Momentum and Conservation

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CognitoMomentum and conservation

Key facts & equations

Momentum

Momentum = mass × velocity. p = mv. Units: kg m/s.
Momentum is a vector — direction matters.
Conservation of momentum: total momentum before a collision = total momentum after (closed system).
Applies to all collisions and explosions.
Elastic collision: KE conserved. Inelastic: KE not conserved (some converted to heat/sound).

Impulse

Impulse = force × time = change in momentum. F × t = mv - mu.
Units of impulse: N s = kg m/s.
Greater time → smaller force for same impulse. This is why safety features work.
Airbags, crumple zones, crash mats, seatbelts all increase collision time → reduce force on passengers.
Catching a ball: move hands back to increase contact time → reduce force on hands.

Conservation of momentum calculations

m1u1 + m2u2 = m1v1 + m2v2 (u = before, v = after).
For objects sticking together: (m1 + m2)v = m1u1 + m2u2.
Explosions: total momentum before = 0, so momenta are equal and opposite after.
E.g. gun recoil: bullet momentum forward = gun momentum backward.
Always define a positive direction first, then treat opposing velocities as negative.

Force and change in momentum (Higher)

Force = rate of change of momentum = (mv - mu) / t.
This is Newton's 2nd law in its full form: F = Δp/Δt.
Rearranges to: Ft = Δp (impulse = change in momentum).
Large force for short time = same impulse as small force for long time.
Safety: increase collision time to reduce peak force.

Exam questions — 4 questions · 10 marks · AQA 8463 style

3 marksConservation of momentumAQA 8463 P1 style 🔢 Calculator

A 2 kg ball moving at 5 m/s collides with a stationary 3 kg ball. After the collision they stick together. Calculate their common velocity after the collision. (3 marks)

Hint: Momentum before = Momentum after. Before: p = m1×u1 + m2×u2. After (stuck together): p = (m1+m2)×v.

+30 XP

3 marksImpulse and safetyAQA 8463 style 🔢 Calculator

A 70 kg person travelling at 15 m/s is stopped by a seatbelt in 0.4 s. Calculate: (a) the change in momentum, (b) the force exerted by the seatbelt. (3 marks)

Hint: (a) Δp = m(v-u), final velocity = 0. (b) F = Δp/t. Make sure units are consistent.

+30 XP

1 markConservation lawAQA 8463 style

A stationary bomb explodes into two fragments of equal mass. What happens to their momenta?

A Both fragments have zero momentum because the bomb was stationary

B The fragments move in the same direction with equal momenta

C The fragments move in opposite directions with equal and opposite momenta

D Only the larger fragment has momentum

1 markWhy airbags workAQA 8463 style

How does an airbag reduce injury in a car crash?

A It prevents the driver from moving at all

B It increases the time of the collision, reducing the force on the driver for the same change in momentum

C It absorbs all the kinetic energy of the driver

D It increases the stopping distance of the car

5 marks Conservation of momentum — opposite directions AQA 8463 Paper 1 style ⚡ Trap question

Two ice hockey players move toward each other and collide, then move together. Player A has mass 78 kg and velocity +7.5 m/s (right). Player B has mass 91 kg and velocity −5.5 m/s (left). (a) Calculate the momentum of each player before the collision. (b) Calculate the total momentum before the collision. (c) Calculate the velocity of the two players immediately after the collision. (5 marks)

Key trap: You MUST calculate p = mv separately for each player first — do NOT just subtract the velocities. Player B's momentum is NEGATIVE because they move left. Then add the two momenta (one positive, one negative) to get total momentum before.

+50 XP

Momentum and Conservation

Momentum

Impulse

Conservation of momentum calculations

Force and change in momentum (Higher)

Module complete! 🎉