Physics 2 — Momentum & Waves

Momentum & impulse

ELI5: momentum p = m·v is "how hard something is to stop" — mass times velocity. The only way to change it is a force acting over time, the impulse J = F·Δt. That trade is why a long, soft contact (a gentle catch, a car's crumple zone) is so much safer than a short, hard one: same momentum change, far less force.

m_{ball} := 0.45 kg

= 0.45 kg a football

v_{kick} := 25 m/s

= 25 m / s

p_{ball} = m_{ball} \cdot v_{kick}

= 11.25 (kg m) / s momentum after the kick

t_{contact} := 0.01 s

= 0.01 s boot-on-ball contact time

F_{kick} = \frac{p_{ball}}{t_{contact}}

= 1125 N the average force — surprisingly large

Real-world hook: impulse is the physics of airbags and crumple zones (stretch the stopping time to cut the force), boxing (roll with a punch), and a rocket (small thrust × long burn = huge momentum).

Try it yourself: what is the momentum of a 0.15 kg ball moving at 40 m/s? (p = m·v.)

p_{you} := 0.15 kg * 40 m/s

= 6 (kg m) / s ✏️ Your turn: multiply mass × velocity. Keep the units (kg·m/s).

✓ pass

abs(p_{you} - 0.15 kg * 40 m/s) < 0.01 kg*m/s

green when your momentum is correct