Lesson overview
Momentum and collisions: Why do airbags and crumple zones save lives?
Collide two trolleys on a track with motion sensors at both ends: predict, then push trolley A into trolley B with Velcro pads so they stick and with magnet bumpers so they bounce, and compare the total momentum before and after. Decide how to make A bounce back. Then crash A into a force sensor with a stiff nose and with a crumple nose, and compare the two force–time graphs.
Suggested sequence
- Lesson 1 · Momentum. Supplement: momentum as mass × velocity, p = mv, with its direction; the conservation of momentum in one dimension, for objects that stick together or bounce apart and for explosions from rest. Read together (10–15 min), show or explore the experiment (10 min), practise with self-checking (15–20 min).
- Lesson 2 · Impulse and safety. Supplement: impulse as force × time, FΔt = Δ(mv); resultant force as the change in momentum per unit time, F = Δp/Δt; the area under a force–time graph; crumple zones, airbags and seat belts. Read together (10–15 min), show or explore the experiment (10 min), practise with self-checking (15–20 min).
- End of module · final check. 2 new questions, 20–30 min, without hints or notes; pupils check their answers once they have answered them all.
- One to two weeks later · return questions. 2 questions, 15 min, lesson closed.
Learning goals
Part 1: Momentum
- Supplement: define momentum as mass × velocity; recall and use the equation p = mv (1.6.1)
- Supplement: apply the principle of the conservation of momentum to solve simple problems in one dimension (1.6.3)
Part 2: Impulse and safety
- Supplement: define impulse as force × time for which force acts; recall and use the equation impulse = F∆t = ∆(mv) (1.6.2)
- Supplement: define resultant force as the change in momentum per unit time; recall and use the equation F = ∆p / ∆t (1.6.4)
Misconceptions to listen for
- “mass × acceleration” — Mass × acceleration is the resultant force, F = ma. Momentum uses the velocity.
- “force × distance” — Force × distance is the work done, measured in joules. Momentum is about mass and velocity.
- “mass ÷ velocity” — Dividing would give a faster object less momentum. A faster object is harder to stop, so momentum is mass multiplied by velocity.
- “p = 0.80 ÷ 2.5 = 0.32 kg m/s.” — Momentum is mass multiplied by velocity, not divided.
- “m = 54 × 1.5 = 81 kg.” — p = mv, so the mass is the momentum divided by the velocity.
- “m = 1.5 ÷ 54 = 0.028 kg.” — That is the velocity divided by the momentum. Divide the momentum by the velocity.
- “Total before = 240 − 60 = 180 kg m/s, so v = 1.8 m/s.” — Both skaters move in the same direction, so both momenta are positive. Add them.
- “The second skater is the one being hit, so count her as at rest: v = 2.4 m/s.” — She is moving at 1.5 m/s, so she has 60 kg m/s of momentum before. Add it.
- “Take the mean of the speeds: v = 2.75 m/s.” — Speeds are not conserved. Add the momenta, then divide by the total mass.
- “v = 5.8 ÷ 145 = 0.040 m/s.” — Change the mass to kilograms first: 145 g = 0.145 kg.
Scope
Supplement throughout: momentum as mass × velocity, p = mv (1.6.1); impulse as force × the time for which it acts, impulse = FΔt = Δ(mv) (1.6.2); the principle of the conservation of momentum for simple problems in one dimension, including explosions from rest (1.6.3); resultant force as the change in momentum per unit time, F = Δp/Δt (1.6.4), with crumple zones, airbags and seat belts. Kinetic energy and sorting collisions by energy are not used (kinetic energy is in Energy); collisions in two dimensions, Newton’s third law by name and rockets beyond a one-line example are left out. Velocity and acceleration are in Speed and motion graphs, F = ma in Resultant force.