Library / Foundations: Physics / FPH-06
Foundations: Physics
Average force from momentum change
Force needed to change momentum in a given time.
- Ref
- FPH-06
- Rev
- v1
- Field
- Foundations: Physics
- Result
- F [N]
The impulse FΔt equals the change in momentum. Use the same direction for u and v.
Changing momentum takes a force acting over time; a shorter time means a much bigger force.
Calculator
- Impulse FΔt4.8 N·s
- Force as multiple of weight611.8 ×
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Crumple zones, airbags and padding all lengthen the stopping time to reduce the force.
- The force is an average; peak force during impact can be much larger.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (N) | Local step | Change in result |
|---|---|---|---|---|---|---|
| m Mass | 0.001 to 100 kg | 6 | 600,000 | 600,000 | +10% | +10 % |
| Δt Contact time | 0.5 to 100 ms | 48 | 9,600 | 9,552 | +10% | −9.09 % |
| v Final velocity | 21 to 100 m/s | 672 | 3,200 | 2,528 | +10% | +10 % |
| u Initial velocity | 0 to 20 m/s | 320 | 960 | 640 | +10% | 0 % |
Sweep of Contact time
| Contact time (ms) | Average force (N) |
|---|---|
| 0.5 | 9,600 |
| 0.9696 | 4,950 |
| 1.88 | 2,553 |
| 3.646 | 1,316 |
| 7.071 | 678.8 |
| 13.71 | 350 |
| 26.59 | 180.5 |
| 51.57 | 93.08 |
| 100 | 48 |
Sweep one variable
Variables and how each one contributes
Average force
What the equation gives you. Everything else feeds it.
Mass
Mass of the object. Directly proportional.
Initial velocity
Velocity before. Reduces the change.
Final velocity
Velocity after. Increases the change.
Contact time
Duration of the force. Inversely proportional: doubling the time halves the force.
Worked example with the values above
- Change in momentum: m(v − u) = 0.16 × 30 = 4.8 kg·m/s.
- Time in seconds: 5 ms = 0.005 s.
- F = 4.8 / 0.005 = 960 N.
Assumptions and limits
- Constant mass.
- Force averaged over the contact time.
Common mistakes
- Leaving time in milliseconds.
- Wrong sign for a rebound.
Statistics and uncertainty
Contact time is hard to measure and short, so it dominates the uncertainty; a ±1 ms error on 5 ms is ±20% on the force.
Where it is used
- Impact and recoil loads.
- Protection and padding design.
Maths you need
- Momentum: p = mv
- Newton’s second law: F = Δp/Δt