Impulse and Momentum Lecture Summary

Sep 28, 2024

Take quiz

Lecture Notes: Impulse and Momentum

Key Formulas

  1. Momentum

    • Formula: ( \text{Momentum} (p) = \text{mass} (m) \times \text{velocity} (v) )
    • Properties:
      • Momentum is a vector.
      • Mass is a scalar.
      • Velocity is a vector.
      • Example: A 10 kg block moving at 6 m/s has a momentum of 60 kg m/s.

  2. Impulse

    • Formula: ( \text{Impulse} (J) = \text{Force} (F) \times \text{Time} (\Delta t) )
    • Example: Applying 100 N force for 8 seconds results in an impulse of 800 N路s.
    • Impulse indicates how much force is applied over a period of time.

  3. Impulse-Momentum Theorem

    • Formula: ( F \Delta t = m \Delta v )
    • Relationship: Impulse equals the change in momentum.

  4. Force from Fluid Dynamics

    • Formula: ( F = \text{mass flow rate} (\frac{\Delta m}{\Delta t}) \times \text{velocity} (v) )
    • Example: A water hose with a mass flow rate of 5 kg/s and water speed of 20 m/s exerts 100 N force.

  5. Force as a Derivative of Momentum

    • Formula: ( F(t) = \frac{d}{dt}(\text{momentum}) )
    • Applicable to calculus-based physics.

Conservation of Momentum

  1. Conservation Law

    • Formula: ( m_1v_1 + m_2v_2 = m_1v_1' + m_2v_2' )
    • Applies when no external forces act on the system.
    • Inelastic Collision:
      • Objects stick together, only momentum conserved.
      • Formula: ( (m_1 + m_2) \times v_f ) when they move at the same final speed.

  2. Elastic Collision

    • Both kinetic energy and momentum are conserved.
    • Use equation 7 for conservation of momentum.
    • System of Equations:
      • If final speeds are unknown, use both momentum and energy conservation equations.
      • Simplified formula: ( v_1 + v_1' = v_2 + v_2' )

Additional Notes

  • For inelastic collisions: Momentum is conserved but kinetic energy is not.
  • For elastic collisions: Both momentum and kinetic energy are conserved.
  • Practice problems and tests are available in linked resources.

Conclusion

These are the main equations for impulse, momentum, and collision types discussed in the lecture. Review these concepts and formulas ahead of exams, and consult additional resources for practice problems.