Notes on Impulse and Momentum

Overview

• Quick review of impulse and momentum.
• Key formulas to pass the upcoming exam.
• Links to example problems and practice test in the description.

Key Formulas

1. Momentum

   • Formula: Momentum = Mass x Velocity
   • Units: kg·m/s
   • Example: A 10 kg block moving at 6 m/s
     • Momentum = 10 kg x 6 m/s = 60 kg·m/s
     • Concept: Momentum is mass in motion.

2. Impulse

   • Formula: Impulse = Force x Time
   • Can be represented as J or I
   • Example: 100 N applied for 8 s
     • Impulse = 100 N x 8 s = 800 N·s
     • Concept: Impulse measures force applied over time.

3. Impulse-Momentum Theorem

   • Formula: Impulse = Change in Momentum
   • Derived from:
     • F = m·a (Newton's second law)
     • a = (v_final - v_initial) / t
     • Impulse (F·Δt) = m·Δv (change in momentum)

4. Force from Fluid Flow

   • Formula: Force = Mass Flow Rate x Velocity
   • Example: Water hose with mass flow rate of 5 kg/s and velocity of 20 m/s
     • Force = 5 kg/s x 20 m/s = 100 N
     • Applicable to fluids like water or air.

5. Force as Rate of Change of Momentum

   • Formula: Force = d(Momentum)/dt
   • If momentum is a function of time, this gives the force acting on the object.

Conservation of Momentum

• Applies to inelastic collisions where two objects stick together.
• Total momentum before collision = Total momentum after collision.
• Only valid with no external forces acting on the system.

Inelastic Collision Example

• If M1 (mass of block 1) moving at 2 m/s collides with block 2:
  • Momentum before = m1v1 + m2v2
  • Momentum after = (m1 + m2) * v_final
  • Use this formula if they stick together.

Elastic Collision Example

• If two balls bounce off each other:
  • Use conservation of momentum and energy.
  • Total initial energy = Total final energy.
  • If unknown speeds, use system of equations.

Special Equations for Elastic Collisions

• Equation 10: v1 + v1_final = v2 + v2_final
• Use when both final speeds are unknown.

Summary

• Key equations for impulse, momentum, elastic and inelastic collisions covered.
• Additional resources available for practice problems.
• Encourage viewing other videos for more examples.