Overview
This lecture reviews essential formulas and concepts for impulse and momentum, including key equations, conservation laws, and problem-solving approaches for collisions.
Momentum
- Momentum (p) is mass (m) times velocity (v): p = m·v, and it is a vector quantity.
- Units for momentum are kg·m/s.
Impulse
- Impulse (J or I) is force (F) applied over a time interval (Δt): J = F·Δt.
- Units for impulse are Newton-seconds (N·s).
- Impulse measures how much force is applied for how long.
Impulse-Momentum Theorem
- Impulse equals change in momentum: F·Δt = m·Δv.
- The theorem connects force, time, mass, and velocity changes during an event.
Force from Mass Flow (Fluids)
- Force exerted by a fluid: F = mass flow rate (Δm/Δt) times velocity (v), F = (Δm/Δt)·v.
- Example: Water leaving a hose at mass flow rate 5 kg/s and speed 20 m/s yields force 100 N.
Force as Rate of Change of Momentum (Calculus)
- Force can be written as the time derivative of momentum: F(t) = dp/dt.
Conservation of Momentum
- Total momentum before a collision equals total momentum after, if no external forces act: m₁v₁ + m₂v₂ = m₁v₁’ + m₂v₂’.
- In inelastic collisions (objects stick together), only momentum is conserved, not kinetic energy.
- For inelastic collision where objects stick: (m₁ + m₂)·v_f = m₁v₁ + m₂v₂.
Elastic Collisions
- In elastic collisions, both momentum and kinetic energy are conserved.
- Use momentum and energy equations to solve for unknowns in elastic collisions.
- Shortcut equation: v₁ + v₁’ = v₂ + v₂’ for perfectly elastic collisions.
Key Terms & Definitions
- Momentum (p) — Mass in motion, calculated as mass times velocity.
- Impulse (J) — Product of force and time interval, representing change in momentum.
- Mass Flow Rate — Mass passing through a point per unit time (kg/s).
- Elastic Collision — Collision where kinetic energy and momentum are conserved.
- Inelastic Collision — Collision where only momentum is conserved; objects may stick together.
Action Items / Next Steps
- Memorize the main formulas listed above.
- Practice example problems on impulse, momentum, and collisions.
- Review conservation of momentum and kinetic energy concepts for upcoming exams.