Physics / Unit 6: Momentum and Collisions
6.6 Explosions and Recoil
Notes
In an explosion or push-apart, the system starts at rest, so the total momentum is zero before and after.
- The pieces move in opposite directions with equal-size momenta: $m_1v_1 = m_2v_2$.
- The lighter piece moves faster.
- Rockets work this way: exhaust goes backward and the rocket gains forward momentum.
- Example: a 60 kg skater and a 40 kg skater push apart. If the 40 kg skater moves at $3 \text{ m/s}$, the 60 kg skater moves at $\displaystyle \frac{40 \times 3}{60} = 2 \text{ m/s}$ the other way.
Practice
A 4 kg rifle fires a 0.01 kg bullet at $400 \text{ m/s}$. What is the rifle's recoil speed?
$0.01 \times 400 = 4v \Rightarrow v = 1 \text{ m/s}$.
A firework at rest explodes into two pieces. What is the total momentum of the pieces just after?
Momentum is conserved and was zero before the explosion.
A 50 kg student on a skateboard at rest throws a 5 kg box forward at $4 \text{ m/s}$. What is the student's velocity afterward?
$0 = 5(4) + 50v \Rightarrow v = -0.4 \text{ m/s}$, opposite the throw.
Ready for more? Take the Unit 6 test.