← Mechanics

Impulse, and why longer collisions are safer

A recurring scenario across every year on record: catching a ball, cushioning a fall, a padded landing. The physics is always the same — impulse, not force alone.

Impulse links force, time and momentum change

  • Impulse J = F × t = Δp — a force applied for a time produces a CHANGE in momentum equal to that impulse.
  • For a given collision, the momentum change Δp (from a known speed change) is FIXED by the physics of the collision.
  • Since Δp is fixed, F and t trade off: F = Δp/t — a LONGER stopping time means a SMALLER average force, and vice versa.
Worked example Why a padded glove reduces force A 0.180 kg ball travelling at 44.4 m s⁻¹ is caught and brought to rest. Compare the average force if it stops in 0.510 s (padded glove, relaxed arm) versus 0.020 s (bare hand, stiff arm). Momentum change is the same in both cases: Δp = mΔv = 0.180 × 44.4 = 7.99 kg m s⁻¹. Padded case: F = Δp/t = 7.99 / 0.510 ≈ 15.7 N. Bare-hand case: F = Δp/t = 7.99 / 0.020 ≈ 400 N. Same impulse, wildly different average force — the padding and relaxed arm do not change how much momentum must be removed, only how QUICKLY. ✓ Extending the stopping time from 0.020 s to 0.510 s cuts the average force by roughly a factor of 25, which is the entire physics behind padding, airbags, and "rolling with" an impact. ✕

Padding does not reduce the momentum change — it reduces the FORCE

A common wrong answer claims padding "absorbs the momentum" or "reduces the energy of the collision". In fact the momentum change Δp is fixed by the mass and speed change alone, regardless of padding — what padding changes is the TIME over which that momentum change happens, and therefore the average force (F = Δp/t). State it as a time-extension effect on force, not an energy or momentum reduction. ℹ

Other everyday examples of the same principle

A car's crumple zone, an airbag, bending your knees when landing a jump, and a boxer "riding" a punch all work the same way: each extends the time over which a fixed momentum change happens, reducing the average force. Naming a second example beyond the one given in the question is a reliable way to show genuine understanding rather than a memorised single case.

Practise just this