs support this relationship?
Yes, the graph of length vs. period shows this relationship as it illustrates a linear relationship. 6. How would the period of a simple pendulum be affected if it were located on the moon instead of the earth? Yes, the period of the pendulum would be differ on the moon and on Earth. This is because the period of a pendulum is affected by only the length of the system and the gravity acting upon the system. Since the gravitational pull is different on the moon than it is on Earth, the pendulum would have a different period. 7. What kind of graph would result if the period T were graphed as a function of the square root of the length, l . The graph of the period as a function of the square root of the length, would be a straight line with a slope of 2 Π / √ ❑ . 8. Given what you observed in this experiment, write a set of rules for constructing a pendulum clock that is reliable under a variety of temperatures. In order to construct a reliable pendulum, the length of the string and location of the experiment should be kept constant. This is because these are the two factors that impact the swing of a pendulum.
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