Impulse-Time Three-Row Scan - Mechanics Step by Step

Three impulse rows hold force fixed while contact time changes, making the accumulated momentum change visible.

mechanics A 4 N push lasting 1 s, 2 s, and 3 s gives impulses 4 kg*m/s, 8 kg*m/s, and 12 kg*m/s.

Example

A fixed force delivers more impulse when contact lasts longer. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Hold force fixed and scan contact time

Impulse is force accumulated over contact time. The force arrow stays the same; the timer decides the momentum change.

J = F\Delta t

Brief contact

A 4 N push for 1 s gives impulse 4 kg*m/s.

J = F\Delta t = 4\ \text{N}\,\cdot\,1\ \text{s} = 4\ \text{kg}\,\text{m}/\text{s}

Middle contact

The same push for 2 s gives impulse 8 kg*m/s.

J = F\Delta t = 4\ \text{N}\,\cdot\,2\ \text{s} = 8\ \text{kg}\,\text{m}/\text{s}

Long contact

The same push for 3 s gives impulse 12 kg*m/s.

J = F\Delta t = 4\ \text{N}\,\cdot\,3\ \text{s} = 12\ \text{kg}\,\text{m}/\text{s}

Longer contact accumulates more impulse

Each row uses the same force. Contact time is the only changing input, and the impulse grows row by row.

\begin{array}{c|c|c}F & \Delta t & J \\ \hline 4\ \text{N} & 1\ \text{s} & 4\ \text{kg}\,\text{m}/\text{s} \\ 4\ \text{N} & 2\ \text{s} & 8\ \text{kg}\,\text{m}/\text{s} \\ 4\ \text{N} & 3\ \text{s} & 12\ \text{kg}\,\text{m}/\text{s}\end{array}