Impulse Formula
The impulse formula J = FΔt calculates the change in momentum from a force applied over time.
Key to collision analysis.
The Formula
Impulse is the product of force and the time interval over which it acts. It equals the change in momentum of the object.
Variables
| Symbol | Meaning |
|---|---|
| J | Impulse (measured in Newton-seconds, N·s, or kg·m/s) |
| F | Average force applied (measured in Newtons, N) |
| Δt | Time interval during which the force acts (measured in seconds, s) |
| Δp | Change in momentum (measured in kg·m/s) |
| m | Mass of the object (measured in kilograms, kg) |
| Δv | Change in velocity (measured in meters per second, m/s) |
Example 1
A baseball (0.145 kg) is hit by a bat. It goes from -40 m/s (pitched) to +50 m/s (hit). What impulse was applied?
Calculate change in velocity: Δv = 50 - (-40) = 90 m/s
Apply the formula: J = mΔv = 0.145 × 90
J = 13.05 N·s
Example 2
If the bat contact lasted 0.001 seconds, what was the average force on the ball?
Rearrange: F = J / Δt = 13.05 / 0.001
F = 13,050 N (about 2,934 lbs of force — enormous but brief)
Example 3
A car airbag extends the collision time from 0.01s to 0.15s. If the impulse is 9,000 N·s, compare the forces.
Without airbag: F = 9,000 / 0.01 = 900,000 N
With airbag: F = 9,000 / 0.15 = 60,000 N
The airbag reduces the force by 15 times — from 900,000 N to 60,000 N
When to Use It
Use the impulse formula for problems involving forces that act over short time periods.
- Analyzing collisions between objects (cars, balls, particles)
- Understanding how safety devices work (airbags, crumple zones, helmets, padding)
- Calculating the force of impact during sports (bat hitting ball, foot kicking ball)
- Rocket propulsion — the impulse from exhaust determines thrust
- Any situation where you need to relate force, time, and change in motion