Sp Unit 1.2

Practicals

kinematics

SP Unit 1.2 Practical kinematics Learners should be able to demonstrate and apply their knowledge and understanding of:
1.	Measurement of g freefall

1. Measurement of g Using a Free-Fall Experiment
⇒ Objective
Determine the acceleration due to gravity (g) by measuring the time it takes for an object to fall a known distance in free fall.
⇒ Apparatus
Object for Free Fall: A small dense ball or metal weight (to minimize air resistance).
Measuring Device: A meter stick or tape measure for the drop height.
Timing Device: A high-speed timer or electronic sensor (or even a photogate) for accurate time measurement.
Release Mechanism: A method to release the object without imparting extra initial velocity (e.g., an electromagnet or a mechanical trigger).
Data Logger (optional): For recording multiple trials and reducing human reaction time errors.
Figure 1 Measurement of g using a free-falling object
⇒ Theory and Equations
When an object is in free fall (ignoring air resistance), its motion is governed by the equation of motion under constant acceleration:
[math]s = ut + \frac{1}{2} g t^2[/math]
Where:
– s = distance fallen (in meters),
– u = initial velocity (m/s; here u=0 if released from rest),
– g = acceleration due to gravity (m/s²),
– t = time of fall (s).
Since the object starts from rest (u=0), the equation simplifies to:
[math]s = \frac{1}{2} g t^2 \Rightarrow g = \frac{2s}{t^2}[/math]
⇒ Experimental Procedure
1. Setup:
– Secure the measuring device vertically to ensure accurate height measurement.
– Position the release mechanism at the desired height (s) from the ground.
– Ensure that the area below is clear and that the ground is flat and marked.
2. Measurement:
– Measure and record the drop height s accurately using the meter stick or tape measure.
– Set up the timer or photogate at the drop point to record the fall time t from release to impact.
– It’s best to conduct several trials (at least 5–10) to obtain an average value and reduce random error.
3. Performing the Experiment:
– Release the object using the release mechanism so that it starts from rest.
– Start the timer at the moment of release and stop it when the object hits the ground (or use a sensor to detect the passage).
– Record the time t for each trial.
– Ensure that the object falls freely with minimal air resistance (use a dense, small object).
4. Data Analysis:
– For each trial, calculate g using:
[math]g = \frac{2s}{t^2}[/math]
– Average the values of g from all trials to improve accuracy.
– Compare your calculated value with the standard gravitational acceleration (approximately 9.81 m/s²).
⇒ Error Analysis and Considerations
Timing Accuracy:
Human reaction time can affect measurements if using a stopwatch. Using electronic timers or photogates improves precision.
Measurement of Height:
Ensure the drop height is measured from the exact point of release to the impact point.
Air Resistance:
While typically small for dense objects over short distances, air resistance can slightly affect the fall time. Minimizing the object’s cross-sectional area and choosing a dense material helps reduce this error.
Multiple Trials:
Performing several trials and averaging results minimizes random error and improves reliability.
⇒ Example Calculation
Suppose you measure a drop height s=0 m, and the average fall time from several trials is t=0.64 s.
Plug these values into the formula:
[math]g = \frac{2s}{t^2} \\
g = \frac{2s}{(0.64)^2} \\
g = \frac{4}{0.4096} \\
g \approx 9.77 \, \text{m/s}^2[/math]
This value is close to the standard value of 9.81 m/s², indicating a successful experiment.
⇒ Conclusion
By measuring the free-fall time over a known distance and applying the equation
[math]g = \frac{2s}{t^2}[/math]
you can experimentally determine the acceleration due to gravity. This experiment illustrates fundamental principles of kinematics and provides insight into experimental error, making it a cornerstone activity in introductory physics laboratories.