To find the value of “g” by free fall method

 

Abstract

This experiment aims to determine the acceleration due to gravity (g) using the free fall method. By measuring the time taken for an object to fall freely from a known height and applying kinematic equations, the value of "g" can be calculated.

Introduction

The acceleration due to gravity, denoted as "g", is a fundamental constant representing the acceleration experienced by objects in free fall near the Earth's surface. This experiment utilizes the principles of kinematics to measure "g" accurately using simple apparatus.

Procedure

1. Set up a vertical support and attach a stopwatch to it.
2. Measure the height (h) from which the object will be dropped.
3. Ensure the area below the drop point is clear and safe.
4. Hold the object at the initial position and release it, starting the stopwatch simultaneously.
5. Record the time (t) taken for the object to fall freely to the ground.
6. Repeat the experiment multiple times for accuracy.

Observations and Calculations

Let's assume the following observations were made during the experiment:

• Height of the drop (h): 2 meters
• Time taken for the object to fall (t): 1.5 seconds

Using the kinematic equation for free fall:

g = 2h / t^2

Substitute the values and calculate the acceleration due to gravity (g).

Conclusion

The experiment successfully determines the value of "g" using the free fall method. The calculated value can be compared with the accepted standard value (9.81 m/s²) to assess the accuracy of the experiment.

Precautions

• Ensure the stopwatch starts and stops accurately.
• Measure the height accurately and avoid any obstructions in the fall path.
• Repeat the experiment multiple times to minimize errors.
• Ensure safety measures are in place, especially if conducting the experiment outdoors.

Short Questions with Answers

1. What is the purpose of the free fall experiment?
   Answer: To determine the value of "g" (acceleration due to gravity).
2. Why is it important to measure the height accurately?
   Answer: The height affects the time taken for the object to fall, hence influencing the calculation of "g".
3. How does air resistance affect the experiment?
   Answer: Air resistance slows down the falling object, leading to a longer fall time and affecting the accuracy of the results.
4. What precautions should be taken to ensure safety?
   Answer: Clearing the area below the drop point, securing the support structure, and wearing appropriate safety gear if necessary.
5. Why is it necessary to repeat the experiment multiple times?
   Answer: To obtain an average value and minimize errors caused by variations in measurements or external factors.
6. How does "g" vary with altitude?
   Answer: "g" decreases slightly with altitude due to the decreasing gravitational force as you move away from the Earth's surface.
7. What other factors can affect the experiment's accuracy?
   Answer: Instrument accuracy, parallax error, and variations in air density.
8. What is the SI unit of acceleration?
   Answer: Meter per second squared (m/s²).
9. What is the theoretical value of "g" near the Earth's surface?
   Answer: Approximately 9.81 m/s².
10. How can systematic errors be minimized in this experiment?
    Answer: By calibrating instruments, ensuring consistent experimental conditions, and using precise timing methods.
11. What is the role of the stopwatch in this experiment?
    Answer: To measure the time taken for the object to fall freely from the specified height.
12. How does changing the height of the drop affect the results?
    Answer: Higher drops result in longer fall times and vice versa, influencing the calculated value of "g".
13. What would happen if the stopwatch is started too early?
    Answer: The recorded fall time would be shorter than the actual, leading to a higher calculated value of "g".
14. How does the mass of the falling object affect the experiment?
    Answer: The mass does not affect the acceleration due to gravity, as demonstrated by Galileo's experiment with different masses falling simultaneously.
15. What is the formula used to calculate "g" in this experiment?
    Answer: \( g = 2h / t^2 \), where "h" is the height and "t" is the time taken for the fall.
16. How should the object be released for the experiment?
    Answer: The object should be released from rest, without imparting any initial velocity.
17. What is the effect of using different objects for the experiment?
    Answer: Different objects may have different aerodynamic properties, affecting the fall time and the calculated value of "g".
18. Why should the experiment be conducted in a vacuum for absolute accuracy?
    Answer: Air resistance significantly affects the fall time, and conducting the experiment in a vacuum eliminates this factor for precise results.
19. What is the role of the support structure in the experiment?
    Answer: The support structure holds the object at the specified height and provides a reference point for measuring the fall distance.
20. How does the accuracy of the stopwatch affect the results?
    Answer: Inaccurate timing leads to errors in the calculated fall time and, consequently, the value of "g".

Multiple-Choice Questions (MCQs)

1. What is the primary objective of this experiment?
   A) To measure the mass of the object
   B) To determine the velocity of the object
   C) To find the value of "g"
   D) To calculate the potential energy of the object
   Correct Answer: C) To find the value of "g"
2. Why is it important to use a stopwatch in this experiment?
   A) To measure the height of the drop
   B) To ensure safety
   C) To record the time taken for free fall
   D) To measure the velocity of the falling object
   Correct Answer: C) To record the time taken for free fall
3. What happens to the value of "g" if the height of the drop is doubled?
   A) It remains the same
   B) It halves
   C) It doubles
   D) It quadruples
   Correct Answer: A) It remains the same
4. Which equation is used to calculate "g" in this experiment?
   A) \( g = h / t \)
   B) \( g = 2h / t \)
   C) \( g = ht^2 \)
   D) \( g = h^2 / 2t \)
   Correct Answer: B) \( g = 2h / t \)
5. What effect does air resistance have on the experiment?
   A) It increases the acceleration
   B) It decreases the acceleration
   C) It has no effect
   D) It stops the object from falling
   Correct Answer: B) It decreases the acceleration