Force formula (Newton's second law)
Newton's second law gives the force needed to accelerate a mass. Force equals mass times acceleration — the heavier the object or the faster you want to change its motion, the more force it takes.
What each symbol means
| Symbol | Meaning | Units |
|---|---|---|
| F | Force | newtons (N) |
| m | Mass | kilograms (kg) |
| a | Acceleration | meters per second squared (m/s²) |
Rearranged forms
Worked example
A 10 kg cart accelerates at 2 m/s². Find the force.
- Start from F = m a.
- Substitute m = 10 kg and a = 2 m/s².
- Multiply: F = 10 × 2.
Use SI units: kilograms, meters per second squared, and newtons. One newton accelerates one kilogram at one meter per second squared. Weight is a force too: W = m g, with g ≈ 9.81 m/s².
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How Newton's second law works
A net force changes an object's motion. The same force produces a large acceleration on a light object and a small one on a heavy object, which is why mass is called inertia — the resistance to being accelerated. Double the force and you double the acceleration; double the mass and you halve it.
Where it is used
F = m a is the workhorse of mechanics — vehicle acceleration and braking, structural and machine design, rocketry, and any problem involving motion under a force. It also leads to weight (W = m g) and to momentum and impulse.
FAQ
What is the force formula?
F = m a: force equals mass times acceleration. Rearranged, m = F / a and a = F / m.
What are the units of force?
Newtons (N) in SI. One newton equals one kg·m/s², the force that accelerates a one-kilogram mass at one meter per second squared.
Is weight the same as force?
Weight is the force of gravity on a mass: W = m g, with g about 9.81 m/s² on Earth. A 10 kg mass weighs about 98 N.