Force Calculator (Newton's Second Law)

How Force Is Calculated (Newton’s Second Law)

Newton’s Second Law of Motion is one of the most fundamental relationships in physics. It defines force as the product of mass and acceleration.

Force Formula: F = m × a

Where:

• F = force in Newtons (N)
• m = mass in kilograms (kg)
• a = acceleration in meters per second squared (m/s²)

Rearrangements:

• Acceleration: a = F / m
• Mass: m = F / a

1 Newton is defined as the force needed to accelerate 1 kg at 1 m/s².

Worked Example — Pushing a Car: A stalled car (1,500 kg) needs 300 N to overcome static friction and start rolling:

• Acceleration = F / m = 300 / 1,500 = 0.2 m/s²

To accelerate from 0 to 100 km/h (27.8 m/s) in 8 seconds:

• a = 27.8 / 8 = 3.47 m/s²
• F = 1,500 × 3.47 = 5,208 N (engine force minus drag)

Weight vs Mass: Weight is a force: W = m × g where g = 9.81 m/s² A 70 kg person weighs: 70 × 9.81 = 687 N

Force Scale Reference:

• Gravity on a 1 kg book: ~10 N
• Human bite force: ~700 N
• Hydraulic car press: 50,000–500,000 N
• Saturn V rocket thrust: ~33,400,000 N
• Earth’s gravity on Moon: ~2.0 × 10²⁰ N

Net Force: When multiple forces act on an object, use vector addition. Only the net (resultant) force causes acceleration.