Force vs Time Impact Comparison
About This Chart
This visualization demonstrates a fundamental principle of the impulse-momentum theorem: the same change in momentum (impulse) can be achieved with either a large force acting briefly, or a smaller force acting over a longer time.
Key Equations
Impulse-Momentum Theorem: \(\(J = F \cdot \Delta t = \Delta p\)\)
For the same change in momentum: \(\(F_1 \cdot \Delta t_1 = F_2 \cdot \Delta t_2\)\)
Scenarios Compared
| Scenario | Duration | Peak Force | Impulse |
|---|---|---|---|
| Concrete Wall | 0.1 s | 60,000 N | 6,000 N·s |
| Crumple Zone + Airbag | 0.5 s | 12,000 N | 6,000 N·s |
Visual Elements
- Solid curves: Force vs time (left y-axis)
- Dashed curves: Cumulative impulse (right y-axis)
- Red: Hard collision scenario
- Green: Soft collision with safety features
Key Insight
Both curves reach the SAME final impulse (6,000 N·s) because both scenarios produce the same change in momentum. However:
- 5× longer time → 5× lower peak force
This is exactly why car safety features work:
- Airbags: Increase the time your head decelerates
- Crumple zones: Extend the time the car takes to stop
- Seat belts: Distribute force over a larger area AND time