Physics

1.11 - Momentum & Force

6 min

Changing momentum

Force and momentum

Second worked example

Car safety

note 1 of 2

Force as the rate of change of momentum

$F = \frac{Δ (m v)}{Δ t}$

For a given change in momentum, the longer the time taken, the smaller the force.

note 2 of 2

A car of mass 1,200 kg slows from 15 m/s to 10 m/s in 10 s. Calculate the resultant force on the car.

$\begin{matrix} Δ (m v) & = (1,200 \times 10) - (1,200 \times 15) \\ = - 6,000 kg m/s \end{matrix}$

$F = \frac{Δ (m v)}{Δ t} = \frac{- 6,000}{10} = - 600 N$

The resultant force on the car is 600 N. The minus sign shows that it acts against the car's motion, which is why the car slows down.

end of notes

Force as the rate of change of momentum

A resultant force causes an object's momentum to change.

The resultant force equals the rate of change of momentum.

Formula for force and change of momentum

$F = \frac{Δ (m v)}{Δ t}$

Where:

F

= Resultant force, in newtons (N)

Δ (m v)

= Change in momentum, in kilogram metres per second (kg m/s)

Δ t

= Time taken for the change, in seconds (s)

For a given change in momentum, the longer the time taken, the smaller the force.