Physics

4.15 - Momentum & Force

6 min

Changing momentum

Force and momentum

Second worked example

Car safety

note 1 of 2

Newton's second law as change of momentum

When a resultant force acts on an object, it changes the object's momentum in the direction of the force.
Newton's second law states that this change of momentum is proportional to the resultant force and to the time for which it acts.

Formula for change of momentum

$Δ p = F \times t$

Where:

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

For a given change of momentum, a longer time ( $t$ ) needs a smaller force, and a shorter time needs a larger force.

note 2 of 2

Worked example - Change of momentum from force and time

A footballer kicks a stationary ball of mass 0.45 kg. The boot applies an average force of 240 N to the ball for 0.050 s. Calculate the change in the ball's momentum caused by the kick.

Step 1 - Identify the force and the time it acts for

$F = 240 N, t = 0.050 s$

Step 2 - Multiply the force by the time

$\begin{matrix} Δ p & = F \times t \\ = 240 \times 0.050 \\ = 12 kg m/s \end{matrix}$

The change in the ball's momentum is 12 kg m/s.

end of notes

Key points to remember

Newton's second law as change of momentum

When a resultant force acts on an object, it changes the object's momentum in the direction of the force.

Newton's second law states that this change of momentum is proportional to the resultant force and to the time for which it acts.

Formula for change of momentum

$Δ p = F \times t$

Where:

Δ p

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

F

= Resultant force, in newtons (N)

t

= Time for which the force acts, in seconds (s)

For a given change of momentum, a longer time (

t

) needs a smaller force, and a shorter time needs a larger force.

Worked example - Change of momentum from force and time

A footballer kicks a stationary ball of mass 0.45 kg. The boot applies an average force of 240 N to the ball for 0.050 s. Calculate the change in the ball's momentum caused by the kick.

Step 1 - Identify the force and the time it acts for

$F = 240 N, t = 0.050 s$

Step 2 - Multiply the force by the time

$\begin{matrix} Δ p & = F \times t \\ = 240 \times 0.050 \\ = 12 kg m/s \end{matrix}$

The change in the ball's momentum is 12 kg m/s.