F = ma, and the newton
Turning a ∝ F ÷ m into an equation needs a constant. The unit of force has been defined so that this constant is exactly one.
The newton (N)
The force needed to give unit mass (1 kg) unit acceleration (1 m s−2) is defined as one newton (1 N).
1 N = 1 kg m s−2
With the unit chosen that way the constant has the value 1, and Newton's second law can be written as:
The equation
F = m a
When a force is applied to an object, an acceleration is produced in it in the direction of that force.
Three ways to use it
One equation, used three ways depending on what you already know.
| Looking for | Formula | Unit |
|---|---|---|
| Force | F = m a | N |
| Acceleration | a = F ÷ m | m s−2 |
| Mass | m = F ÷ a | kg |
What a = F ÷ m tells you
Under a constant force, the greater an object's mass the smaller its acceleration, and the smaller its mass the greater its acceleration.
Which is why an empty cart is easier to push than a loaded one.