One law, three rearrangements
Newton's second law ties force, mass and acceleration together. Know any two and the third follows by rearranging the same equation.
Force is in newtons (N), mass in kilograms (kg), and acceleration in meters per second squared (m/s²). One newton is exactly the force that accelerates 1 kg at 1 m/s². Mass has to be greater than zero; a force of zero simply means no acceleration.
The same force, different masses
| Object | Mass | Force | Acceleration |
|---|---|---|---|
| Small car from rest | 1,200 kg | 6,000 N | 5 m/s² |
| Heavy truck | 8,000 kg | 40,000 N | 5 m/s² |
| Person in free fall | 70 kg | 687 N (gravity) | 9.81 m/s² |
| Tennis ball off a racket | 0.057 kg | 150 N | ~2,630 m/s² |
The car and truck reach the same acceleration, but the truck needs almost seven times the force because it has almost seven times the mass. Every 9.81 m/s² is one g.
Mass and weight are not interchangeable
- Mass is the amount of matter, measured in kilograms, and is the same everywhere.
- Weight is the gravitational force on that mass, W = m × g, measured in newtons, and changes with location.
- On the Moon a 70 kg person still has 70 kg of mass but weighs about 113 N instead of 687 N, because g is only 1.62 m/s².
Common questions
How do I find acceleration from force and mass?
Divide the force by the mass: a = F / m. A 50 N force on a 10 kg object gives 50 / 10 = 5 meters per second squared. Force must be in newtons and mass in kilograms for the answer to come out in m/s squared.
What happens to acceleration if I double the force?
Acceleration doubles, as long as the mass stays the same. Because a = F / m, the relationship is straight-line: twice the force gives twice the acceleration, half the force gives half.
Is weight the same as force in this equation?
Weight is a specific force, the pull of gravity, equal to mass times g. On Earth a 10 kg mass weighs about 98 N. In F = ma the F is whatever net force you apply, which may or may not be gravity.
