Grade 12 Physics · Impulse meets momentum
The bridge
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The bridge

Two lessons, one equation: FΔt=ΔpF \, \Delta t = \Delta p — the impulse-momentum theorem, read aloud F delta-t equals delta p. On the left, a force FF in newtons held for a time Δt\Delta t in seconds. On the right, Δp\Delta p, the change in momentum in kgm/s\mathrm{kg \cdot m/s}, which is Δp=mΔv=m(vu)\Delta p = m \, \Delta v = m(v - u): the mass in kilograms times the velocity it gained or lost, where uu is the velocity before and vv the velocity after. Something brought to rest loses all of it, so Δp=mu\Delta p = mu in size.

Work it in that order — momentum change first, force second — and the physics reads itself: F=ΔpΔtF = \dfrac{\Delta p}{\Delta t}. Same Δp\Delta p, a longer stop, a smaller force. One warning that costs more marks than any concept here: contact times arrive in milliseconds, and milli means a thousandth — 20 ms=0.020 s20\ \mathrm{ms} = 0.020\ \mathrm{s}. Feed the raw 20 into the division and your force comes out a thousand times too gentle, which is exactly the direction that makes a dangerous design look safe. Estimate the order of magnitude first, every time; the estimate catches the slip before the marker does.