Lab 8: Linear Momentum

Lab 8: Linear Momentum Notes

Introduction to Linear Momentum

  • The law of conservation of linear momentum states that in a closed system with no external forces, the total linear momentum before and after any event (such as a collision) must be equal.
  • Historical evolution of momentum concepts:
    • Aristotle: Introduced the concept of impetus (weight x speed).
    • Jean Buridan (14th Century): Defined impetus.
    • René Descartes (1644): Introduced quantity of motion as size x speed.
    • John Wallis (1670): Coined the term 'momentum' and formulated the conservation law.
    • Isaac Newton: Unified quantity of motion and momentum; derived conservation law from his laws of motion.

Importance of Linear Momentum

  • Fundamental principle applicable in numerous fields of Physics:
    • Collisions
    • Fluid Dynamics
    • Electromagnetism
    • Relativity
    • Quantum Mechanics

Experimental Setup

Equipment Required
  • Air Track (2.0 m)
  • Variable Output Air Supply (SF-9216)
  • Air Track Accessory Kit (SF-9295)
  • Two Gliders (SF-6306)
  • Two Photogates (PS-2180)
  • PASPORT Digital Adapter (PS-2159)
  • 850 Universal Interface (UI-5000)
  • Two Magnetic Collision Attachments
  • Vernier Caliper
General Setup Instructions
  1. Preparing the Air Track:
    • Ensure the air track is level to minimize external forces from gravity.
    • Use a glider on the track to test levelness at multiple points.
  2. Preparing the Photogates:
    • Connect photogates and position them accurately along the track to measure the gliders' velocities.
  3. Preparing the Gliders:
    • Attach flags to gliders for photogate triggering, ensuring proper alignment.
  4. Setting Up Capstone Software:
    • Launch the Capstone app and configure settings for photogate data collection.

Theory on Momentum Conservation

Elastic Collisions
  • In elastic collisions, both momentum and kinetic energy are conserved.
    • Before impact: One glider is moving and the other is stationary.
    • Momentum Calculation:
    • Initial Momentum: p₀ = mₐvₐ₀ + mᵦvᵦ₀
    • Final Momentum: p_f = mₐvₐf + mᵦvᵦf
    • Percentage Lost: %pₗₒₛₜ = |p₀ − p_f| / |p₀| × 100
  • Kinetic Energy Calculation:
    • Before Collision: KE₀ = 1/2 mₐvₐ₀²
    • After Collision: KE_f = 1/2 mₐvₐf² + 1/2 mᵦvᵦf²
    • Energy Lost: %KElost = |KE₀ − KE_f| / |KE₀| × 100
Perfectly Inelastic Collisions
  • In perfectly inelastic collisions, bodies collide and combine, pouring kinetic energy into heat and sound.
    • Momentum: p₀ = mₐvₐ₀; p_f = (mₐ + mᵦ)vₐₗʹ
    • Energy calculations and loss percentages follow similar logic to elastic collisions.

Experimental Procedures

Setup A: Elastic Collision (Equal Masses)
  1. Attach magnets to both gliders for collision.
  2. Measure glider masses.
  3. Position gliders and initiate collision, measuring velocities.
  4. Repeat for accuracy and calculate average %pₗₒₛₜ and %KElost.
Setup B: Elastic Collision (Different Masses)
  • Similar to Setup A but with one glider heavier.
  • Two sub-procedures:
    • 5.2.1 Heavy glider against light glider
    • 5.2.2 Light glider against heavy glider
Setup C: Inelastic Collision (Equal Masses)
  • Replace magnetic attachments with needle and wax attachments.
  • Repeat collision process measuring momentum and energy losses.

Analysis

  • A complete lab report is required analyzing your findings and equations. This includes reviewing the experiments' outcomes regarding momentum and kinetic energy conservation under varied collision conditions.