Impulse and Momentum - Formulas and Equations - College Physics

Introduction

This tutorial covers the essential concepts of impulse and momentum as presented in the video by The Organic Chemistry Tutor. Understanding these concepts is crucial for physics students, especially when preparing for exams. We will explore key formulas, the relationship between impulse and momentum, and their applications in collisions.

Step 1: Understand Momentum

• Definition: Momentum is defined as mass times velocity.
• Formula: [ p = m \cdot v ] Where:
  • ( p ) is momentum (in kg·m/s)
  • ( m ) is mass (in kg)
  • ( v ) is velocity (in m/s)
• Example: For a block with a mass of 10 kg moving at 6 m/s:
  • Momentum ( p = 10 , \text{kg} \times 6 , \text{m/s} = 60 , \text{kg·m/s} )

Step 2: Learn About Impulse

• Definition: Impulse is the product of force and the time duration over which it acts.
• Formula: [ J = F \cdot \Delta t ] Where:
  • ( J ) is impulse (in N·s)
  • ( F ) is force (in Newtons)
  • ( \Delta t ) is time (in seconds)
• Example: If a force of 100 N is applied for 8 seconds:
  • Impulse ( J = 100 , \text{N} \times 8 , \text{s} = 800 , \text{N·s} )

Step 3: Connect Impulse and Momentum

• Impulse-Momentum Theorem: Impulse is equal to the change in momentum.
• Formula: [ J = \Delta p = m \cdot \Delta v ] Where:
  • ( \Delta p ) is the change in momentum.
  • ( \Delta v ) is the change in velocity.
• Key Relationship: This theorem shows how forces applied over time change an object's momentum.

Step 4: Explore Mass Flow Rate and Force

• Mass Flow Rate: The mass of fluid passing through a section per unit time.
• Formula for Force from Mass Flow Rate: [ F = \dot{m} \cdot v ] Where:
  • ( \dot{m} ) is the mass flow rate (in kg/s)
  • ( v ) is the velocity of the fluid (in m/s)
• Example: If water flows from a hose at 5 kg/s and exits at 20 m/s:
  • Force ( F = 5 , \text{kg/s} \times 20 , \text{m/s} = 100 , \text{N} )

Step 5: Understand Conservation of Momentum

• Definition: In a closed system with no external forces, the total momentum before a collision is equal to the total momentum after the collision.
• Formula: [ m_1 \cdot v_{1i} + m_2 \cdot v_{2i} = m_1 \cdot v_{1f} + m_2 \cdot v_{2f} ]
• Inelastic Collisions: Objects stick together, and only momentum is conserved. The final speed can be simplified to: [ (m_1 + m_2) \cdot v_f ]

Step 6: Analyze Elastic Collisions

• Elastic Collisions: Both momentum and kinetic energy are conserved.
• Equations Used:
  • Conservation of Momentum: Same as above.
  • Conservation of Energy: [ KE_{initial} = KE_{final} ]
• Simplified Equation: If you're missing final speeds: [ v_{1i} + v_{1f} = v_{2i} + v_{2f} ]

Conclusion

This tutorial provided a comprehensive overview of impulse and momentum, including their definitions, formulas, and applications in different types of collisions. Mastery of these concepts is essential for solving physics problems effectively. For practice, consider reviewing example problems related to these topics, which can be found in additional resources or practice tests.