Determining 'g' with a Simple Pendulum The simple pendulum is a classic physics experiment that demonstrates the relationship between gravitational accelerat...
The simple pendulum is a classic physics experiment that demonstrates the relationship between gravitational acceleration, period, and displacement. This experiment allows us to measure the value of the gravitational acceleration 'g' on Earth.
Procedure:
A pendulum made of a material with negligible mass (e.g., a string with negligible weight).
A stopwatch or a timer.
A weight (e.g., a mass hanger with negligible mass).
Choose a location with a significant amount of vertical drop (at least 1 meter).
Tie one end of the string to the mass hanger.
Attach the pendulum to the string at the other end.
Adjust the length of the pendulum so it hangs approximately 15-20 cm above the ground.
Start the stopwatch and allow the pendulum to swing.
Record the time it takes for the pendulum to complete 10 complete swings.
Repeat steps 5-7 for different lengths of the pendulum.
Data Analysis:
Calculate the average time taken for each pendulum swing.
Calculate the period of the pendulum for each length.
Plot a graph of time vs. length.
Analyze the graph to find the relationship between the period and the length.
Use the graph to calculate the value of 'g' at the location of the experiment.
Interpretation:
The slope of the graph of time vs. length is a constant, equal to the square root of the mass of the pendulum. This means that the square root of the mass is equal to the period of the pendulum.
Therefore, the value of 'g' can be calculated using the following formula:
g = (1/sq.root(m)) * (d^2) / (4T^2)
where:
g is the acceleration due to gravity (9.8 m/s²)
m is the mass of the pendulum (0.1 kg)
d is the length of the pendulum string (0.15 m)
T is the period of the pendulum (0.1 s)