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http://weelookang.blogspot.sg/2016/08/sypt2016-workshop-materials.html

"4/6 Paper Square Drag to Terminal Velocity SYPT2016 by Tze Kwang Leong"

This document examines the motion of a 4/6 paper square as it falls under the influence of gravity and air resistance. Using Tracker software, the study evaluates how the larger surface area affects drag force, terminal velocity, and stabilization during descent.

Study Guide:

Objective:

• Analyze the descent and terminal velocity of a 4/6 paper square.
• Explore the relationship between drag force, surface area, and stabilization during free fall.

Key Concepts:

1. Drag Force and Larger Surface Areas:

   • The 4/6 paper square experiences increased drag due to its larger surface area.

2. Terminal Velocity Dynamics:

   • The point where drag force equals gravitational force, leading to constant velocity.

3. Fluttering and Stability:

   • Larger objects are prone to oscillations and require analysis of motion patterns.

4. Air Resistance Effects on Lightweight Materials:

   • Lightweight objects like paper are significantly impacted by air resistance compared to heavier materials.

Experiment Overview:

• Setup:
  A 4/6 paper square is released from a consistent height, and its motion is recorded for analysis using Tracker software.

• Procedure:

  1. Drop the 4/6 paper square under controlled conditions.
  2. Record the motion using high-speed video.
  3. Use Tracker software to analyze velocity, displacement, and stabilization patterns.
  4. Compare results with smaller-sized squares.

• Observation Points:

  • Time taken to achieve terminal velocity.
  • Stabilization behavior during descent.
  • Drag-induced variations in motion.

Questions to Consider:

1. How does the 4/6 square’s larger surface area influence terminal velocity?

   • Answer: Larger surface area increases drag, resulting in lower terminal velocity and a prolonged fall.

2. What patterns of instability are observed in the larger square?

   • Answer: Fluttering and oscillations may occur due to uneven air resistance and the large area exposed to airflow.

3. How does the descent behavior compare to smaller squares?

   • Answer: The larger square takes more time to stabilize and reach terminal velocity due to its increased drag.

4. Why is Tracker software essential for this analysis?

   • Answer: It provides detailed data on motion variables, enabling precise measurements of velocity, displacement, and stabilization behavior.

5. What other factors might affect the square's descent?

   • Answer: Environmental factors, initial orientation, and minor asymmetries in shape can influence motion.

Applications:

• Physics Education: Demonstrating the principles of air resistance and terminal velocity.
• Design Optimization: Insights can be applied to the development of drag-based devices like parachutes.
• Aerodynamics Research: Understanding motion behavior of flat, lightweight objects in airflow.

FAQ:

1. What makes the 4/6 paper square unique in this series?

   • Its larger size results in greater drag forces, lower terminal velocity, and more pronounced instability compared to smaller squares.

2. What challenges are associated with larger paper squares?

   • Stabilizing the descent and minimizing fluttering due to uneven drag distribution are key challenges.

3. How can the findings be applied to real-world scenarios?

   • Applications include designing parachutes, sails, and other devices where drag forces are critical.

4. What are the limitations of the experiment?

   • Variations in environmental conditions and achieving a perfect release can introduce inconsistencies.

5. Can the study be expanded?

   • Yes, by testing different shapes, materials, or analyzing the effects of airflow variations.