A.2.17—Impulse

Impulse changes momentum

Impulse is the integral of resultant force over time. For a constant average force,

$\vec J=\vec F_{net}\Delta t=\Delta\vec p$

Use the momentum change

Calculate $\Delta\vec p=\vec p_f-\vec p_i$ , including direction. A rebound reverses the velocity component and can make the momentum change larger than either momentum magnitude alone.

Average force

If the force varies, $F\Delta t$ represents average resultant force over the contact interval. Use consistent units for impulse in N s or kg m s⁻¹.

Common trap

Do not use the initial momentum alone when the object rebounds or ends with a non-zero final velocity.

How it is assessed

The evidence asks for contact time from average force and momentum change, or tests the magnitude of impulse for a change in velocity.

Command terms

Determine / Calculate

What earns marks

Find the vector change in momentum and use J=Δp. For a rebound, choose a sign convention and subtract the initial momentum from the final momentum; then divide by contact time only if average force is requested.

Watch for

Adding the initial and final momentum magnitudes without accounting for their opposite directions during a rebound.

Representative question

[Maximum number: 2]

The ball rebounds from the ground with speed $7.8 \mathrm{~ms}^{-1}$ . The ball is in contact with the ground for a time T. The average resultant force on the ball during this time is 1.1 N .
Determine T.

ALTERNATE 1
$\begin{aligned} & \Delta p=\ll 2.7 \times 10^{-3} \times(7.8+9.5)=>0.0467<\mathrm{Ns}>d & \ll 1.1=\frac{\Delta p}{\Delta t} \text { so } T=\frac{0.0467}{1.1} \Rightarrow \gg 0.042 \ll s \gg \end{aligned}$

ALTERNATE 2
$\begin{aligned} & a=\ll \frac{F}{m} \Rightarrow \gg \frac{1.1}{2.7 \times 10^{-3}}=407 \ll \mathrm{~m} \mathrm{~s}^{-2} \gg & T=\ll \frac{9.5+7.8}{407}=\gg 0.042 \ll s \gg \end{aligned}$

Watch for ECF from incorrect value of v in cii).

Award [1] for $t=0.076 \ll s \gg$ using an impact speed of $23 \mathrm{~m} \mathrm{~s}^{-1}$ .

[2]

A.2.17—Impulse

Calculate Impulse from Force and Time

A.2.17 Exam Analysis

Assessment in practice

Question 1