Library / Fundamentals / FUN-01
Fundamentals
Newton’s second law
Force needed to give a mass a stated acceleration.
- Ref
- FUN-01
- Rev
- v1
- Field
- Fundamentals
- Result
- F [kN]
F in newtons (N), m in kilograms (kg), a in metres per second squared (m/s²). For a body of constant mass in an inertial frame, with a the acceleration of its centre of mass.
The net force on an object equals its mass times its acceleration. A heavier object needs a bigger force to speed up, slow down or change direction at the same rate.
Calculator
- Acceleration in g0.3059 g
- Force ÷ weight, F/(mg)0.3059
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.
- Force is linear in both mass and acceleration, so the sweep chart is a straight line through the origin.
- Dividing the force by the weight mg gives the acceleration in g, a quick way to judge how hard a manoeuvre is on a person or a structure.
- F is the net force. Friction, drag and gravity all have to be included in the sum before comparing with ma.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kN) | Local step | Change in result |
|---|---|---|---|---|---|---|
| a Acceleration | 0.5 to 30 m/s² | 0.6 | 36 | 35.4 | +10% | +10 % |
| m Mass | 100 to 5,000 kg | 0.3 | 15 | 14.7 | +10% | +10 % |
Sweep of Acceleration
| Acceleration (m/s²) | Net force (kN) |
|---|---|
| 0.5 | 0.6 |
| 0.8341 | 1.001 |
| 1.392 | 1.67 |
| 2.322 | 2.786 |
| 3.873 | 4.648 |
| 6.461 | 7.753 |
| 10.78 | 12.93 |
| 17.98 | 21.58 |
| 30 | 36 |
Sweep one variable
Variables and how each one contributes
Net force
What the equation gives you. Everything else feeds it.
Mass
The mass being accelerated (constant mass assumed). Directly proportional: doubling the mass doubles the force needed for the same acceleration.
Acceleration
Rate of change of velocity of the centre of mass. Directly proportional: doubling the acceleration doubles the force.
Worked example with the values above
- Units: kilogram × metre per second squared = newton.
- F = ma = 1,200 kg × 3 m/s² = 3,600 N.
- In kilonewtons the net force is 3.6 kN.
Assumptions and limits
- Constant mass (for a rocket or a leaking tank use F = d(mv)/dt).
- An inertial reference frame, not an accelerating one.
- Speeds well below the speed of light.
Common mistakes
- Using the applied force instead of the net force after friction and drag are subtracted.
- Using grams or tonnes without converting to kilograms.
- Confusing mass (kg) with weight (N).
Statistics and uncertainty
The law is exact within its assumptions. If m and a are measured, independent relative errors combine as δF/F ≈ √[(δm/m)² + (δa/a)²]. Acceleration is usually the noisier measurement, so it normally dominates.
Where it is used
- Sizing vehicle brakes, launcher rails and catapults.
- Estimating loads on mountings for equipment under acceleration.
- Starting point for almost every dynamics problem.
Maths you need
- Units and prefixes: kg, m and s; convert before substituting
- Vectors: force and acceleration point the same way