Physics

6.2 - Momentum - Force & Impulse

7 min

Changing momentum

Force and momentum

Second worked example

Car safety

note 1 of 4

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.

note 2 of 4

Worked example - Resultant force from a change in momentum

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.

The same car drawn twice, the left one labelled mass = 1,200 kg and speed = 15 m/s, the right one speed = 10 m/s, with an arrow between them marked 10 s.

Step 1 - Find the change in momentum

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

Step 2 - Divide the change in momentum by the time taken

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

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.

note 3 of 4

Impulse

The impulse of a force is the force multiplied by the time for which it acts.
Impulse is equal to the change of momentum it produces.

Formula for impulse

$Impulse = F Δ t = Δ (m v)$

Where:

Impulse is in newton seconds (N s)
$F$ = Force, in newtons (N)
$Δ t$ = Time for which the force acts, in seconds (s)
$Δ (m v)$ = Change of momentum, in kilogram metres per second (kg m/s)

Applying a force for a longer time gives a greater impulse, producing a greater change of momentum.

note 4 of 4

Worked example - Calculating an impulse

A golf club strikes a golf ball, applying an average force of 4,000 N for a time of 0.50 ms. Calculate the impulse applied to the ball.

Step 1 - Convert the time to seconds

0.50 ms = 0.00050 s

Step 2 - Multiply the force by the time

$\begin{matrix} Impulse & = F Δ t \\ = 4,000 \times 0.00050 \\ = 2.0 N s \end{matrix}$

The impulse applied to the ball is 2.0 N s.

key terms

TermDefinition

ImpulseThe force acting on an object multiplied by the time for which it acts.

end of notes

Key points to remember

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7.1 - Energy StoresNext up