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- bouncing cart.mp4

Credits

Author: Leong Tze Kwang, Douglas Brown

Title: "Tracker Bouncing Cart Model by Leong Tze Kwang"

This document explores the physics of a bouncing cart using the Tracker software. It focuses on modeling energy transformations, momentum conservation, and the effects of elasticity during collisions. The model allows for detailed analysis of the motion and behavior of the cart in response to various impact scenarios.

Study Guide:

Objective:

• Investigate the dynamics of a bouncing cart, including the interaction of forces and the conservation principles governing its motion.
• Analyze the energy and momentum before and after collisions.

Key Concepts:

1. Elastic Collisions:

   • Collisions where kinetic energy and momentum are conserved.

2. Inelastic Collisions:

   • Collisions where some kinetic energy is lost, though momentum remains conserved.

3. Energy Transformations:

   • Potential energy converts to kinetic energy as the cart falls and vice versa after impact.

4. Momentum Conservation:

   • The total momentum of the system remains constant during the collision.

5. Damping and Repeated Bounces:

   • Energy loss due to air resistance, surface friction, and deformation reduces the height of successive bounces.

Experiment Overview:

• Setup:
  A cart is allowed to bounce off a surface, and its motion is tracked using Tracker software. Variables such as initial velocity, mass, and surface elasticity are controlled to observe their effects on the bouncing behavior.

• Procedure:

  1. Record the cart's motion using a high-speed camera or Tracker software.
  2. Identify key points: initial drop height, rebound height, velocities, and impact duration.
  3. Analyze the trajectories and calculate energy and momentum changes.

• Observation Points:

  • Peak height of each bounce.
  • Velocity before and after impact.
  • Energy lost in each collision.

Questions to Consider:

1. How does the initial height affect the number of bounces?

   • Answer: Higher initial heights increase potential energy, leading to more pronounced bounces, though energy loss limits the number of bounces.

2. What determines whether a collision is elastic or inelastic?

   • Answer: The material properties of the cart and surface, and whether kinetic energy is conserved.

3. How can we calculate the coefficient of restitution?

   • Answer: By measuring the ratio of rebound velocity to impact velocity: \( e = \frac{v_{rebound}}{v_{impact}} \).

4. Why do successive bounces lose height?

   • Answer: Energy dissipates due to factors like heat, sound, and deformation.

5. What real-world systems mimic this motion?

   • Answer: Basketballs bouncing on a court, pogo sticks, and damping systems in vehicles.

Applications:

• Understanding collision dynamics in sports.
• Designing shock absorbers and resilient materials.
• Exploring real-life examples of energy conservation and dissipation.

FAQ:

1. What tools are needed to replicate this study?

   • Tracker software, a high-speed camera, and a cart setup.

2. How does surface material affect the bounce?

   • Harder surfaces result in more elastic collisions with higher rebound heights. Softer surfaces dissipate more energy, reducing bounces.

3. What role does mass play in the experiment?

   • While mass affects the momentum, the ratio of rebound height to drop height is mass-independent, depending only on the coefficient of restitution.

4. Can this model simulate real-world damping systems?

   • Yes, by incorporating energy loss factors, it can approximate damping in vehicles or other mechanical systems.

5. How does Tracker software enhance this analysis?

   • It provides precise measurements of position, velocity, and time, enabling detailed motion analysis.