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- atwoodmachine 3 mass.mp4

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Author: Leong Tze Kwang

Document Brief: Title: "Atwood Machine 3 Dynamics: A Tracker Model by Leong Tze Kwang"

This document explores the motion of an advanced Atwood machine setup, analyzed using Tracker software. The study investigates additional complexities such as pulley mass, rotational inertia, and non-negligible string mass, offering a comprehensive look at real-world deviations from the ideal Atwood machine.

Study Guide:

Objective:

• Analyze the dynamics of a complex Atwood machine.

• Use Tracker to measure and model the motion of the system, incorporating additional factors.

Key Concepts:

1. Newton’s Second Law with Rotational Dynamics:

   • Net force = mass × acceleration (F = ma).

   • Rotational inertia and torque are included for the pulley.

2. Tension in the String:

   • The string transmits force between the masses and the pulley, and its mass affects the system.

3. Rotational Inertia of the Pulley:

   • The pulley’s moment of inertia contributes to the dynamics and affects acceleration.

4. Energy Conservation with Rotational Kinetic Energy:

   • Potential energy transforms into both linear and rotational kinetic energy.

Experiment Setup:

• Materials:

  • Atwood machine setup with measurable pulley mass.

  • High-speed camera or smartphone for video recording.

  • Tracker software for motion analysis.

• Procedure:

  1. Assemble the Atwood machine with known masses and a measurable pulley.

  2. Ensure the string is uniform and its mass is measured.

  3. Release the masses from rest and record their motion.

  4. Import the video into Tracker.

  5. Analyze displacement, velocity, and acceleration over time for each mass.

Expected Observations:

• Acceleration is reduced compared to the ideal model due to the pulley’s inertia and string mass.

• Energy conservation includes rotational kinetic energy of the pulley.

• Tensions in the string may differ slightly on either side of the pulley.

Questions to Consider:

1. How does pulley mass affect the acceleration of the system?

   • Answer: Pulley mass introduces rotational inertia, reducing the net acceleration.

2. What role does string mass play?

   • Answer: String mass adds to the system’s total inertia and can alter tension calculations.

3. What assumptions are made in this experiment?

   • Answer: The string is inextensible, and friction at the pulley is minimal.

4. Can energy conservation be observed with rotational effects?

   • Answer: Yes, energy transforms into linear and rotational kinetic forms.

5. How do unequal string tensions arise?

   • Answer: Pulley inertia and string mass can cause slight differences in tension on either side.

FAQ:

1. Why study a more complex Atwood machine?

   • It demonstrates real-world dynamics and helps refine theoretical models by including rotational and inertial effects.

2. How accurate is Tracker for this analysis?

   • Tracker provides precise measurements for displacement and velocity, aiding in detailed motion analysis.

3. What improvements can reduce experimental error?

   • Use a lightweight, uniform string and a high-precision pulley with minimal friction.

4. How does the pulley’s rotational inertia impact energy conservation?

   • It adds a rotational kinetic energy term, slightly altering the system’s energy distribution.

5. Can this model accommodate more complex setups?

   • Yes, additional factors like varying string elasticity or multiple pulleys can be included for advanced analysis.

Would you like detailed equations or simulations for this enhanced model?

The cart are 0.2, 0.3, 0.4 kg respectively.
The same mass are suspended from the pulley.
Why are the forces different?
What is the mass being suspended?

A: Tension is reduced when mass is accelerated. mass is 100 g.

Author: Leong Tze Kwang