What is impulse?
Force multiplied by the time it acts, measured in newton seconds. Impulse equals the change in momentum an object experiences, which is why the two share units. A small force over a long time can produce exactly the same momentum change as a large force applied briefly — and that equivalence is the basis of most impact protection.
How does impulse explain airbags and crumple zones?
In a crash the momentum change is fixed: the occupant must go from travelling to stationary. Impulse says force times time equals that fixed change, so extending the time reduces the peak force. An airbag lengthens the stop from milliseconds to tens of milliseconds, cutting the force by roughly the same factor. Crumple zones do the same by deforming progressively rather than stopping rigidly.
Why do you bend your knees when landing?
To extend the stopping time. Landing stiff-legged brings you to rest in perhaps 50 milliseconds; bending the knees stretches it to 300 or more, cutting the peak force by a factor of six. The same principle governs catching a cricket ball with hands moving backwards, gymnasts rolling on landing, and the padding under playground equipment.
What is the relationship between impulse and momentum?
They are the same quantity viewed differently: impulse is what you apply, momentum change is what results. The impulse-momentum theorem states FΔt = mΔv. Rearranged for force, it shows why the duration of an interaction matters as much as its magnitude — a point that force alone never reveals.
How is impulse calculated when force is not constant?
It is the area under the force–time curve — J = ∫F dt. That is what the shaded region in the plot on this page is: not an illustration of the impulse but the impulse itself. The average-force rectangle drawn over it encloses exactly the same area, which is what "average force" means. Change the shape of the curve and the area stays put while the peak moves, which is the whole reason the shape matters.
Does impulse apply to propulsion as well as impacts?
Yes. Rocket engines are rated by specific impulse — impulse per unit of propellant — because what matters is total momentum imparted, not instantaneous thrust. A low-thrust ion engine firing for months can deliver more total impulse than a chemical rocket burning for minutes, which is why deep-space missions use them despite their feeble push.
What is the difference between average force and peak force?
Average force is the impulse divided by the contact time — a single number that would produce the same momentum change if it acted steadily. Peak force is the largest force at any instant, and it is what actually breaks things. No real impact delivers a constant force, so the two are never equal: design to the peak, reason with the impulse, and never size a component from the average alone.
How much higher is peak force than average force?
It depends entirely on the shape of the force–time curve. A half-sine, which is what most real impacts resemble, peaks at π/2 — about 1.57 — times the average. A triangular pulse from a sharp, hard strike peaks at exactly twice the average. Only the textbook rectangular idealisation has a peak equal to its average, and nothing in the physical world does that. Working from the average alone under-specifies by 57% to 100%.
What is a survivable deceleration in g?
Impact severity is usually quoted in g rather than newtons because it does not depend on mass. Everyday activity produces a few g; a well-restrained car occupant can survive a brief 30 to 50 g; sustained exposure above roughly 50 g makes serious injury likely. The figure follows directly from Δv and Δt, which is why extending the contact time is the single most effective safety measure available.
Why does a small increase in speed matter so much?
Because impulse and energy scale differently. Impulse goes as Δv, so doubling the speed doubles the momentum that has to be absorbed. Kinetic energy goes as v², so doubling the speed quadruples it. The structure has to shed both, and the energy term is what grows fastest — which is also why stopping distance grows faster than speed does.