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Force is a push or pull that changes the state of motion of an object. Newton's second law of motion provides the quantitative relationship: F = ma, where net force (F) equals mass (m) times acceleration (a). This single equation is the cornerstone of classical mechanics and explains everything from rockets launching to cars braking.
Force is measured in Newtons (N): 1 N is the force required to accelerate a 1 kg mass at 1 m/s². When multiple forces act on an object, the net force is their vector sum. It is the net force — not any individual force — that determines the acceleration.
Weight is a specific force: the gravitational pull on an object's mass. Weight W = mg, where g = 9.81 m/s² on Earth's surface. A 70 kg person weighs 70 × 9.81 ≈ 686.7 N on Earth but only about 114 N on the Moon (g_Moon ≈ 1.62 m/s²). Mass is intrinsic and unchanged by location; weight varies with gravitational field strength.
Worked example: A 1200 kg car must slow from 25 m/s to 0 in 5 seconds (emergency stop). Acceleration a = (0−25)/5 = −5 m/s². Required braking force F = 1200 × 5 = 6000 N in the direction opposing motion.
F = ma | W = mg
F = m × a
Newton's Laws of Motion
1st Law (Inertia)
An object remains at rest or in uniform motion unless acted on by a net force.
2nd Law (F = ma)
The acceleration of an object is proportional to the net force and inversely proportional to its mass.
3rd Law (Action-Reaction)
For every action there is an equal and opposite reaction.
| Formula | Solve For |
|---|---|
| F = ma | Force (N) |
| m = F/a | Mass (kg) |
| a = F/m | Acceleration (m/s²) |
| W = mg | Weight (N), g = 9.81 m/s² |
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.