Energy & momentum · Topic 10 of 17

Momentum & Impulse

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Physics · momentum

Momentum is mass times velocity; impulse (force × time) changes it; in a collision total momentum is conserved, and kinetic energy only if elastic.

01 · Momentump = m × v

02 · ImpulseImpulse = F × Δt = Δp

03 · ConservationTotal p before = total p after

Longer stopping time → smaller force (airbags, padding)

Perfectly inelastic: objects stick together (most KE lost)

Recoil: push-off gives equal and opposite momenta (total stays 0)

Total momentum before = total momentum after (isolated system) must know

More mass or more speed → more momentum; at rest → p = 0

Momentum p = m × v (kg·m/s), in the direction of motion must know

Impulse = F × Δt = change in momentum (Δp = m × Δv) must know

p₁ + p₂ (before) = p₁′ + p₂′ (after), each p = mass × velocity

1,200 kg × 15 m/s = 18,000 kg·m/s

Δp = 0.5 × 20 = 10 N·s; over 0.02 s → F = 500 N

3 kg at 4 m/s sticks to 1 kg: 12 ÷ 4 = 3 m/s together

Elastic keeps KE; inelastic loses KE — both keep momentum

Commonly confused

	Elastic	Inelastic
Total momentum	Conserved	Conserved
Kinetic energy	Conserved	Not conserved — some becomes heat etc.
After the hit	Objects bounce apart	May stick together (perfectly inelastic)
Real examples	Truly elastic only for subatomic particles	Most everyday collisions

Opposite directions get opposite signs — equal and opposite p sum to 0

Show 2 more facts

Truly elastic only for subatomic particles; real hits lose some KE

F_net = Δp / Δt (Newton's 2nd law in momentum form)

Pearl

Every collision keeps its momentum; only an elastic one keeps its kinetic energy too.

Practice this topic, then test the whole section.

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