Impulse and Momentum Review

Key Concepts

• Momentum:

  • Defined as mass times velocity.
  • Momentum is a vector, mass is scalar, velocity is a vector.
  • Formula: ( p = m \times v )
  • Example: A 10 kg block moving at 6 m/s has a momentum of 60 kg·m/s.

• Impulse:

  • Calculated as force multiplied by time.
  • Impulse can be represented by the letter "J" or "I".
  • Formula: ( J = F \times \Delta t )
  • Units: Newton-seconds (N·s)
  • Example: A force of 100 N applied for 8 seconds results in an impulse of 800 N·s.

Relationship between Impulse and Momentum

• Impulse-Momentum Theorem:
  • Impulse is equal to the change in momentum.
  • Derived from Newton’s Second Law: ( F = m \times a )
  • With acceleration as the change in velocity over time, ( a = \frac{\Delta v}{\Delta t} )
  • Impulse-Momentum formula: ( F \times \Delta t = m \times \Delta v )

Additional Equations

• Force by Mass Flow Rate:

  • Applied in scenarios like water flowing out of a hose.
  • Formula: ( F = \dot{m} \times v )
  • Example: Water at a flow rate of 5 kg/s and speed of 20 m/s exerts a force of 100 N.

• Force as Rate of Change of Momentum:

  • For calculus applications: ( F(t) = \frac{d}{dt}(mv) )

Conservation of Momentum

• Inelastic Collisions:

  • Momentum conserved, kinetic energy not conserved.
  • Objects stick together post-collision.
  • Formula: ( m_1v_1 + m_2v_2 = (m_1 + m_2)v_f )

• Elastic Collisions:

  • Both momentum and kinetic energy are conserved.
  • Use the conservation of momentum and energy equations.
  • Simplified formula for perfectly elastic collisions: ( v_1 + v_1' = v_2 + v_2' )

Key Equations to Remember

1. ( p = m \times v )
2. ( J = F \times \Delta t )
3. ( F \times \Delta t = m \times \Delta v )
4. ( F = \dot{m} \times v )
5. ( F(t) = \frac{d}{dt}(mv) )
6. ( m_1v_1 + m_2v_2 = m_1v_1' + m_2v_2' )
7. ( v_1 + v_1' = v_2 + v_2' )

Additional Resources

• Practice problems and tests available via links in the video description.