Acceleration due to Gravity Using Simple Pendulum Experiment
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To measure the acceleration due to gravity (g) using a simple pendulum, you can use the relationship between the period of the pendulum and the length of the string. Here’s a step-by-step guide to perform the experiment and calculate g:
Materials Needed
- A small, dense bob (like a metal ball)
- A string or light, inextensible cord
- A stopwatch
- A ruler or measuring tape
- A protractor (optional, for small angle measurement)
Procedure
1. Set Up the Pendulum: Attach the bob to one end of the string. Fix the other end of the string to a stable support so that the bob can swing freely. The length of the string should be measured from the point of suspension to the center of the bob.
2. Measure the Length: Measure the length L of the pendulum string accurately using a ruler or measuring tape. Ensure this length is in meters (m).
3. Displace the Pendulum: Pull the bob to one side so that the pendulum makes a small angle (less than 15 degrees) with the vertical. This small angle ensures that the motion approximates simple harmonic motion.
4. Release and Time the Swings: Release the bob without pushing it and start the stopwatch. Measure the time it takes for the pendulum to complete several oscillations (a complete oscillation is from one side to the other and back again).
5. Calculate the Period: The period T is the time it takes for one complete oscillation. To get an accurate value, measure the time for multiple oscillations (say, 10 or 20), and then divide this total time by the number of oscillations to get the average period. For example, if the time for 20 oscillations is t, then the period T is: T = t/20
6. Use the Pendulum Formula: The period of a simple pendulum is given by:
T = 2π√(L/g)
Rearrange this formula to solve for g:
g = 4π^2 / T^2
By carefully following these steps and calculations, you can accurately measure the acceleration due to gravity using a simple pendulum.
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