How to Measure Acceleration Due to Gravity: Practical Examples

In this article, we'll explore simple yet effective methods for measuring the acceleration due to gravity. Using basic materials and straightforward techniques, you can conduct experiments to understand this fundamental force of nature.
By Jamie

Understanding Acceleration Due to Gravity

Acceleration due to gravity (denoted as ‘g’) is the acceleration experienced by an object due solely to the force of gravity. On Earth, this value is approximately 9.81 m/s². In this article, we will discuss two practical examples of measuring this value through experimentation.

Example 1: Free Fall Experiment

Objective

To measure the acceleration due to gravity using a simple free fall experiment.

Materials Needed

  • A small object (e.g., a ball or a piece of paper)
  • A stopwatch
  • A measuring tape or ruler

Procedure

  1. Measure Height: Measure a vertical distance (h) from which you will drop the object. For example, 2 meters.
  2. Drop the Object: Hold the object at the measured height and release it without applying any force.
  3. Time the Fall: Use the stopwatch to measure the time (t) it takes for the object to hit the ground. Repeat this step three times for accuracy.
  4. Calculate Average Time: Compute the average time taken for the three trials.

  5. Apply the Formula: Use the formula for distance under constant acceleration:

    egin{equation}
    h =
    rac{1}{2} g t^2
    ag{1}

    Rearranging gives us:

    egin{equation}
    g =
    rac{2h}{t^2}
    ag{2}

    1. Calculate g: Plug your average time and height into the formula to find ‘g’. For example, if h = 2 m and average time t = 0.64 s, then:

    egin{equation}
    g =
    rac{2 imes 2}{(0.64)^2}
    ag{3}

    This should yield approximately 9.81 m/s².

Example 2: Pendulum Experiment

Objective

To measure the acceleration due to gravity using the period of a pendulum.

Materials Needed

  • A string or lightweight rope (about 1 meter long)
  • A small weight (like a washer or a small bag of sand)
  • A protractor
  • A stopwatch

Procedure

  1. Set Up the Pendulum: Attach the weight to one end of the string. Secure the other end to a fixed point, allowing the weight to swing freely.
  2. Measure the Angle: Pull the pendulum back to a small angle (less than 15 degrees) and release it. Use the protractor to measure this angle.
  3. Time the Period: Start the stopwatch as you release the pendulum and measure the time it takes to complete 10 full swings (back and forth). Divide this time by 10 to get the average period (T) of one swing.

  4. Apply the Formula: Use the formula for the period of a simple pendulum:

    egin{equation}
    T = 2C0 imes
    rac{L}{g}
    ag{4}

    Rearranging gives us:

    egin{equation}
    g =
    rac{4C0^2L}{T^2}
    ag{5}

    1. Calculate g: Plug your average period and the length of the pendulum into the formula. For example, if L = 1 m and T = 2.0 s, then:

    egin{equation}
    g =
    rac{4 imes
    rac{22}{7}^2 imes 1}{(2)^2}
    ag{6}

    This should yield a value close to 9.81 m/s².

Conclusion

Both of these experiments provide practical ways to measure the acceleration due to gravity using basic materials. They demonstrate fundamental principles of physics while allowing you to engage with the concepts of kinematics and dynamics in a hands-on manner.