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How It Works
Impulse (J = F · Δt) measures the effect of a force applied over time, while momentum (p = m · v) measures an object's motion. The impulse-momentum theorem connects them: the impulse on an object equals its change in momentum. This is why airbags work — they increase the collision time, reducing the peak force on the body.
Example Problem
A 0.145 kg baseball is pitched at 40 m/s and hit back at 50 m/s. The bat contacts the ball for 0.001 s. What average force does the bat exert?
- Δp = 0.145 × (50 − (−40)) = 0.145 × 90 = 13.05 N·s
- F = 13.05 / 0.001 = 13,050 N
Frequently Asked Questions
What is the difference between impulse and momentum?
Momentum is a property of a moving object (p = mv). Impulse is the change in momentum caused by a force over time (J = F·Δt). They have the same units (N·s or kg·m/s).
Why do airbags reduce injury in a crash?
Airbags increase the time over which momentum changes. Since J = F·Δt, a longer Δt means a smaller average force on the occupant for the same impulse.
Is momentum conserved in all collisions?
Yes, total momentum is always conserved in a closed system (no external forces). Kinetic energy, however, is only conserved in perfectly elastic collisions.
Related Calculators
- Force Equation Calculator — calculate force from mass and acceleration.
- Kinetic Energy Calculator — find the energy of a moving object.
- Work Calculator — compute work from force and displacement.
- Newton's Second Law Calculator — the foundation of the impulse-momentum theorem.
- Projectile Motion Calculator — analyze motion where impulse from gravity drives the trajectory.
- Mass Unit Converter — convert between kilograms, pounds, slugs, and other mass units.
Reference: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.