Physics 2 — Momentum & Waves

Collisions — momentum is conserved

continues from lesson 1 — values defined earlier in the course stay live here

ELI5: in any collision, the total momentum before equals the total after — always, no exceptions, even in a wreck. If the objects stick together (a perfectly inelastic collision), one tidy equation gives their shared final speed.

m_{1} := 1200 kg

= 1200 kg moving car

v_{i1} := 15 m/s

= 15 m / s

m_{2} := 800 kg

= 800 kg car it rear-ends, initially parked

v_{f} = \frac{m_{1} \cdot v_{i1}}{m_{1} + m_{2}}

= 9 m / s they lock bumpers and move off together

✓ pass

abs(m_{1} * v_{i1} - (m_{1} + m_{2}) * v_{f}) < 0.001 kg*m/s

momentum books balance

E_{lost} = \frac{1}{2} \cdot m_{1} \cdot v_{i1}^{2} - \frac{1}{2} \cdot \left(m_{1} + m_{2}\right) \cdot v_{f}^{2}

= 54000 J kinetic energy is NOT conserved — it became crumpled metal and heat

Real-world hook: momentum conservation is how rockets work (throw mass backward, you go forward), how pool players plan a break, and how physicists weigh subatomic particles from collision debris.

Try it yourself: a 1000 kg car at 20 m/s rear-ends a parked 1000 kg car and they stick. What is their shared speed afterward?

vf_{you} := 10 m/s

= 10 m / s ✏️ Your turn: find the stuck-together speed. The check verifies momentum before = momentum after — so you must conserve it yourself.

✓ pass

abs(1000 kg * 20 m/s - 2000 kg * vf_{you}) < 0.1 kg*m/s

green when total momentum is conserved