Overview
This lecture introduces the concepts of impulse and linear momentum, focusing on how forces applied over time can change an object's momentum and how to calculate related quantities.
Forces Varying Over Time
- Many real-world forces (e.g., bat hitting a baseball) are not constant but act over short time intervals.
- The actual force during contact varies, typically rising to a peak then dropping to zero.
- Average force during a time interval is used to simplify calculations.
Impulse
- Impulse (J) is defined as the product of average force and the time interval it acts: J = F̅ × Δt.
- Impulse is a vector with the same direction as the average force.
- Units: Newton-seconds (N·s).
- Impulse describes how the velocity of an object changes due to a force acting over a time period.
Linear Momentum
- Linear momentum (p) is defined as the product of an object's mass and its velocity: p = m × v.
- Linear momentum is a vector in the same direction as velocity.
- Units: kilogram-meters per second (kg·m/s).
Impulse-Momentum Theorem
- The impulse-momentum theorem states: J = Δp = p_f − p_i (impulse equals change in momentum).
- This theorem links the net force acting over time to the change in an object's momentum.
- A greater impulse (more force or longer contact) causes a greater change in velocity.
Example Problems
- Example: Raindrops hitting a car roof and coming to rest—calculate average force using impulse-momentum theorem.
- Given mass of rain per second and initial/final velocities, average force is F̅ = (Δm/Δt) × (v_f − v_i).
- For raindrops that stop, change in velocity is large; for hail that bounces, change is even larger, resulting in greater force.
Key Terms & Definitions
- Impulse (J) — Average force times the time interval it acts: J = F̅ × Δt.
- Linear Momentum (p) — Mass times velocity: p = m × v.
- Impulse-Momentum Theorem — Impulse equals change in momentum: J = Δp = p_f − p_i.
- Average Force (F̅) — The mean value of a force exerted over a specific time interval.
Action Items / Next Steps
- Practice applying the impulse-momentum theorem to different collision scenarios.
- Try example calculations involving both stopping and bouncing objects.