A formula to calculate the magnitude of the force

The most common formula for force is derived from Newton's Second Law, which states that the net force ($\vec{F}_{net}$) acting on an object is equal to the product of its mass ($m$) and its acceleration ($\vec{a}$).

$$\boxed{\vec{F}_{net} = m\vec{a}}$$

The magnitude of the force is $F_{net} = ma$.

• $m$: mass of the object (in kilograms, kg).
• $\vec{a}$: acceleration of the object (in meters per second squared, $\text{m/s}^2$).
• $\vec{F}_{net}$: net force (in Newtons, N).

Newton's Second Law can also be expressed as the rate of change of momentum. The net force ($\vec{F}_{net}$) acting on an object is equal to the change in its momentum ($\Delta \vec{p}$) over the change in time ($\Delta t$).

$$\boxed{\vec{F}_{net} = \frac{\Delta \vec{p}}{\Delta t}}$$

This can also be written as $\vec{F}_{net} = \frac{m\Delta \vec{v}}{\Delta t}$ or $\vec{F}_{net} = \frac{m(\vec{v}_f - \vec{v}_i)}{\Delta t}$.
The magnitude of the force is $F_{net} = \frac{\Delta p}{\Delta t}$.

• $\Delta \vec{p}$: change in momentum (in $\text{kg} \cdot \text{m/s}$).
• $\Delta t$: time interval over which the momentum changes (in seconds, s).
• $\vec{F}_{net}$: net force (in Newtons, N).