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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 l of the pendulum and the corresponding values for the periodic time T - Leaving Cert Physics - Question 1 - 2012

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Question 1

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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 l of the pendulum and the corresponding... 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 l 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.

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Answer

  1. Measure the Length of the Pendulum: The student measured the length of the pendulum from the fixed point to the center of the bob using a meter stick. This distance is crucial as it directly influences the period of the pendulum.

  2. Determine the Diameter of the Bob: The diameter of the bob should be measured to ensure accurate calculations when determining the center of mass. This can be done using calipers.

  3. Reference Tool Usage: The student used a Vernier caliper or a micrometer, if necessary, to obtain a more precise measurement of the pendulum's length.

  4. Measure the Periodic Time: The periodic time T of the pendulum was measured by timing several oscillations (usually 10 or more) and then dividing this total time by the number of oscillations to find the average time for one oscillation.

Step 2

Draw the appropriate graph on this examination paper and use it to calculate a value for g, the acceleration due to gravity.

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Answer

  1. Plot the Graph: On the graph paper, plot the square of the periodic time T² (y-axis) against the length l of the pendulum (x-axis). Each point corresponds to the measured values.

  2. Fit a Line of Best Fit: Draw a line of best fit through the points.

  3. Calculate the Slope (m): The slope of the line can be found using the formula for the linear relationship:

    T2=4π2lgT^2 = 4\pi^2 \frac{l}{g}

    Rearranging gives:

    g=4π2lT2g = \frac{4\pi^2 l}{T^2}

  4. Use Slope to Determine g: The slope of the graph will be equal to rac{4\pi^2}{g}. From the slope calculated, rearrange to find g:

    g=4π2slopeg = \frac{4\pi^2}{\text{slope}}

  5. Substitute the Values: Insert the obtained slope from your graph to find the value of g.

Step 3

Give two factors that affect the accuracy of the measurement of the periodic time.

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Answer

  1. Timing Errors: The precision of the stopwatch or timing device can affect accuracy. Human reaction time can introduce a delay, especially during the start and end of timing.

  2. Environmental Factors: Changes in air resistance, temperature, or even the length of the string (due to elasticity) can affect the periodic time, leading to inaccuracies in measurements.

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