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1/6 Paper Square Drag to Terminal Velocity SYPT2016 by Tze Kwang Leong"

This document explores the aerodynamic behavior of a 1/6 paper square as it falls through air, analyzing drag forces and terminal velocity. Using Tracker software, the study visualizes motion data to understand how shape, air resistance, and gravity interact to determine the terminal velocity of lightweight objects.

Study Guide:

Objective:

• Investigate the motion of a paper square as it falls and reaches terminal velocity.
• Analyze the impact of air resistance and shape on the motion dynamics.

Key Concepts:

1. Drag Force:

   • Air resistance opposing the motion, proportional to velocity squared at high speeds.

2. Terminal Velocity:

   • The constant speed achieved when drag force equals gravitational force.

3. Shape and Surface Area:

   • Wider surfaces experience more drag, influencing the time taken to reach terminal velocity.

4. Free Fall Dynamics:

   • The transition from acceleration to constant speed under gravitational force.

Experiment Overview:

• Setup:
  A 1/6 paper square is dropped from a height, and its motion is recorded using high-speed video and analyzed with Tracker software.

• Procedure:

  1. Release the paper square from a controlled height.
  2. Record the fall with a focus on the transition to terminal velocity.
  3. Use Tracker to measure position, velocity, and acceleration over time.
  4. Repeat the experiment with different orientations or initial disturbances.

• Observation Points:

  • Time to reach terminal velocity.
  • Velocity profile over the fall.
  • Effects of shape and disturbances on stability and drag.

Questions to Consider:

1. What is the relationship between drag force and velocity?

   • Answer: Drag force increases with the square of velocity, balancing gravitational force at terminal velocity.

2. How does the shape affect the motion?

   • Answer: A larger surface area increases drag, reducing terminal velocity and causing potential fluttering or instability.

3. What factors influence terminal velocity?

   • Answer: Mass, surface area, and air density play key roles.

4. How does the paper's orientation affect its descent?

   • Answer: Irregular orientations can create unstable drag forces, leading to oscillatory or tumbling motion.

5. How does Tracker software enhance this study?

   • Answer: Tracker provides precise velocity and acceleration data, allowing for detailed analysis of the motion dynamics.

Applications:

• Physics Education: Demonstrating fundamental principles of drag and terminal velocity.
• Aerodynamics Research: Insights into air resistance on flat surfaces.
• Engineering Design: Optimizing lightweight materials for controlled descent or stability.

Theory

the equation for the drag force on the square paper is may be assumed to be is the form of \( F = \frac{1}{2} \rho v^{2} C_{D} A \)

where F is the aerodynamic drag force

\( \rho \) is the is the density of the fluid

\( v \) is the speed of the object relative to the fluid

\( A \) is the cross sectional area

\( C_{D} \)  is the drag coefficient – a dimensionless number.

Data

Version

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

FAQ:

1. Why study a paper square's fall?

   • It provides a simple yet rich example of drag and terminal velocity, concepts relevant to many fields of physics and engineering.

2. What challenges might arise in this experiment?

   • Capturing stable motion data and controlling external factors like air currents.

3. Can the results be applied to other objects?

   • Yes, the principles of drag and terminal velocity are universal, though specific values depend on object properties.

4. How does this study relate to real-world applications?

   • Understanding drag is crucial for parachute design, wind resistance analysis, and lightweight material development.

5. What additional studies could complement this research?

   • Varying paper sizes, masses, or testing in controlled wind tunnels for enhanced insights.