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In an experiment to measure the acceleration due to gravity using a simple pendulum, a student obtained values for the length / t of the pendulum and the corresponding values for the periodic time T - Leaving Cert Physics - Question 1 - 2012
Question 1
In an experiment to measure the acceleration due to gravity using a simple pendulum, a student obtained values for the length / t of the pendulum and the correspondi... show full transcript
Worked Solution & Example Answer:In an experiment to measure the acceleration due to gravity using a simple pendulum, a student obtained values for the length / t of the pendulum and the corresponding values for the periodic time T - Leaving Cert Physics - Question 1 - 2012
Step 1
Describe how the student obtained a value for the length of the pendulum and its corresponding periodic time.
Answer
The student followed a systematic approach to obtain the values of the pendulum's length and periodic time:
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Measurement of Length: The length of the pendulum was measured using a ruler or measuring tape, ensuring that the measurement was taken from the pivot point to the center of mass of the bob. The diameter of the bob was measured and subtracted to find the effective length.
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Measurement of Periodic Time: The student conducted multiple oscillations of the pendulum. A stopwatch was used to time the oscillations, taking care to avoid parallax errors. The time was recorded for a fixed number of oscillations, usually 10 or more, and the total time was divided by the number of oscillations to find the average time for a single oscillation (period).
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Recording Data: The values of length and corresponding periodic time were systematically recorded in a table for analysis.
Step 2
Draw the appropriate graph on this examination paper and use it to calculate a value for g.
Answer
To graph the relationship between the squared period and the length , plot the values from the given data:
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Graph Axes: Place periodic time squared () on the y-axis and length () on the x-axis.
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Plot Points: Using the data points collected, plot the corresponding values on the graph.
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Line of Best Fit: Draw a straight line that best fits the plotted points, which should be approximately linear according to the formula T^2 = rac{4\\pi^2}{g}L.
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Calculating the Slope: The slope (m) of the graph is calculated using the formula:
ext{slope} = rac{\Delta T^2}{\Delta L}
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Using the Slope to Find g: From the relationship, we know that:
By substituting the obtained slope into this equation, calculate the acceleration due to gravity g.
Step 3
Give two factors that affect the accuracy of the measurement of the periodic time.
Answer
Several factors can influence the accuracy of the measurement of the periodic time:
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Number of Oscillations: Measuring the time over a larger number of oscillations reduces random errors and improves accuracy compared to measuring a single period.
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Air Resistance and Friction: Environmental factors such as air resistance acting on the pendulum and friction at the pivot can alter the pendulum's motion, leading to inaccuracies.